This page was generated from unit-3.8-nonlmin/nonlmin.ipynb.

3.8 Nonlinear minimization problems

We consider problems of the form

$$\text{find } u \in V \text{ s.t. } E(u) \leq E(v) \quad \forall~ v \in V.$$

from netgen import gui
from ngsolve import *

Scalar minimization problems

As a first example we take $V = H^1_0$ and

$$E(u) = \int_{\Omega} \vert \nabla u \vert^2 + u^4 - fu ~dx.$$

The minimization is equivalent to solving the nonlinear PDE:

$$- \Delta u + 4 u^3 = f \text{ in } \Omega$$

We solve the PDE with a Newton iteration.

from netgen.geom2d import unit_square

mesh = Mesh (unit_square.GenerateMesh(maxh=0.2))
V = H1(mesh, order=4, dirichlet=[1,2,3,4])
u = V.TrialFunction()

To solve the problem we use the Variation integrator. Based on the symbolic description of the energy functional, it is able to

• evaluate the energy functional (Energy)

$$E(u) \qquad (E:V \to \mathbb{R})$$

• compute the Gateau derivative for a given $u$ (Apply):

$$A(u)(v) = E'(u)(v) \qquad (A(u): V \to \mathbb{R})$$

• compute the second derivative (AssembleLinearization)

$$(\delta A)(w)(u,v) \qquad (\delta A(w): V\times V \to \mathbb{R})$$

a = BilinearForm (V, symmetric=True)
a += Variation ( (grad(u)*grad(u) + u**4-u) * dx)

Equivalent to:

a += (2 * grad(u) * grad(v) + 4*u*u*u*v - 1 * v)*dx

(which has the same form as the problems in the nonlinear example)

We recall the Newton iteration (cf. unit-3.7 ) we make the loop:

• Given an initial guess $u^0$

• loop over $i=0,..$ until convergence:

  • Compute linearization: $A u^i + \delta `A(u^i) :nbsphinx-math:Delta `u^{i} = 0 $:

    • $f^i = A u^i$

    • $B^i = \delta A(u^i)$

    • Solve $B^i \Delta u^i = -f^i$

  • Update $u^{i+1} = u^i + \Delta u^{i}$

  • Evaluate stopping criteria

• Evaluate $E(u^{i+1})$

As a stopping criteria we take $\langle A u^i,\Delta u^i \rangle = \langle A u^i, A u^i \rangle_{(B^i)^{-1}}< \varepsilon$.

def SolveNonlinearMinProblem(a,gfu,tol=1e-13,maxits=25):
    res = gfu.vec.CreateVector()
    du  = gfu.vec.CreateVector()

    for it in range(maxits):
        print ("Newton iteration {:3}".format(it),end="")
        print ("energy = {:16}".format(a.Energy(gfu.vec)),end="")

        #solve linearized problem:
        a.Apply (gfu.vec, res)
        a.AssembleLinearization (gfu.vec)
        inv = a.mat.Inverse(V.FreeDofs())
        du.data = inv * res

        #update iteration
        gfu.vec.data -= du

        #stopping criteria
        stopcritval = sqrt(abs(InnerProduct(du,res)))
        print ("<A u",it,", A u",it,">_{-1}^0.5 = ", stopcritval)
        if stopcritval < tol:
            break
        Redraw(blocking=True)

gfu = GridFunction (V)
gfu.vec[:] = 0
Draw(gfu,mesh,"u")

SolveNonlinearMinProblem(a,gfu)

print ("energy = ", a.Energy(gfu.vec))

Newton iteration   0energy =              0.0<A u 0 , A u 0 >_{-1}^0.5 =  0.13255958653113628
Newton iteration   1energy = -0.008785678644368577<A u 1 , A u 1 >_{-1}^0.5 =  1.1107598523198008e-05
Newton iteration   2energy = -0.008785678706057953<A u 2 , A u 2 >_{-1}^0.5 =  2.8075898252642246e-13
Newton iteration   3energy = -0.008785678706057952<A u 3 , A u 3 >_{-1}^0.5 =  3.741902157776e-17
energy =  -0.008785678706057952

Again, a Newton for minimization is shipped with NGSolve:

from ngsolve.solvers import *
gfu.vec[:] = 0
NewtonMinimization(a,gfu)
Redraw()

Newton iteration  0
Energy:  0.0
err =  0.13255958653113625
Newton iteration  1
Energy:  -0.00878567864436858
err =  1.1107598523178109e-05
Newton iteration  2
Energy:  -0.008785678706057952
err =  2.807455664350966e-13

Nonlinear elasticity

We consider a beam which is fixed on one side and is subject to gravity only. We assume a Neo-Hookean hyperelastic material. The model is a nonlinear minimization problem with

$$E(v) := \int_{\Omega} \frac{\mu}{2} ( \operatorname{tr}(F^T F-I)+\frac{2 \mu}{\lambda} \operatorname{det}(F^T F)^{\frac{\lambda}{2\mu}} - 1) - \gamma ~ (f,v) ~~ dx$$

where $\mu$ and $\lambda$ are the Lamé parameters and $F = I + D v$ where $v: \Omega \to \mathbb{R}^2$ is the sought for displacement.

import netgen.geom2d as geom2d
from ngsolve import *

geo = geom2d.SplineGeometry()
pnums = [ geo.AddPoint (x,y,maxh=0.01) for x,y in [(0,0), (1,0), (1,0.1), (0,0.1)] ]
for p1,p2,bc in [(0,1,"bot"), (1,2,"right"), (2,3,"top"), (3,0,"left")]:
     geo.Append(["line", pnums[p1], pnums[p2]], bc=bc)
mesh = Mesh(geo.GenerateMesh(maxh=0.05))

# E module and poisson number:
E, nu = 210, 0.2
# Lamé constants:
mu  = E / 2 / (1+nu)
lam = E * nu / ((1+nu)*(1-2*nu))

V = H1(mesh, order=2, dirichlet="left", dim=mesh.dim)
u  = V.TrialFunction()

#gravity:
force = CoefficientFunction( (0,-1) )

def Pow(a, b):
    return exp (log(a)*b)

def NeoHook (C):
    return 0.5 * mu * (Trace(C-I) + 2*mu/lam * Pow(Det(C), -lam/2/mu) - 1)

I = Id(mesh.dim)
F = I + Grad(u)
C = F.trans * F.trans

factor = Parameter(1.0)

a = BilinearForm(V, symmetric=True)
a += Variation(  NeoHook (C).Compile() * dx
                -factor * (InnerProduct(force,u) ).Compile() * dx)

We want to solve the minimization problem for $\gamma = 5$. Due to the high nonlinearity in the problem, the Newton iteration will not convergence with any initial guess. We approach the case $\gamma = 5$ by solving problems with $\gamma = i/10$ for $i=1,..,50$ and taking the solution of the previous problem as an initial guess.

gfu = GridFunction(V)
gfu.vec[:] = 0

Draw (gfu, mesh, "u")
SetVisualization (deformation=True)

res = gfu.vec.CreateVector()
du = gfu.vec.CreateVector()

for loadstep in range(50):
    print ("loadstep", loadstep)
    factor.Set ((loadstep+1)/10)
    SolveNonlinearMinProblem(a,gfu)
    Redraw()

loadstep 0
Newton iteration   0energy = 8.749999999999998<A u 0 , A u 0 >_{-1}^0.5 =  0.0011109609185296946
Newton iteration   1energy = 8.75005276617483<A u 1 , A u 1 >_{-1}^0.5 =  0.009148322973133765
Newton iteration   2energy = 8.751477850270941<A u 2 , A u 2 >_{-1}^0.5 =  0.04772739026732187
Newton iteration   3energy = 8.758125165185952<A u 3 , A u 3 >_{-1}^0.5 =  0.11337401648217023
Newton iteration   4energy = 8.753021775938693<A u 4 , A u 4 >_{-1}^0.5 =  0.06546139967597644
Newton iteration   5energy = 17.103342030948674<A u 5 , A u 5 >_{-1}^0.5 =  2.7931046809405693
Newton iteration   6energy = 9.681624244626434<A u 6 , A u 6 >_{-1}^0.5 =  7.121338031267679
Newton iteration   7energy = -411.66269569145055<A u 7 , A u 7 >_{-1}^0.5 =  28.867702165200257
Newton iteration   8energy = 3.663918575946365<A u 8 , A u 8 >_{-1}^0.5 =  3.427818843815449
Newton iteration   9energy = -18.995359467921844<A u 9 , A u 9 >_{-1}^0.5 =  6.697070258969443
Newton iteration  10energy = -74.50022980913081<A u 10 , A u 10 >_{-1}^0.5 =  11.955595040587365
Newton iteration  11energy = -18.598626544437593<A u 11 , A u 11 >_{-1}^0.5 =  7.017303947035795
Newton iteration  12energy = 32.02731805741041<A u 12 , A u 12 >_{-1}^0.5 =  8.02903487065813
Newton iteration  13energy = 5.478032449287156<A u 13 , A u 13 >_{-1}^0.5 =  2.3997455854448324
Newton iteration  14energy = -159.8138035930931<A u 14 , A u 14 >_{-1}^0.5 =  17.9716084482156
Newton iteration  15energy = -18.513252215288958<A u 15 , A u 15 >_{-1}^0.5 =  6.632060780213734
Newton iteration  16energy = -15.75237975642085<A u 16 , A u 16 >_{-1}^0.5 =  5.4720311076794905
Newton iteration  17energy = 11.700383454561234<A u 17 , A u 17 >_{-1}^0.5 =  1.9998306026547423
Newton iteration  18energy = -149.55175018310547<A u 18 , A u 18 >_{-1}^0.5 =  17.939989756084167
Newton iteration  19energy = -122.21556091308594<A u 19 , A u 19 >_{-1}^0.5 =  16.464950840685667
Newton iteration  20energy = 20.068984985351562<A u 20 , A u 20 >_{-1}^0.5 =  756.492828790009
Newton iteration  21energy =  -112312975360.0<A u 21 , A u 21 >_{-1}^0.5 =  473916.53343712824
Newton iteration  22energy =        4194304.0<A u 22 , A u 22 >_{-1}^0.5 =  851.2840572008482
Newton iteration  23energy =        6291456.0<A u 23 , A u 23 >_{-1}^0.5 =  1372.9056640273288
Newton iteration  24energy =        2097152.0<A u 24 , A u 24 >_{-1}^0.5 =  2046.5928896695846
loadstep 1
Newton iteration   0energy =              nan<A u 0 , A u 0 >_{-1}^0.5 =  nan
Newton iteration   1energy =              nan<A u 1 , A u 1 >_{-1}^0.5 =  nan
Newton iteration   2energy =              nan<A u 2 , A u 2 >_{-1}^0.5 =  nan
Newton iteration   3energy =              nan<A u 3 , A u 3 >_{-1}^0.5 =  nan
Newton iteration   4energy =              nan<A u 4 , A u 4 >_{-1}^0.5 =  nan
Newton iteration   5energy =              nan<A u 5 , A u 5 >_{-1}^0.5 =  nan
Newton iteration   6energy =              nan<A u 6 , A u 6 >_{-1}^0.5 =  nan
Newton iteration   7energy =              nan<A u 7 , A u 7 >_{-1}^0.5 =  nan
Newton iteration   8energy =              nan<A u 8 , A u 8 >_{-1}^0.5 =  nan
Newton iteration   9energy =              nan<A u 9 , A u 9 >_{-1}^0.5 =  nan
Newton iteration  10energy =              nan<A u 10 , A u 10 >_{-1}^0.5 =  nan
Newton iteration  11energy =              nan<A u 11 , A u 11 >_{-1}^0.5 =  nan
Newton iteration  12energy =              nan<A u 12 , A u 12 >_{-1}^0.5 =  nan
Newton iteration  13energy =              nan<A u 13 , A u 13 >_{-1}^0.5 =  nan
Newton iteration  14energy =              nan<A u 14 , A u 14 >_{-1}^0.5 =  nan
Newton iteration  15energy =              nan<A u 15 , A u 15 >_{-1}^0.5 =  nan
Newton iteration  16energy =              nan<A u 16 , A u 16 >_{-1}^0.5 =  nan
Newton iteration  17energy =              nan<A u 17 , A u 17 >_{-1}^0.5 =  nan
Newton iteration  18energy =              nan<A u 18 , A u 18 >_{-1}^0.5 =  nan
Newton iteration  19energy =              nan<A u 19 , A u 19 >_{-1}^0.5 =  nan
Newton iteration  20energy =              nan<A u 20 , A u 20 >_{-1}^0.5 =  nan
Newton iteration  21energy =              nan<A u 21 , A u 21 >_{-1}^0.5 =  nan
Newton iteration  22energy =              nan<A u 22 , A u 22 >_{-1}^0.5 =  nan
Newton iteration  23energy =              nan<A u 23 , A u 23 >_{-1}^0.5 =  nan
Newton iteration  24energy =              nan<A u 24 , A u 24 >_{-1}^0.5 =  nan
loadstep 2
Newton iteration   0energy =              nan<A u 0 , A u 0 >_{-1}^0.5 =  nan
Newton iteration   1energy =              nan<A u 1 , A u 1 >_{-1}^0.5 =  nan
Newton iteration   2energy =              nan<A u 2 , A u 2 >_{-1}^0.5 =  nan
Newton iteration   3energy =              nan<A u 3 , A u 3 >_{-1}^0.5 =  nan
Newton iteration   4energy =              nan<A u 4 , A u 4 >_{-1}^0.5 =  nan
Newton iteration   5energy =              nan<A u 5 , A u 5 >_{-1}^0.5 =  nan
Newton iteration   6energy =              nan<A u 6 , A u 6 >_{-1}^0.5 =  nan
Newton iteration   7energy =              nan<A u 7 , A u 7 >_{-1}^0.5 =  nan
Newton iteration   8energy =              nan<A u 8 , A u 8 >_{-1}^0.5 =  nan
Newton iteration   9energy =              nan<A u 9 , A u 9 >_{-1}^0.5 =  nan
Newton iteration  10energy =              nan<A u 10 , A u 10 >_{-1}^0.5 =  nan
Newton iteration  11energy =              nan<A u 11 , A u 11 >_{-1}^0.5 =  nan
Newton iteration  12energy =              nan<A u 12 , A u 12 >_{-1}^0.5 =  nan
Newton iteration  13energy =              nan<A u 13 , A u 13 >_{-1}^0.5 =  nan
Newton iteration  14energy =              nan<A u 14 , A u 14 >_{-1}^0.5 =  nan
Newton iteration  15energy =              nan<A u 15 , A u 15 >_{-1}^0.5 =  nan
Newton iteration  16energy =              nan<A u 16 , A u 16 >_{-1}^0.5 =  nan
Newton iteration  17energy =              nan<A u 17 , A u 17 >_{-1}^0.5 =  nan
Newton iteration  18energy =              nan<A u 18 , A u 18 >_{-1}^0.5 =  nan
Newton iteration  19energy =              nan<A u 19 , A u 19 >_{-1}^0.5 =  nan
Newton iteration  20energy =              nan<A u 20 , A u 20 >_{-1}^0.5 =  nan
Newton iteration  21energy =              nan<A u 21 , A u 21 >_{-1}^0.5 =  nan
Newton iteration  22energy =              nan<A u 22 , A u 22 >_{-1}^0.5 =  nan
Newton iteration  23energy =              nan<A u 23 , A u 23 >_{-1}^0.5 =  nan
Newton iteration  24energy =              nan<A u 24 , A u 24 >_{-1}^0.5 =  nan
loadstep 3
Newton iteration   0energy =              nan<A u 0 , A u 0 >_{-1}^0.5 =  nan
Newton iteration   1energy =              nan<A u 1 , A u 1 >_{-1}^0.5 =  nan
Newton iteration   2energy =              nan<A u 2 , A u 2 >_{-1}^0.5 =  nan
Newton iteration   3energy =              nan<A u 3 , A u 3 >_{-1}^0.5 =  nan
Newton iteration   4energy =              nan<A u 4 , A u 4 >_{-1}^0.5 =  nan
Newton iteration   5energy =              nan<A u 5 , A u 5 >_{-1}^0.5 =  nan
Newton iteration   6energy =              nan<A u 6 , A u 6 >_{-1}^0.5 =  nan
Newton iteration   7energy =              nan<A u 7 , A u 7 >_{-1}^0.5 =  nan
Newton iteration   8energy =              nan<A u 8 , A u 8 >_{-1}^0.5 =  nan
Newton iteration   9energy =              nan<A u 9 , A u 9 >_{-1}^0.5 =  nan
Newton iteration  10energy =              nan<A u 10 , A u 10 >_{-1}^0.5 =  nan
Newton iteration  11energy =              nan<A u 11 , A u 11 >_{-1}^0.5 =  nan
Newton iteration  12energy =              nan<A u 12 , A u 12 >_{-1}^0.5 =  nan
Newton iteration  13energy =              nan<A u 13 , A u 13 >_{-1}^0.5 =  nan
Newton iteration  14energy =              nan<A u 14 , A u 14 >_{-1}^0.5 =  nan
Newton iteration  15energy =              nan<A u 15 , A u 15 >_{-1}^0.5 =  nan
Newton iteration  16energy =              nan<A u 16 , A u 16 >_{-1}^0.5 =  nan
Newton iteration  17energy =              nan<A u 17 , A u 17 >_{-1}^0.5 =  nan
Newton iteration  18energy =              nan<A u 18 , A u 18 >_{-1}^0.5 =  nan
Newton iteration  19energy =              nan<A u 19 , A u 19 >_{-1}^0.5 =  nan
Newton iteration  20energy =              nan<A u 20 , A u 20 >_{-1}^0.5 =  nan
Newton iteration  21energy =              nan<A u 21 , A u 21 >_{-1}^0.5 =  nan
Newton iteration  22energy =              nan<A u 22 , A u 22 >_{-1}^0.5 =  nan
Newton iteration  23energy =              nan<A u 23 , A u 23 >_{-1}^0.5 =  nan
Newton iteration  24energy =              nan<A u 24 , A u 24 >_{-1}^0.5 =  nan
loadstep 4
Newton iteration   0energy =              nan<A u 0 , A u 0 >_{-1}^0.5 =  nan
Newton iteration   1energy =              nan<A u 1 , A u 1 >_{-1}^0.5 =  nan
Newton iteration   2energy =              nan<A u 2 , A u 2 >_{-1}^0.5 =  nan
Newton iteration   3energy =              nan<A u 3 , A u 3 >_{-1}^0.5 =  nan
Newton iteration   4energy =              nan<A u 4 , A u 4 >_{-1}^0.5 =  nan
Newton iteration   5energy =              nan<A u 5 , A u 5 >_{-1}^0.5 =  nan
Newton iteration   6energy =              nan<A u 6 , A u 6 >_{-1}^0.5 =  nan
Newton iteration   7energy =              nan<A u 7 , A u 7 >_{-1}^0.5 =  nan
Newton iteration   8energy =              nan<A u 8 , A u 8 >_{-1}^0.5 =  nan
Newton iteration   9energy =              nan<A u 9 , A u 9 >_{-1}^0.5 =  nan
Newton iteration  10energy =              nan<A u 10 , A u 10 >_{-1}^0.5 =  nan
Newton iteration  11energy =              nan<A u 11 , A u 11 >_{-1}^0.5 =  nan
Newton iteration  12energy =              nan<A u 12 , A u 12 >_{-1}^0.5 =  nan
Newton iteration  13energy =              nan<A u 13 , A u 13 >_{-1}^0.5 =  nan
Newton iteration  14energy =              nan<A u 14 , A u 14 >_{-1}^0.5 =  nan
Newton iteration  15energy =              nan<A u 15 , A u 15 >_{-1}^0.5 =  nan
Newton iteration  16energy =              nan<A u 16 , A u 16 >_{-1}^0.5 =  nan
Newton iteration  17energy =              nan<A u 17 , A u 17 >_{-1}^0.5 =  nan
Newton iteration  18energy =              nan<A u 18 , A u 18 >_{-1}^0.5 =  nan
Newton iteration  19energy =              nan<A u 19 , A u 19 >_{-1}^0.5 =  nan
Newton iteration  20energy =              nan<A u 20 , A u 20 >_{-1}^0.5 =  nan
Newton iteration  21energy =              nan<A u 21 , A u 21 >_{-1}^0.5 =  nan
Newton iteration  22energy =              nan<A u 22 , A u 22 >_{-1}^0.5 =  nan
Newton iteration  23energy =              nan<A u 23 , A u 23 >_{-1}^0.5 =  nan
Newton iteration  24energy =              nan<A u 24 , A u 24 >_{-1}^0.5 =  nan
loadstep 5
Newton iteration   0energy =              nan<A u 0 , A u 0 >_{-1}^0.5 =  nan
Newton iteration   1energy =              nan<A u 1 , A u 1 >_{-1}^0.5 =  nan
Newton iteration   2energy =              nan<A u 2 , A u 2 >_{-1}^0.5 =  nan
Newton iteration   3energy =              nan<A u 3 , A u 3 >_{-1}^0.5 =  nan
Newton iteration   4energy =              nan<A u 4 , A u 4 >_{-1}^0.5 =  nan
Newton iteration   5energy =              nan<A u 5 , A u 5 >_{-1}^0.5 =  nan
Newton iteration   6energy =              nan<A u 6 , A u 6 >_{-1}^0.5 =  nan
Newton iteration   7energy =              nan<A u 7 , A u 7 >_{-1}^0.5 =  nan
Newton iteration   8energy =              nan<A u 8 , A u 8 >_{-1}^0.5 =  nan
Newton iteration   9energy =              nan<A u 9 , A u 9 >_{-1}^0.5 =  nan
Newton iteration  10energy =              nan<A u 10 , A u 10 >_{-1}^0.5 =  nan
Newton iteration  11energy =              nan<A u 11 , A u 11 >_{-1}^0.5 =  nan
Newton iteration  12energy =              nan<A u 12 , A u 12 >_{-1}^0.5 =  nan
Newton iteration  13energy =              nan<A u 13 , A u 13 >_{-1}^0.5 =  nan
Newton iteration  14energy =              nan<A u 14 , A u 14 >_{-1}^0.5 =  nan
Newton iteration  15energy =              nan<A u 15 , A u 15 >_{-1}^0.5 =  nan
Newton iteration  16energy =              nan<A u 16 , A u 16 >_{-1}^0.5 =  nan
Newton iteration  17energy =              nan<A u 17 , A u 17 >_{-1}^0.5 =  nan
Newton iteration  18energy =              nan<A u 18 , A u 18 >_{-1}^0.5 =  nan
Newton iteration  19energy =              nan<A u 19 , A u 19 >_{-1}^0.5 =  nan
Newton iteration  20energy =              nan<A u 20 , A u 20 >_{-1}^0.5 =  nan
Newton iteration  21energy =              nan<A u 21 , A u 21 >_{-1}^0.5 =  nan
Newton iteration  22energy =              nan<A u 22 , A u 22 >_{-1}^0.5 =  nan
Newton iteration  23energy =              nan<A u 23 , A u 23 >_{-1}^0.5 =  nan
Newton iteration  24energy =              nan<A u 24 , A u 24 >_{-1}^0.5 =  nan
loadstep 6
Newton iteration   0energy =              nan<A u 0 , A u 0 >_{-1}^0.5 =  nan
Newton iteration   1energy =              nan<A u 1 , A u 1 >_{-1}^0.5 =  nan
Newton iteration   2energy =              nan<A u 2 , A u 2 >_{-1}^0.5 =  nan
Newton iteration   3energy =              nan<A u 3 , A u 3 >_{-1}^0.5 =  nan
Newton iteration   4energy =              nan<A u 4 , A u 4 >_{-1}^0.5 =  nan
Newton iteration   5energy =              nan<A u 5 , A u 5 >_{-1}^0.5 =  nan
Newton iteration   6energy =              nan<A u 6 , A u 6 >_{-1}^0.5 =  nan
Newton iteration   7energy =              nan<A u 7 , A u 7 >_{-1}^0.5 =  nan
Newton iteration   8energy =              nan<A u 8 , A u 8 >_{-1}^0.5 =  nan
Newton iteration   9energy =              nan<A u 9 , A u 9 >_{-1}^0.5 =  nan
Newton iteration  10energy =              nan<A u 10 , A u 10 >_{-1}^0.5 =  nan
Newton iteration  11energy =              nan<A u 11 , A u 11 >_{-1}^0.5 =  nan
Newton iteration  12energy =              nan<A u 12 , A u 12 >_{-1}^0.5 =  nan
Newton iteration  13energy =              nan<A u 13 , A u 13 >_{-1}^0.5 =  nan
Newton iteration  14energy =              nan<A u 14 , A u 14 >_{-1}^0.5 =  nan
Newton iteration  15energy =              nan<A u 15 , A u 15 >_{-1}^0.5 =  nan
Newton iteration  16energy =              nan<A u 16 , A u 16 >_{-1}^0.5 =  nan
Newton iteration  17energy =              nan<A u 17 , A u 17 >_{-1}^0.5 =  nan
Newton iteration  18energy =              nan<A u 18 , A u 18 >_{-1}^0.5 =  nan
Newton iteration  19energy =              nan<A u 19 , A u 19 >_{-1}^0.5 =  nan
Newton iteration  20energy =              nan<A u 20 , A u 20 >_{-1}^0.5 =  nan
Newton iteration  21energy =              nan<A u 21 , A u 21 >_{-1}^0.5 =  nan
Newton iteration  22energy =              nan<A u 22 , A u 22 >_{-1}^0.5 =  nan
Newton iteration  23energy =              nan<A u 23 , A u 23 >_{-1}^0.5 =  nan
Newton iteration  24energy =              nan<A u 24 , A u 24 >_{-1}^0.5 =  nan
loadstep 7
Newton iteration   0energy =              nan<A u 0 , A u 0 >_{-1}^0.5 =  nan
Newton iteration   1energy =              nan<A u 1 , A u 1 >_{-1}^0.5 =  nan
Newton iteration   2energy =              nan<A u 2 , A u 2 >_{-1}^0.5 =  nan
Newton iteration   3energy =              nan<A u 3 , A u 3 >_{-1}^0.5 =  nan
Newton iteration   4energy =              nan<A u 4 , A u 4 >_{-1}^0.5 =  nan
Newton iteration   5energy =              nan<A u 5 , A u 5 >_{-1}^0.5 =  nan
Newton iteration   6energy =              nan<A u 6 , A u 6 >_{-1}^0.5 =  nan
Newton iteration   7energy =              nan<A u 7 , A u 7 >_{-1}^0.5 =  nan
Newton iteration   8energy =              nan<A u 8 , A u 8 >_{-1}^0.5 =  nan
Newton iteration   9energy =              nan<A u 9 , A u 9 >_{-1}^0.5 =  nan
Newton iteration  10energy =              nan<A u 10 , A u 10 >_{-1}^0.5 =  nan
Newton iteration  11energy =              nan<A u 11 , A u 11 >_{-1}^0.5 =  nan
Newton iteration  12energy =              nan<A u 12 , A u 12 >_{-1}^0.5 =  nan
Newton iteration  13energy =              nan<A u 13 , A u 13 >_{-1}^0.5 =  nan
Newton iteration  14energy =              nan<A u 14 , A u 14 >_{-1}^0.5 =  nan
Newton iteration  15energy =              nan<A u 15 , A u 15 >_{-1}^0.5 =  nan
Newton iteration  16energy =              nan<A u 16 , A u 16 >_{-1}^0.5 =  nan
Newton iteration  17energy =              nan<A u 17 , A u 17 >_{-1}^0.5 =  nan
Newton iteration  18energy =              nan<A u 18 , A u 18 >_{-1}^0.5 =  nan
Newton iteration  19energy =              nan<A u 19 , A u 19 >_{-1}^0.5 =  nan
Newton iteration  20energy =              nan<A u 20 , A u 20 >_{-1}^0.5 =  nan
Newton iteration  21energy =              nan<A u 21 , A u 21 >_{-1}^0.5 =  nan
Newton iteration  22energy =              nan<A u 22 , A u 22 >_{-1}^0.5 =  nan
Newton iteration  23energy =              nan<A u 23 , A u 23 >_{-1}^0.5 =  nan
Newton iteration  24energy =              nan<A u 24 , A u 24 >_{-1}^0.5 =  nan
loadstep 8
Newton iteration   0energy =              nan<A u 0 , A u 0 >_{-1}^0.5 =  nan
Newton iteration   1energy =              nan<A u 1 , A u 1 >_{-1}^0.5 =  nan
Newton iteration   2energy =              nan<A u 2 , A u 2 >_{-1}^0.5 =  nan
Newton iteration   3energy =              nan<A u 3 , A u 3 >_{-1}^0.5 =  nan
Newton iteration   4energy =              nan<A u 4 , A u 4 >_{-1}^0.5 =  nan
Newton iteration   5energy =              nan<A u 5 , A u 5 >_{-1}^0.5 =  nan
Newton iteration   6energy =              nan<A u 6 , A u 6 >_{-1}^0.5 =  nan
Newton iteration   7energy =              nan<A u 7 , A u 7 >_{-1}^0.5 =  nan
Newton iteration   8energy =              nan<A u 8 , A u 8 >_{-1}^0.5 =  nan
Newton iteration   9energy =              nan<A u 9 , A u 9 >_{-1}^0.5 =  nan
Newton iteration  10energy =              nan<A u 10 , A u 10 >_{-1}^0.5 =  nan
Newton iteration  11energy =              nan<A u 11 , A u 11 >_{-1}^0.5 =  nan
Newton iteration  12energy =              nan<A u 12 , A u 12 >_{-1}^0.5 =  nan
Newton iteration  13energy =              nan<A u 13 , A u 13 >_{-1}^0.5 =  nan
Newton iteration  14energy =              nan<A u 14 , A u 14 >_{-1}^0.5 =  nan
Newton iteration  15energy =              nan<A u 15 , A u 15 >_{-1}^0.5 =  nan
Newton iteration  16energy =              nan<A u 16 , A u 16 >_{-1}^0.5 =  nan
Newton iteration  17energy =              nan<A u 17 , A u 17 >_{-1}^0.5 =  nan
Newton iteration  18energy =              nan<A u 18 , A u 18 >_{-1}^0.5 =  nan
Newton iteration  19energy =              nan<A u 19 , A u 19 >_{-1}^0.5 =  nan
Newton iteration  20energy =              nan<A u 20 , A u 20 >_{-1}^0.5 =  nan
Newton iteration  21energy =              nan<A u 21 , A u 21 >_{-1}^0.5 =  nan
Newton iteration  22energy =              nan<A u 22 , A u 22 >_{-1}^0.5 =  nan
Newton iteration  23energy =              nan<A u 23 , A u 23 >_{-1}^0.5 =  nan
Newton iteration  24energy =              nan<A u 24 , A u 24 >_{-1}^0.5 =  nan
loadstep 9
Newton iteration   0energy =              nan<A u 0 , A u 0 >_{-1}^0.5 =  nan
Newton iteration   1energy =              nan<A u 1 , A u 1 >_{-1}^0.5 =  nan
Newton iteration   2energy =              nan<A u 2 , A u 2 >_{-1}^0.5 =  nan
Newton iteration   3energy =              nan<A u 3 , A u 3 >_{-1}^0.5 =  nan
Newton iteration   4energy =              nan<A u 4 , A u 4 >_{-1}^0.5 =  nan
Newton iteration   5energy =              nan<A u 5 , A u 5 >_{-1}^0.5 =  nan
Newton iteration   6energy =              nan<A u 6 , A u 6 >_{-1}^0.5 =  nan
Newton iteration   7energy =              nan<A u 7 , A u 7 >_{-1}^0.5 =  nan
Newton iteration   8energy =              nan<A u 8 , A u 8 >_{-1}^0.5 =  nan
Newton iteration   9energy =              nan<A u 9 , A u 9 >_{-1}^0.5 =  nan
Newton iteration  10energy =              nan<A u 10 , A u 10 >_{-1}^0.5 =  nan
Newton iteration  11energy =              nan<A u 11 , A u 11 >_{-1}^0.5 =  nan
Newton iteration  12energy =              nan<A u 12 , A u 12 >_{-1}^0.5 =  nan
Newton iteration  13energy =              nan<A u 13 , A u 13 >_{-1}^0.5 =  nan
Newton iteration  14energy =              nan<A u 14 , A u 14 >_{-1}^0.5 =  nan
Newton iteration  15energy =              nan<A u 15 , A u 15 >_{-1}^0.5 =  nan
Newton iteration  16energy =              nan<A u 16 , A u 16 >_{-1}^0.5 =  nan
Newton iteration  17energy =              nan<A u 17 , A u 17 >_{-1}^0.5 =  nan
Newton iteration  18energy =              nan<A u 18 , A u 18 >_{-1}^0.5 =  nan
Newton iteration  19energy =              nan<A u 19 , A u 19 >_{-1}^0.5 =  nan
Newton iteration  20energy =              nan<A u 20 , A u 20 >_{-1}^0.5 =  nan
Newton iteration  21energy =              nan<A u 21 , A u 21 >_{-1}^0.5 =  nan
Newton iteration  22energy =              nan<A u 22 , A u 22 >_{-1}^0.5 =  nan
Newton iteration  23energy =              nan<A u 23 , A u 23 >_{-1}^0.5 =  nan
Newton iteration  24energy =              nan<A u 24 , A u 24 >_{-1}^0.5 =  nan
loadstep 10
Newton iteration   0energy =              nan<A u 0 , A u 0 >_{-1}^0.5 =  nan
Newton iteration   1energy =              nan<A u 1 , A u 1 >_{-1}^0.5 =  nan
Newton iteration   2energy =              nan<A u 2 , A u 2 >_{-1}^0.5 =  nan
Newton iteration   3energy =              nan<A u 3 , A u 3 >_{-1}^0.5 =  nan
Newton iteration   4energy =              nan<A u 4 , A u 4 >_{-1}^0.5 =  nan
Newton iteration   5energy =              nan<A u 5 , A u 5 >_{-1}^0.5 =  nan
Newton iteration   6energy =              nan<A u 6 , A u 6 >_{-1}^0.5 =  nan
Newton iteration   7energy =              nan<A u 7 , A u 7 >_{-1}^0.5 =  nan
Newton iteration   8energy =              nan<A u 8 , A u 8 >_{-1}^0.5 =  nan
Newton iteration   9energy =              nan<A u 9 , A u 9 >_{-1}^0.5 =  nan
Newton iteration  10energy =              nan<A u 10 , A u 10 >_{-1}^0.5 =  nan
Newton iteration  11energy =              nan<A u 11 , A u 11 >_{-1}^0.5 =  nan
Newton iteration  12energy =              nan<A u 12 , A u 12 >_{-1}^0.5 =  nan
Newton iteration  13energy =              nan<A u 13 , A u 13 >_{-1}^0.5 =  nan
Newton iteration  14energy =              nan<A u 14 , A u 14 >_{-1}^0.5 =  nan
Newton iteration  15energy =              nan<A u 15 , A u 15 >_{-1}^0.5 =  nan
Newton iteration  16energy =              nan<A u 16 , A u 16 >_{-1}^0.5 =  nan
Newton iteration  17energy =              nan<A u 17 , A u 17 >_{-1}^0.5 =  nan
Newton iteration  18energy =              nan<A u 18 , A u 18 >_{-1}^0.5 =  nan
Newton iteration  19energy =              nan<A u 19 , A u 19 >_{-1}^0.5 =  nan
Newton iteration  20energy =              nan<A u 20 , A u 20 >_{-1}^0.5 =  nan
Newton iteration  21energy =              nan<A u 21 , A u 21 >_{-1}^0.5 =  nan
Newton iteration  22energy =              nan<A u 22 , A u 22 >_{-1}^0.5 =  nan
Newton iteration  23energy =              nan<A u 23 , A u 23 >_{-1}^0.5 =  nan
Newton iteration  24energy =              nan<A u 24 , A u 24 >_{-1}^0.5 =  nan
loadstep 11
Newton iteration   0energy =              nan<A u 0 , A u 0 >_{-1}^0.5 =  nan
Newton iteration   1energy =              nan<A u 1 , A u 1 >_{-1}^0.5 =  nan
Newton iteration   2energy =              nan<A u 2 , A u 2 >_{-1}^0.5 =  nan
Newton iteration   3energy =              nan<A u 3 , A u 3 >_{-1}^0.5 =  nan
Newton iteration   4energy =              nan<A u 4 , A u 4 >_{-1}^0.5 =  nan
Newton iteration   5energy =              nan<A u 5 , A u 5 >_{-1}^0.5 =  nan
Newton iteration   6energy =              nan<A u 6 , A u 6 >_{-1}^0.5 =  nan
Newton iteration   7energy =              nan<A u 7 , A u 7 >_{-1}^0.5 =  nan
Newton iteration   8energy =              nan<A u 8 , A u 8 >_{-1}^0.5 =  nan
Newton iteration   9energy =              nan<A u 9 , A u 9 >_{-1}^0.5 =  nan
Newton iteration  10energy =              nan<A u 10 , A u 10 >_{-1}^0.5 =  nan
Newton iteration  11energy =              nan<A u 11 , A u 11 >_{-1}^0.5 =  nan
Newton iteration  12energy =              nan<A u 12 , A u 12 >_{-1}^0.5 =  nan
Newton iteration  13energy =              nan<A u 13 , A u 13 >_{-1}^0.5 =  nan
Newton iteration  14energy =              nan<A u 14 , A u 14 >_{-1}^0.5 =  nan
Newton iteration  15energy =              nan<A u 15 , A u 15 >_{-1}^0.5 =  nan
Newton iteration  16energy =              nan<A u 16 , A u 16 >_{-1}^0.5 =  nan
Newton iteration  17energy =              nan<A u 17 , A u 17 >_{-1}^0.5 =  nan
Newton iteration  18energy =              nan<A u 18 , A u 18 >_{-1}^0.5 =  nan
Newton iteration  19energy =              nan<A u 19 , A u 19 >_{-1}^0.5 =  nan
Newton iteration  20energy =              nan<A u 20 , A u 20 >_{-1}^0.5 =  nan
Newton iteration  21energy =              nan<A u 21 , A u 21 >_{-1}^0.5 =  nan
Newton iteration  22energy =              nan<A u 22 , A u 22 >_{-1}^0.5 =  nan
Newton iteration  23energy =              nan<A u 23 , A u 23 >_{-1}^0.5 =  nan
Newton iteration  24energy =              nan<A u 24 , A u 24 >_{-1}^0.5 =  nan
loadstep 12
Newton iteration   0energy =              nan<A u 0 , A u 0 >_{-1}^0.5 =  nan
Newton iteration   1energy =              nan<A u 1 , A u 1 >_{-1}^0.5 =  nan
Newton iteration   2energy =              nan<A u 2 , A u 2 >_{-1}^0.5 =  nan
Newton iteration   3energy =              nan<A u 3 , A u 3 >_{-1}^0.5 =  nan
Newton iteration   4energy =              nan<A u 4 , A u 4 >_{-1}^0.5 =  nan
Newton iteration   5energy =              nan<A u 5 , A u 5 >_{-1}^0.5 =  nan
Newton iteration   6energy =              nan<A u 6 , A u 6 >_{-1}^0.5 =  nan
Newton iteration   7energy =              nan<A u 7 , A u 7 >_{-1}^0.5 =  nan
Newton iteration   8energy =              nan<A u 8 , A u 8 >_{-1}^0.5 =  nan
Newton iteration   9energy =              nan<A u 9 , A u 9 >_{-1}^0.5 =  nan
Newton iteration  10energy =              nan<A u 10 , A u 10 >_{-1}^0.5 =  nan
Newton iteration  11energy =              nan<A u 11 , A u 11 >_{-1}^0.5 =  nan
Newton iteration  12energy =              nan<A u 12 , A u 12 >_{-1}^0.5 =  nan
Newton iteration  13energy =              nan<A u 13 , A u 13 >_{-1}^0.5 =  nan
Newton iteration  14energy =              nan<A u 14 , A u 14 >_{-1}^0.5 =  nan
Newton iteration  15energy =              nan<A u 15 , A u 15 >_{-1}^0.5 =  nan
Newton iteration  16energy =              nan<A u 16 , A u 16 >_{-1}^0.5 =  nan
Newton iteration  17energy =              nan<A u 17 , A u 17 >_{-1}^0.5 =  nan
Newton iteration  18energy =              nan<A u 18 , A u 18 >_{-1}^0.5 =  nan
Newton iteration  19energy =              nan<A u 19 , A u 19 >_{-1}^0.5 =  nan
Newton iteration  20energy =              nan<A u 20 , A u 20 >_{-1}^0.5 =  nan
Newton iteration  21energy =              nan<A u 21 , A u 21 >_{-1}^0.5 =  nan
Newton iteration  22energy =              nan<A u 22 , A u 22 >_{-1}^0.5 =  nan
Newton iteration  23energy =              nan<A u 23 , A u 23 >_{-1}^0.5 =  nan
Newton iteration  24energy =              nan<A u 24 , A u 24 >_{-1}^0.5 =  nan
loadstep 13
Newton iteration   0energy =              nan<A u 0 , A u 0 >_{-1}^0.5 =  nan
Newton iteration   1energy =              nan<A u 1 , A u 1 >_{-1}^0.5 =  nan
Newton iteration   2energy =              nan<A u 2 , A u 2 >_{-1}^0.5 =  nan
Newton iteration   3energy =              nan<A u 3 , A u 3 >_{-1}^0.5 =  nan
Newton iteration   4energy =              nan<A u 4 , A u 4 >_{-1}^0.5 =  nan
Newton iteration   5energy =              nan<A u 5 , A u 5 >_{-1}^0.5 =  nan
Newton iteration   6energy =              nan<A u 6 , A u 6 >_{-1}^0.5 =  nan
Newton iteration   7energy =              nan<A u 7 , A u 7 >_{-1}^0.5 =  nan
Newton iteration   8energy =              nan<A u 8 , A u 8 >_{-1}^0.5 =  nan
Newton iteration   9energy =              nan<A u 9 , A u 9 >_{-1}^0.5 =  nan
Newton iteration  10energy =              nan<A u 10 , A u 10 >_{-1}^0.5 =  nan
Newton iteration  11energy =              nan<A u 11 , A u 11 >_{-1}^0.5 =  nan
Newton iteration  12energy =              nan<A u 12 , A u 12 >_{-1}^0.5 =  nan
Newton iteration  13energy =              nan<A u 13 , A u 13 >_{-1}^0.5 =  nan
Newton iteration  14energy =              nan<A u 14 , A u 14 >_{-1}^0.5 =  nan
Newton iteration  15energy =              nan<A u 15 , A u 15 >_{-1}^0.5 =  nan
Newton iteration  16energy =              nan<A u 16 , A u 16 >_{-1}^0.5 =  nan
Newton iteration  17energy =              nan<A u 17 , A u 17 >_{-1}^0.5 =  nan
Newton iteration  18energy =              nan<A u 18 , A u 18 >_{-1}^0.5 =  nan
Newton iteration  19energy =              nan<A u 19 , A u 19 >_{-1}^0.5 =  nan
Newton iteration  20energy =              nan<A u 20 , A u 20 >_{-1}^0.5 =  nan
Newton iteration  21energy =              nan<A u 21 , A u 21 >_{-1}^0.5 =  nan
Newton iteration  22energy =              nan<A u 22 , A u 22 >_{-1}^0.5 =  nan
Newton iteration  23energy =              nan<A u 23 , A u 23 >_{-1}^0.5 =  nan
Newton iteration  24energy =              nan<A u 24 , A u 24 >_{-1}^0.5 =  nan
loadstep 14
Newton iteration   0energy =              nan<A u 0 , A u 0 >_{-1}^0.5 =  nan
Newton iteration   1energy =              nan<A u 1 , A u 1 >_{-1}^0.5 =  nan
Newton iteration   2energy =              nan<A u 2 , A u 2 >_{-1}^0.5 =  nan
Newton iteration   3energy =              nan<A u 3 , A u 3 >_{-1}^0.5 =  nan
Newton iteration   4energy =              nan<A u 4 , A u 4 >_{-1}^0.5 =  nan
Newton iteration   5energy =              nan<A u 5 , A u 5 >_{-1}^0.5 =  nan
Newton iteration   6energy =              nan<A u 6 , A u 6 >_{-1}^0.5 =  nan
Newton iteration   7energy =              nan<A u 7 , A u 7 >_{-1}^0.5 =  nan
Newton iteration   8energy =              nan<A u 8 , A u 8 >_{-1}^0.5 =  nan
Newton iteration   9energy =              nan<A u 9 , A u 9 >_{-1}^0.5 =  nan
Newton iteration  10energy =              nan<A u 10 , A u 10 >_{-1}^0.5 =  nan
Newton iteration  11energy =              nan<A u 11 , A u 11 >_{-1}^0.5 =  nan
Newton iteration  12energy =              nan<A u 12 , A u 12 >_{-1}^0.5 =  nan
Newton iteration  13energy =              nan<A u 13 , A u 13 >_{-1}^0.5 =  nan
Newton iteration  14energy =              nan<A u 14 , A u 14 >_{-1}^0.5 =  nan
Newton iteration  15energy =              nan<A u 15 , A u 15 >_{-1}^0.5 =  nan
Newton iteration  16energy =              nan<A u 16 , A u 16 >_{-1}^0.5 =  nan
Newton iteration  17energy =              nan<A u 17 , A u 17 >_{-1}^0.5 =  nan
Newton iteration  18energy =              nan<A u 18 , A u 18 >_{-1}^0.5 =  nan
Newton iteration  19energy =              nan<A u 19 , A u 19 >_{-1}^0.5 =  nan
Newton iteration  20energy =              nan<A u 20 , A u 20 >_{-1}^0.5 =  nan
Newton iteration  21energy =              nan<A u 21 , A u 21 >_{-1}^0.5 =  nan
Newton iteration  22energy =              nan<A u 22 , A u 22 >_{-1}^0.5 =  nan
Newton iteration  23energy =              nan<A u 23 , A u 23 >_{-1}^0.5 =  nan
Newton iteration  24energy =              nan<A u 24 , A u 24 >_{-1}^0.5 =  nan
loadstep 15
Newton iteration   0energy =              nan<A u 0 , A u 0 >_{-1}^0.5 =  nan
Newton iteration   1energy =              nan<A u 1 , A u 1 >_{-1}^0.5 =  nan
Newton iteration   2energy =              nan<A u 2 , A u 2 >_{-1}^0.5 =  nan
Newton iteration   3energy =              nan<A u 3 , A u 3 >_{-1}^0.5 =  nan
Newton iteration   4energy =              nan<A u 4 , A u 4 >_{-1}^0.5 =  nan
Newton iteration   5energy =              nan<A u 5 , A u 5 >_{-1}^0.5 =  nan
Newton iteration   6energy =              nan<A u 6 , A u 6 >_{-1}^0.5 =  nan
Newton iteration   7energy =              nan<A u 7 , A u 7 >_{-1}^0.5 =  nan
Newton iteration   8energy =              nan<A u 8 , A u 8 >_{-1}^0.5 =  nan
Newton iteration   9energy =              nan<A u 9 , A u 9 >_{-1}^0.5 =  nan
Newton iteration  10energy =              nan<A u 10 , A u 10 >_{-1}^0.5 =  nan
Newton iteration  11energy =              nan<A u 11 , A u 11 >_{-1}^0.5 =  nan
Newton iteration  12energy =              nan<A u 12 , A u 12 >_{-1}^0.5 =  nan
Newton iteration  13energy =              nan<A u 13 , A u 13 >_{-1}^0.5 =  nan
Newton iteration  14energy =              nan<A u 14 , A u 14 >_{-1}^0.5 =  nan
Newton iteration  15energy =              nan<A u 15 , A u 15 >_{-1}^0.5 =  nan
Newton iteration  16energy =              nan<A u 16 , A u 16 >_{-1}^0.5 =  nan
Newton iteration  17energy =              nan<A u 17 , A u 17 >_{-1}^0.5 =  nan
Newton iteration  18energy =              nan<A u 18 , A u 18 >_{-1}^0.5 =  nan
Newton iteration  19energy =              nan<A u 19 , A u 19 >_{-1}^0.5 =  nan
Newton iteration  20energy =              nan<A u 20 , A u 20 >_{-1}^0.5 =  nan
Newton iteration  21energy =              nan<A u 21 , A u 21 >_{-1}^0.5 =  nan
Newton iteration  22energy =              nan<A u 22 , A u 22 >_{-1}^0.5 =  nan
Newton iteration  23energy =              nan<A u 23 , A u 23 >_{-1}^0.5 =  nan
Newton iteration  24energy =              nan<A u 24 , A u 24 >_{-1}^0.5 =  nan
loadstep 16
Newton iteration   0energy =              nan<A u 0 , A u 0 >_{-1}^0.5 =  nan
Newton iteration   1energy =              nan<A u 1 , A u 1 >_{-1}^0.5 =  nan
Newton iteration   2energy =              nan<A u 2 , A u 2 >_{-1}^0.5 =  nan
Newton iteration   3energy =              nan<A u 3 , A u 3 >_{-1}^0.5 =  nan
Newton iteration   4energy =              nan<A u 4 , A u 4 >_{-1}^0.5 =  nan
Newton iteration   5energy =              nan<A u 5 , A u 5 >_{-1}^0.5 =  nan
Newton iteration   6energy =              nan<A u 6 , A u 6 >_{-1}^0.5 =  nan
Newton iteration   7energy =              nan<A u 7 , A u 7 >_{-1}^0.5 =  nan
Newton iteration   8energy =              nan<A u 8 , A u 8 >_{-1}^0.5 =  nan
Newton iteration   9energy =              nan<A u 9 , A u 9 >_{-1}^0.5 =  nan
Newton iteration  10energy =              nan<A u 10 , A u 10 >_{-1}^0.5 =  nan
Newton iteration  11energy =              nan<A u 11 , A u 11 >_{-1}^0.5 =  nan
Newton iteration  12energy =              nan<A u 12 , A u 12 >_{-1}^0.5 =  nan
Newton iteration  13energy =              nan<A u 13 , A u 13 >_{-1}^0.5 =  nan
Newton iteration  14energy =              nan<A u 14 , A u 14 >_{-1}^0.5 =  nan
Newton iteration  15energy =              nan<A u 15 , A u 15 >_{-1}^0.5 =  nan
Newton iteration  16energy =              nan<A u 16 , A u 16 >_{-1}^0.5 =  nan
Newton iteration  17energy =              nan<A u 17 , A u 17 >_{-1}^0.5 =  nan
Newton iteration  18energy =              nan<A u 18 , A u 18 >_{-1}^0.5 =  nan
Newton iteration  19energy =              nan<A u 19 , A u 19 >_{-1}^0.5 =  nan
Newton iteration  20energy =              nan<A u 20 , A u 20 >_{-1}^0.5 =  nan
Newton iteration  21energy =              nan<A u 21 , A u 21 >_{-1}^0.5 =  nan
Newton iteration  22energy =              nan<A u 22 , A u 22 >_{-1}^0.5 =  nan
Newton iteration  23energy =              nan<A u 23 , A u 23 >_{-1}^0.5 =  nan
Newton iteration  24energy =              nan<A u 24 , A u 24 >_{-1}^0.5 =  nan
loadstep 17
Newton iteration   0energy =              nan<A u 0 , A u 0 >_{-1}^0.5 =  nan
Newton iteration   1energy =              nan<A u 1 , A u 1 >_{-1}^0.5 =  nan
Newton iteration   2energy =              nan<A u 2 , A u 2 >_{-1}^0.5 =  nan
Newton iteration   3energy =              nan<A u 3 , A u 3 >_{-1}^0.5 =  nan
Newton iteration   4energy =              nan<A u 4 , A u 4 >_{-1}^0.5 =  nan
Newton iteration   5energy =              nan<A u 5 , A u 5 >_{-1}^0.5 =  nan
Newton iteration   6energy =              nan<A u 6 , A u 6 >_{-1}^0.5 =  nan
Newton iteration   7energy =              nan<A u 7 , A u 7 >_{-1}^0.5 =  nan
Newton iteration   8energy =              nan<A u 8 , A u 8 >_{-1}^0.5 =  nan
Newton iteration   9energy =              nan<A u 9 , A u 9 >_{-1}^0.5 =  nan
Newton iteration  10energy =              nan<A u 10 , A u 10 >_{-1}^0.5 =  nan
Newton iteration  11energy =              nan<A u 11 , A u 11 >_{-1}^0.5 =  nan
Newton iteration  12energy =              nan<A u 12 , A u 12 >_{-1}^0.5 =  nan
Newton iteration  13energy =              nan<A u 13 , A u 13 >_{-1}^0.5 =  nan
Newton iteration  14energy =              nan<A u 14 , A u 14 >_{-1}^0.5 =  nan
Newton iteration  15energy =              nan<A u 15 , A u 15 >_{-1}^0.5 =  nan
Newton iteration  16energy =              nan<A u 16 , A u 16 >_{-1}^0.5 =  nan
Newton iteration  17energy =              nan<A u 17 , A u 17 >_{-1}^0.5 =  nan
Newton iteration  18energy =              nan<A u 18 , A u 18 >_{-1}^0.5 =  nan
Newton iteration  19energy =              nan<A u 19 , A u 19 >_{-1}^0.5 =  nan
Newton iteration  20energy =              nan<A u 20 , A u 20 >_{-1}^0.5 =  nan
Newton iteration  21energy =              nan<A u 21 , A u 21 >_{-1}^0.5 =  nan
Newton iteration  22energy =              nan<A u 22 , A u 22 >_{-1}^0.5 =  nan
Newton iteration  23energy =              nan<A u 23 , A u 23 >_{-1}^0.5 =  nan
Newton iteration  24energy =              nan<A u 24 , A u 24 >_{-1}^0.5 =  nan
loadstep 18
Newton iteration   0energy =              nan<A u 0 , A u 0 >_{-1}^0.5 =  nan
Newton iteration   1energy =              nan<A u 1 , A u 1 >_{-1}^0.5 =  nan
Newton iteration   2energy =              nan<A u 2 , A u 2 >_{-1}^0.5 =  nan
Newton iteration   3energy =              nan<A u 3 , A u 3 >_{-1}^0.5 =  nan
Newton iteration   4energy =              nan<A u 4 , A u 4 >_{-1}^0.5 =  nan
Newton iteration   5energy =              nan<A u 5 , A u 5 >_{-1}^0.5 =  nan
Newton iteration   6energy =              nan<A u 6 , A u 6 >_{-1}^0.5 =  nan
Newton iteration   7energy =              nan<A u 7 , A u 7 >_{-1}^0.5 =  nan
Newton iteration   8energy =              nan<A u 8 , A u 8 >_{-1}^0.5 =  nan
Newton iteration   9energy =              nan<A u 9 , A u 9 >_{-1}^0.5 =  nan
Newton iteration  10energy =              nan<A u 10 , A u 10 >_{-1}^0.5 =  nan
Newton iteration  11energy =              nan<A u 11 , A u 11 >_{-1}^0.5 =  nan
Newton iteration  12energy =              nan<A u 12 , A u 12 >_{-1}^0.5 =  nan
Newton iteration  13energy =              nan<A u 13 , A u 13 >_{-1}^0.5 =  nan
Newton iteration  14energy =              nan<A u 14 , A u 14 >_{-1}^0.5 =  nan
Newton iteration  15energy =              nan<A u 15 , A u 15 >_{-1}^0.5 =  nan
Newton iteration  16energy =              nan<A u 16 , A u 16 >_{-1}^0.5 =  nan
Newton iteration  17energy =              nan<A u 17 , A u 17 >_{-1}^0.5 =  nan
Newton iteration  18energy =              nan<A u 18 , A u 18 >_{-1}^0.5 =  nan
Newton iteration  19energy =              nan<A u 19 , A u 19 >_{-1}^0.5 =  nan
Newton iteration  20energy =              nan<A u 20 , A u 20 >_{-1}^0.5 =  nan
Newton iteration  21energy =              nan<A u 21 , A u 21 >_{-1}^0.5 =  nan
Newton iteration  22energy =              nan<A u 22 , A u 22 >_{-1}^0.5 =  nan
Newton iteration  23energy =              nan<A u 23 , A u 23 >_{-1}^0.5 =  nan
Newton iteration  24energy =              nan<A u 24 , A u 24 >_{-1}^0.5 =  nan
loadstep 19
Newton iteration   0energy =              nan<A u 0 , A u 0 >_{-1}^0.5 =  nan
Newton iteration   1energy =              nan<A u 1 , A u 1 >_{-1}^0.5 =  nan
Newton iteration   2energy =              nan<A u 2 , A u 2 >_{-1}^0.5 =  nan
Newton iteration   3energy =              nan<A u 3 , A u 3 >_{-1}^0.5 =  nan
Newton iteration   4energy =              nan<A u 4 , A u 4 >_{-1}^0.5 =  nan
Newton iteration   5energy =              nan<A u 5 , A u 5 >_{-1}^0.5 =  nan
Newton iteration   6energy =              nan<A u 6 , A u 6 >_{-1}^0.5 =  nan
Newton iteration   7energy =              nan<A u 7 , A u 7 >_{-1}^0.5 =  nan
Newton iteration   8energy =              nan<A u 8 , A u 8 >_{-1}^0.5 =  nan
Newton iteration   9energy =              nan<A u 9 , A u 9 >_{-1}^0.5 =  nan
Newton iteration  10energy =              nan<A u 10 , A u 10 >_{-1}^0.5 =  nan
Newton iteration  11energy =              nan<A u 11 , A u 11 >_{-1}^0.5 =  nan
Newton iteration  12energy =              nan<A u 12 , A u 12 >_{-1}^0.5 =  nan
Newton iteration  13energy =              nan<A u 13 , A u 13 >_{-1}^0.5 =  nan
Newton iteration  14energy =              nan<A u 14 , A u 14 >_{-1}^0.5 =  nan
Newton iteration  15energy =              nan<A u 15 , A u 15 >_{-1}^0.5 =  nan
Newton iteration  16energy =              nan<A u 16 , A u 16 >_{-1}^0.5 =  nan
Newton iteration  17energy =              nan<A u 17 , A u 17 >_{-1}^0.5 =  nan
Newton iteration  18energy =              nan<A u 18 , A u 18 >_{-1}^0.5 =  nan
Newton iteration  19energy =              nan<A u 19 , A u 19 >_{-1}^0.5 =  nan
Newton iteration  20energy =              nan<A u 20 , A u 20 >_{-1}^0.5 =  nan
Newton iteration  21energy =              nan<A u 21 , A u 21 >_{-1}^0.5 =  nan
Newton iteration  22energy =              nan<A u 22 , A u 22 >_{-1}^0.5 =  nan
Newton iteration  23energy =              nan<A u 23 , A u 23 >_{-1}^0.5 =  nan
Newton iteration  24energy =              nan<A u 24 , A u 24 >_{-1}^0.5 =  nan
loadstep 20
Newton iteration   0energy =              nan<A u 0 , A u 0 >_{-1}^0.5 =  nan
Newton iteration   1energy =              nan<A u 1 , A u 1 >_{-1}^0.5 =  nan
Newton iteration   2energy =              nan<A u 2 , A u 2 >_{-1}^0.5 =  nan
Newton iteration   3energy =              nan<A u 3 , A u 3 >_{-1}^0.5 =  nan
Newton iteration   4energy =              nan<A u 4 , A u 4 >_{-1}^0.5 =  nan
Newton iteration   5energy =              nan<A u 5 , A u 5 >_{-1}^0.5 =  nan
Newton iteration   6energy =              nan<A u 6 , A u 6 >_{-1}^0.5 =  nan
Newton iteration   7energy =              nan<A u 7 , A u 7 >_{-1}^0.5 =  nan
Newton iteration   8energy =              nan<A u 8 , A u 8 >_{-1}^0.5 =  nan
Newton iteration   9energy =              nan<A u 9 , A u 9 >_{-1}^0.5 =  nan
Newton iteration  10energy =              nan<A u 10 , A u 10 >_{-1}^0.5 =  nan
Newton iteration  11energy =              nan<A u 11 , A u 11 >_{-1}^0.5 =  nan
Newton iteration  12energy =              nan<A u 12 , A u 12 >_{-1}^0.5 =  nan
Newton iteration  13energy =              nan<A u 13 , A u 13 >_{-1}^0.5 =  nan
Newton iteration  14energy =              nan<A u 14 , A u 14 >_{-1}^0.5 =  nan
Newton iteration  15energy =              nan<A u 15 , A u 15 >_{-1}^0.5 =  nan
Newton iteration  16energy =              nan<A u 16 , A u 16 >_{-1}^0.5 =  nan
Newton iteration  17energy =              nan<A u 17 , A u 17 >_{-1}^0.5 =  nan
Newton iteration  18energy =              nan<A u 18 , A u 18 >_{-1}^0.5 =  nan
Newton iteration  19energy =              nan<A u 19 , A u 19 >_{-1}^0.5 =  nan
Newton iteration  20energy =              nan<A u 20 , A u 20 >_{-1}^0.5 =  nan
Newton iteration  21energy =              nan<A u 21 , A u 21 >_{-1}^0.5 =  nan
Newton iteration  22energy =              nan<A u 22 , A u 22 >_{-1}^0.5 =  nan
Newton iteration  23energy =              nan<A u 23 , A u 23 >_{-1}^0.5 =  nan
Newton iteration  24energy =              nan<A u 24 , A u 24 >_{-1}^0.5 =  nan
loadstep 21
Newton iteration   0energy =              nan<A u 0 , A u 0 >_{-1}^0.5 =  nan
Newton iteration   1energy =              nan<A u 1 , A u 1 >_{-1}^0.5 =  nan
Newton iteration   2energy =              nan<A u 2 , A u 2 >_{-1}^0.5 =  nan
Newton iteration   3energy =              nan<A u 3 , A u 3 >_{-1}^0.5 =  nan
Newton iteration   4energy =              nan<A u 4 , A u 4 >_{-1}^0.5 =  nan
Newton iteration   5energy =              nan<A u 5 , A u 5 >_{-1}^0.5 =  nan
Newton iteration   6energy =              nan<A u 6 , A u 6 >_{-1}^0.5 =  nan
Newton iteration   7energy =              nan<A u 7 , A u 7 >_{-1}^0.5 =  nan
Newton iteration   8energy =              nan<A u 8 , A u 8 >_{-1}^0.5 =  nan
Newton iteration   9energy =              nan<A u 9 , A u 9 >_{-1}^0.5 =  nan
Newton iteration  10energy =              nan<A u 10 , A u 10 >_{-1}^0.5 =  nan
Newton iteration  11energy =              nan<A u 11 , A u 11 >_{-1}^0.5 =  nan
Newton iteration  12energy =              nan<A u 12 , A u 12 >_{-1}^0.5 =  nan
Newton iteration  13energy =              nan<A u 13 , A u 13 >_{-1}^0.5 =  nan
Newton iteration  14energy =              nan<A u 14 , A u 14 >_{-1}^0.5 =  nan
Newton iteration  15energy =              nan<A u 15 , A u 15 >_{-1}^0.5 =  nan
Newton iteration  16energy =              nan<A u 16 , A u 16 >_{-1}^0.5 =  nan
Newton iteration  17energy =              nan<A u 17 , A u 17 >_{-1}^0.5 =  nan
Newton iteration  18energy =              nan<A u 18 , A u 18 >_{-1}^0.5 =  nan
Newton iteration  19energy =              nan<A u 19 , A u 19 >_{-1}^0.5 =  nan
Newton iteration  20energy =              nan<A u 20 , A u 20 >_{-1}^0.5 =  nan
Newton iteration  21energy =              nan<A u 21 , A u 21 >_{-1}^0.5 =  nan
Newton iteration  22energy =              nan<A u 22 , A u 22 >_{-1}^0.5 =  nan
Newton iteration  23energy =              nan<A u 23 , A u 23 >_{-1}^0.5 =  nan
Newton iteration  24energy =              nan<A u 24 , A u 24 >_{-1}^0.5 =  nan
loadstep 22
Newton iteration   0energy =              nan<A u 0 , A u 0 >_{-1}^0.5 =  nan
Newton iteration   1energy =              nan<A u 1 , A u 1 >_{-1}^0.5 =  nan
Newton iteration   2energy =              nan<A u 2 , A u 2 >_{-1}^0.5 =  nan
Newton iteration   3energy =              nan<A u 3 , A u 3 >_{-1}^0.5 =  nan
Newton iteration   4energy =              nan<A u 4 , A u 4 >_{-1}^0.5 =  nan
Newton iteration   5energy =              nan<A u 5 , A u 5 >_{-1}^0.5 =  nan
Newton iteration   6energy =              nan<A u 6 , A u 6 >_{-1}^0.5 =  nan
Newton iteration   7energy =              nan<A u 7 , A u 7 >_{-1}^0.5 =  nan
Newton iteration   8energy =              nan<A u 8 , A u 8 >_{-1}^0.5 =  nan
Newton iteration   9energy =              nan<A u 9 , A u 9 >_{-1}^0.5 =  nan
Newton iteration  10energy =              nan<A u 10 , A u 10 >_{-1}^0.5 =  nan
Newton iteration  11energy =              nan<A u 11 , A u 11 >_{-1}^0.5 =  nan
Newton iteration  12energy =              nan<A u 12 , A u 12 >_{-1}^0.5 =  nan
Newton iteration  13energy =              nan<A u 13 , A u 13 >_{-1}^0.5 =  nan
Newton iteration  14energy =              nan<A u 14 , A u 14 >_{-1}^0.5 =  nan
Newton iteration  15energy =              nan<A u 15 , A u 15 >_{-1}^0.5 =  nan
Newton iteration  16energy =              nan<A u 16 , A u 16 >_{-1}^0.5 =  nan
Newton iteration  17energy =              nan<A u 17 , A u 17 >_{-1}^0.5 =  nan
Newton iteration  18energy =              nan<A u 18 , A u 18 >_{-1}^0.5 =  nan
Newton iteration  19energy =              nan<A u 19 , A u 19 >_{-1}^0.5 =  nan
Newton iteration  20energy =              nan<A u 20 , A u 20 >_{-1}^0.5 =  nan
Newton iteration  21energy =              nan<A u 21 , A u 21 >_{-1}^0.5 =  nan
Newton iteration  22energy =              nan<A u 22 , A u 22 >_{-1}^0.5 =  nan
Newton iteration  23energy =              nan<A u 23 , A u 23 >_{-1}^0.5 =  nan
Newton iteration  24energy =              nan<A u 24 , A u 24 >_{-1}^0.5 =  nan
loadstep 23
Newton iteration   0energy =              nan<A u 0 , A u 0 >_{-1}^0.5 =  nan
Newton iteration   1energy =              nan<A u 1 , A u 1 >_{-1}^0.5 =  nan
Newton iteration   2energy =              nan<A u 2 , A u 2 >_{-1}^0.5 =  nan
Newton iteration   3energy =              nan<A u 3 , A u 3 >_{-1}^0.5 =  nan
Newton iteration   4energy =              nan<A u 4 , A u 4 >_{-1}^0.5 =  nan
Newton iteration   5energy =              nan<A u 5 , A u 5 >_{-1}^0.5 =  nan
Newton iteration   6energy =              nan<A u 6 , A u 6 >_{-1}^0.5 =  nan
Newton iteration   7energy =              nan<A u 7 , A u 7 >_{-1}^0.5 =  nan
Newton iteration   8energy =              nan<A u 8 , A u 8 >_{-1}^0.5 =  nan
Newton iteration   9energy =              nan<A u 9 , A u 9 >_{-1}^0.5 =  nan
Newton iteration  10energy =              nan<A u 10 , A u 10 >_{-1}^0.5 =  nan
Newton iteration  11energy =              nan<A u 11 , A u 11 >_{-1}^0.5 =  nan
Newton iteration  12energy =              nan<A u 12 , A u 12 >_{-1}^0.5 =  nan
Newton iteration  13energy =              nan<A u 13 , A u 13 >_{-1}^0.5 =  nan
Newton iteration  14energy =              nan<A u 14 , A u 14 >_{-1}^0.5 =  nan
Newton iteration  15energy =              nan<A u 15 , A u 15 >_{-1}^0.5 =  nan
Newton iteration  16energy =              nan<A u 16 , A u 16 >_{-1}^0.5 =  nan
Newton iteration  17energy =              nan<A u 17 , A u 17 >_{-1}^0.5 =  nan
Newton iteration  18energy =              nan<A u 18 , A u 18 >_{-1}^0.5 =  nan
Newton iteration  19energy =              nan<A u 19 , A u 19 >_{-1}^0.5 =  nan
Newton iteration  20energy =              nan<A u 20 , A u 20 >_{-1}^0.5 =  nan
Newton iteration  21energy =              nan<A u 21 , A u 21 >_{-1}^0.5 =  nan
Newton iteration  22energy =              nan<A u 22 , A u 22 >_{-1}^0.5 =  nan
Newton iteration  23energy =              nan<A u 23 , A u 23 >_{-1}^0.5 =  nan
Newton iteration  24energy =              nan<A u 24 , A u 24 >_{-1}^0.5 =  nan
loadstep 24
Newton iteration   0energy =              nan<A u 0 , A u 0 >_{-1}^0.5 =  nan
Newton iteration   1energy =              nan<A u 1 , A u 1 >_{-1}^0.5 =  nan
Newton iteration   2energy =              nan<A u 2 , A u 2 >_{-1}^0.5 =  nan
Newton iteration   3energy =              nan<A u 3 , A u 3 >_{-1}^0.5 =  nan
Newton iteration   4energy =              nan<A u 4 , A u 4 >_{-1}^0.5 =  nan
Newton iteration   5energy =              nan<A u 5 , A u 5 >_{-1}^0.5 =  nan
Newton iteration   6energy =              nan<A u 6 , A u 6 >_{-1}^0.5 =  nan
Newton iteration   7energy =              nan<A u 7 , A u 7 >_{-1}^0.5 =  nan
Newton iteration   8energy =              nan<A u 8 , A u 8 >_{-1}^0.5 =  nan
Newton iteration   9energy =              nan<A u 9 , A u 9 >_{-1}^0.5 =  nan
Newton iteration  10energy =              nan<A u 10 , A u 10 >_{-1}^0.5 =  nan
Newton iteration  11energy =              nan<A u 11 , A u 11 >_{-1}^0.5 =  nan
Newton iteration  12energy =              nan<A u 12 , A u 12 >_{-1}^0.5 =  nan
Newton iteration  13energy =              nan<A u 13 , A u 13 >_{-1}^0.5 =  nan
Newton iteration  14energy =              nan<A u 14 , A u 14 >_{-1}^0.5 =  nan
Newton iteration  15energy =              nan<A u 15 , A u 15 >_{-1}^0.5 =  nan
Newton iteration  16energy =              nan<A u 16 , A u 16 >_{-1}^0.5 =  nan
Newton iteration  17energy =              nan<A u 17 , A u 17 >_{-1}^0.5 =  nan
Newton iteration  18energy =              nan<A u 18 , A u 18 >_{-1}^0.5 =  nan
Newton iteration  19energy =              nan<A u 19 , A u 19 >_{-1}^0.5 =  nan
Newton iteration  20energy =              nan<A u 20 , A u 20 >_{-1}^0.5 =  nan
Newton iteration  21energy =              nan<A u 21 , A u 21 >_{-1}^0.5 =  nan
Newton iteration  22energy =              nan<A u 22 , A u 22 >_{-1}^0.5 =  nan
Newton iteration  23energy =              nan<A u 23 , A u 23 >_{-1}^0.5 =  nan
Newton iteration  24energy =              nan<A u 24 , A u 24 >_{-1}^0.5 =  nan
loadstep 25
Newton iteration   0energy =              nan<A u 0 , A u 0 >_{-1}^0.5 =  nan
Newton iteration   1energy =              nan<A u 1 , A u 1 >_{-1}^0.5 =  nan
Newton iteration   2energy =              nan<A u 2 , A u 2 >_{-1}^0.5 =  nan
Newton iteration   3energy =              nan<A u 3 , A u 3 >_{-1}^0.5 =  nan
Newton iteration   4energy =              nan<A u 4 , A u 4 >_{-1}^0.5 =  nan
Newton iteration   5energy =              nan<A u 5 , A u 5 >_{-1}^0.5 =  nan
Newton iteration   6energy =              nan<A u 6 , A u 6 >_{-1}^0.5 =  nan
Newton iteration   7energy =              nan<A u 7 , A u 7 >_{-1}^0.5 =  nan
Newton iteration   8energy =              nan<A u 8 , A u 8 >_{-1}^0.5 =  nan
Newton iteration   9energy =              nan<A u 9 , A u 9 >_{-1}^0.5 =  nan
Newton iteration  10energy =              nan<A u 10 , A u 10 >_{-1}^0.5 =  nan
Newton iteration  11energy =              nan<A u 11 , A u 11 >_{-1}^0.5 =  nan
Newton iteration  12energy =              nan<A u 12 , A u 12 >_{-1}^0.5 =  nan
Newton iteration  13energy =              nan<A u 13 , A u 13 >_{-1}^0.5 =  nan
Newton iteration  14energy =              nan<A u 14 , A u 14 >_{-1}^0.5 =  nan
Newton iteration  15energy =              nan<A u 15 , A u 15 >_{-1}^0.5 =  nan
Newton iteration  16energy =              nan<A u 16 , A u 16 >_{-1}^0.5 =  nan
Newton iteration  17energy =              nan<A u 17 , A u 17 >_{-1}^0.5 =  nan
Newton iteration  18energy =              nan<A u 18 , A u 18 >_{-1}^0.5 =  nan
Newton iteration  19energy =              nan<A u 19 , A u 19 >_{-1}^0.5 =  nan
Newton iteration  20energy =              nan<A u 20 , A u 20 >_{-1}^0.5 =  nan
Newton iteration  21energy =              nan<A u 21 , A u 21 >_{-1}^0.5 =  nan
Newton iteration  22energy =              nan<A u 22 , A u 22 >_{-1}^0.5 =  nan
Newton iteration  23energy =              nan<A u 23 , A u 23 >_{-1}^0.5 =  nan
Newton iteration  24energy =              nan<A u 24 , A u 24 >_{-1}^0.5 =  nan
loadstep 26
Newton iteration   0energy =              nan<A u 0 , A u 0 >_{-1}^0.5 =  nan
Newton iteration   1energy =              nan<A u 1 , A u 1 >_{-1}^0.5 =  nan
Newton iteration   2energy =              nan<A u 2 , A u 2 >_{-1}^0.5 =  nan
Newton iteration   3energy =              nan<A u 3 , A u 3 >_{-1}^0.5 =  nan
Newton iteration   4energy =              nan<A u 4 , A u 4 >_{-1}^0.5 =  nan
Newton iteration   5energy =              nan<A u 5 , A u 5 >_{-1}^0.5 =  nan
Newton iteration   6energy =              nan<A u 6 , A u 6 >_{-1}^0.5 =  nan
Newton iteration   7energy =              nan<A u 7 , A u 7 >_{-1}^0.5 =  nan
Newton iteration   8energy =              nan<A u 8 , A u 8 >_{-1}^0.5 =  nan
Newton iteration   9energy =              nan<A u 9 , A u 9 >_{-1}^0.5 =  nan
Newton iteration  10energy =              nan<A u 10 , A u 10 >_{-1}^0.5 =  nan
Newton iteration  11energy =              nan<A u 11 , A u 11 >_{-1}^0.5 =  nan
Newton iteration  12energy =              nan<A u 12 , A u 12 >_{-1}^0.5 =  nan
Newton iteration  13energy =              nan<A u 13 , A u 13 >_{-1}^0.5 =  nan
Newton iteration  14energy =              nan<A u 14 , A u 14 >_{-1}^0.5 =  nan
Newton iteration  15energy =              nan<A u 15 , A u 15 >_{-1}^0.5 =  nan
Newton iteration  16energy =              nan<A u 16 , A u 16 >_{-1}^0.5 =  nan
Newton iteration  17energy =              nan<A u 17 , A u 17 >_{-1}^0.5 =  nan
Newton iteration  18energy =              nan<A u 18 , A u 18 >_{-1}^0.5 =  nan
Newton iteration  19energy =              nan<A u 19 , A u 19 >_{-1}^0.5 =  nan
Newton iteration  20energy =              nan<A u 20 , A u 20 >_{-1}^0.5 =  nan
Newton iteration  21energy =              nan<A u 21 , A u 21 >_{-1}^0.5 =  nan
Newton iteration  22energy =              nan<A u 22 , A u 22 >_{-1}^0.5 =  nan
Newton iteration  23energy =              nan<A u 23 , A u 23 >_{-1}^0.5 =  nan
Newton iteration  24energy =              nan<A u 24 , A u 24 >_{-1}^0.5 =  nan
loadstep 27
Newton iteration   0energy =              nan<A u 0 , A u 0 >_{-1}^0.5 =  nan
Newton iteration   1energy =              nan<A u 1 , A u 1 >_{-1}^0.5 =  nan
Newton iteration   2energy =              nan<A u 2 , A u 2 >_{-1}^0.5 =  nan
Newton iteration   3energy =              nan<A u 3 , A u 3 >_{-1}^0.5 =  nan
Newton iteration   4energy =              nan<A u 4 , A u 4 >_{-1}^0.5 =  nan
Newton iteration   5energy =              nan<A u 5 , A u 5 >_{-1}^0.5 =  nan
Newton iteration   6energy =              nan<A u 6 , A u 6 >_{-1}^0.5 =  nan
Newton iteration   7energy =              nan<A u 7 , A u 7 >_{-1}^0.5 =  nan
Newton iteration   8energy =              nan<A u 8 , A u 8 >_{-1}^0.5 =  nan
Newton iteration   9energy =              nan<A u 9 , A u 9 >_{-1}^0.5 =  nan
Newton iteration  10energy =              nan<A u 10 , A u 10 >_{-1}^0.5 =  nan
Newton iteration  11energy =              nan<A u 11 , A u 11 >_{-1}^0.5 =  nan
Newton iteration  12energy =              nan<A u 12 , A u 12 >_{-1}^0.5 =  nan
Newton iteration  13energy =              nan<A u 13 , A u 13 >_{-1}^0.5 =  nan
Newton iteration  14energy =              nan<A u 14 , A u 14 >_{-1}^0.5 =  nan
Newton iteration  15energy =              nan<A u 15 , A u 15 >_{-1}^0.5 =  nan
Newton iteration  16energy =              nan<A u 16 , A u 16 >_{-1}^0.5 =  nan
Newton iteration  17energy =              nan<A u 17 , A u 17 >_{-1}^0.5 =  nan
Newton iteration  18energy =              nan<A u 18 , A u 18 >_{-1}^0.5 =  nan
Newton iteration  19energy =              nan<A u 19 , A u 19 >_{-1}^0.5 =  nan
Newton iteration  20energy =              nan<A u 20 , A u 20 >_{-1}^0.5 =  nan
Newton iteration  21energy =              nan<A u 21 , A u 21 >_{-1}^0.5 =  nan
Newton iteration  22energy =              nan<A u 22 , A u 22 >_{-1}^0.5 =  nan
Newton iteration  23energy =              nan<A u 23 , A u 23 >_{-1}^0.5 =  nan
Newton iteration  24energy =              nan<A u 24 , A u 24 >_{-1}^0.5 =  nan
loadstep 28
Newton iteration   0energy =              nan<A u 0 , A u 0 >_{-1}^0.5 =  nan
Newton iteration   1energy =              nan<A u 1 , A u 1 >_{-1}^0.5 =  nan
Newton iteration   2energy =              nan<A u 2 , A u 2 >_{-1}^0.5 =  nan
Newton iteration   3energy =              nan<A u 3 , A u 3 >_{-1}^0.5 =  nan
Newton iteration   4energy =              nan<A u 4 , A u 4 >_{-1}^0.5 =  nan
Newton iteration   5energy =              nan<A u 5 , A u 5 >_{-1}^0.5 =  nan
Newton iteration   6energy =              nan<A u 6 , A u 6 >_{-1}^0.5 =  nan
Newton iteration   7energy =              nan<A u 7 , A u 7 >_{-1}^0.5 =  nan
Newton iteration   8energy =              nan<A u 8 , A u 8 >_{-1}^0.5 =  nan
Newton iteration   9energy =              nan<A u 9 , A u 9 >_{-1}^0.5 =  nan
Newton iteration  10energy =              nan<A u 10 , A u 10 >_{-1}^0.5 =  nan
Newton iteration  11energy =              nan<A u 11 , A u 11 >_{-1}^0.5 =  nan
Newton iteration  12energy =              nan<A u 12 , A u 12 >_{-1}^0.5 =  nan
Newton iteration  13energy =              nan<A u 13 , A u 13 >_{-1}^0.5 =  nan
Newton iteration  14energy =              nan<A u 14 , A u 14 >_{-1}^0.5 =  nan
Newton iteration  15energy =              nan<A u 15 , A u 15 >_{-1}^0.5 =  nan
Newton iteration  16energy =              nan<A u 16 , A u 16 >_{-1}^0.5 =  nan
Newton iteration  17energy =              nan<A u 17 , A u 17 >_{-1}^0.5 =  nan
Newton iteration  18energy =              nan<A u 18 , A u 18 >_{-1}^0.5 =  nan
Newton iteration  19energy =              nan<A u 19 , A u 19 >_{-1}^0.5 =  nan
Newton iteration  20energy =              nan<A u 20 , A u 20 >_{-1}^0.5 =  nan
Newton iteration  21energy =              nan<A u 21 , A u 21 >_{-1}^0.5 =  nan
Newton iteration  22energy =              nan<A u 22 , A u 22 >_{-1}^0.5 =  nan
Newton iteration  23energy =              nan<A u 23 , A u 23 >_{-1}^0.5 =  nan
Newton iteration  24energy =              nan<A u 24 , A u 24 >_{-1}^0.5 =  nan
loadstep 29
Newton iteration   0energy =              nan<A u 0 , A u 0 >_{-1}^0.5 =  nan
Newton iteration   1energy =              nan<A u 1 , A u 1 >_{-1}^0.5 =  nan
Newton iteration   2energy =              nan<A u 2 , A u 2 >_{-1}^0.5 =  nan
Newton iteration   3energy =              nan<A u 3 , A u 3 >_{-1}^0.5 =  nan
Newton iteration   4energy =              nan<A u 4 , A u 4 >_{-1}^0.5 =  nan
Newton iteration   5energy =              nan<A u 5 , A u 5 >_{-1}^0.5 =  nan
Newton iteration   6energy =              nan<A u 6 , A u 6 >_{-1}^0.5 =  nan
Newton iteration   7energy =              nan<A u 7 , A u 7 >_{-1}^0.5 =  nan
Newton iteration   8energy =              nan<A u 8 , A u 8 >_{-1}^0.5 =  nan
Newton iteration   9energy =              nan<A u 9 , A u 9 >_{-1}^0.5 =  nan
Newton iteration  10energy =              nan<A u 10 , A u 10 >_{-1}^0.5 =  nan
Newton iteration  11energy =              nan<A u 11 , A u 11 >_{-1}^0.5 =  nan
Newton iteration  12energy =              nan<A u 12 , A u 12 >_{-1}^0.5 =  nan
Newton iteration  13energy =              nan<A u 13 , A u 13 >_{-1}^0.5 =  nan
Newton iteration  14energy =              nan<A u 14 , A u 14 >_{-1}^0.5 =  nan
Newton iteration  15energy =              nan<A u 15 , A u 15 >_{-1}^0.5 =  nan
Newton iteration  16energy =              nan<A u 16 , A u 16 >_{-1}^0.5 =  nan
Newton iteration  17energy =              nan<A u 17 , A u 17 >_{-1}^0.5 =  nan
Newton iteration  18energy =              nan<A u 18 , A u 18 >_{-1}^0.5 =  nan
Newton iteration  19energy =              nan<A u 19 , A u 19 >_{-1}^0.5 =  nan
Newton iteration  20energy =              nan<A u 20 , A u 20 >_{-1}^0.5 =  nan
Newton iteration  21energy =              nan<A u 21 , A u 21 >_{-1}^0.5 =  nan
Newton iteration  22energy =              nan<A u 22 , A u 22 >_{-1}^0.5 =  nan
Newton iteration  23energy =              nan<A u 23 , A u 23 >_{-1}^0.5 =  nan
Newton iteration  24energy =              nan<A u 24 , A u 24 >_{-1}^0.5 =  nan
loadstep 30
Newton iteration   0energy =              nan<A u 0 , A u 0 >_{-1}^0.5 =  nan
Newton iteration   1energy =              nan<A u 1 , A u 1 >_{-1}^0.5 =  nan
Newton iteration   2energy =              nan<A u 2 , A u 2 >_{-1}^0.5 =  nan
Newton iteration   3energy =              nan<A u 3 , A u 3 >_{-1}^0.5 =  nan
Newton iteration   4energy =              nan<A u 4 , A u 4 >_{-1}^0.5 =  nan
Newton iteration   5energy =              nan<A u 5 , A u 5 >_{-1}^0.5 =  nan
Newton iteration   6energy =              nan<A u 6 , A u 6 >_{-1}^0.5 =  nan
Newton iteration   7energy =              nan<A u 7 , A u 7 >_{-1}^0.5 =  nan
Newton iteration   8energy =              nan<A u 8 , A u 8 >_{-1}^0.5 =  nan
Newton iteration   9energy =              nan<A u 9 , A u 9 >_{-1}^0.5 =  nan
Newton iteration  10energy =              nan<A u 10 , A u 10 >_{-1}^0.5 =  nan
Newton iteration  11energy =              nan<A u 11 , A u 11 >_{-1}^0.5 =  nan
Newton iteration  12energy =              nan<A u 12 , A u 12 >_{-1}^0.5 =  nan
Newton iteration  13energy =              nan<A u 13 , A u 13 >_{-1}^0.5 =  nan
Newton iteration  14energy =              nan<A u 14 , A u 14 >_{-1}^0.5 =  nan
Newton iteration  15energy =              nan<A u 15 , A u 15 >_{-1}^0.5 =  nan
Newton iteration  16energy =              nan<A u 16 , A u 16 >_{-1}^0.5 =  nan
Newton iteration  17energy =              nan<A u 17 , A u 17 >_{-1}^0.5 =  nan
Newton iteration  18energy =              nan<A u 18 , A u 18 >_{-1}^0.5 =  nan
Newton iteration  19energy =              nan<A u 19 , A u 19 >_{-1}^0.5 =  nan
Newton iteration  20energy =              nan<A u 20 , A u 20 >_{-1}^0.5 =  nan
Newton iteration  21energy =              nan<A u 21 , A u 21 >_{-1}^0.5 =  nan
Newton iteration  22energy =              nan<A u 22 , A u 22 >_{-1}^0.5 =  nan
Newton iteration  23energy =              nan<A u 23 , A u 23 >_{-1}^0.5 =  nan
Newton iteration  24energy =              nan<A u 24 , A u 24 >_{-1}^0.5 =  nan
loadstep 31
Newton iteration   0energy =              nan<A u 0 , A u 0 >_{-1}^0.5 =  nan
Newton iteration   1energy =              nan<A u 1 , A u 1 >_{-1}^0.5 =  nan
Newton iteration   2energy =              nan<A u 2 , A u 2 >_{-1}^0.5 =  nan
Newton iteration   3energy =              nan<A u 3 , A u 3 >_{-1}^0.5 =  nan
Newton iteration   4energy =              nan<A u 4 , A u 4 >_{-1}^0.5 =  nan
Newton iteration   5energy =              nan<A u 5 , A u 5 >_{-1}^0.5 =  nan
Newton iteration   6energy =              nan<A u 6 , A u 6 >_{-1}^0.5 =  nan
Newton iteration   7energy =              nan<A u 7 , A u 7 >_{-1}^0.5 =  nan
Newton iteration   8energy =              nan<A u 8 , A u 8 >_{-1}^0.5 =  nan
Newton iteration   9energy =              nan<A u 9 , A u 9 >_{-1}^0.5 =  nan
Newton iteration  10energy =              nan<A u 10 , A u 10 >_{-1}^0.5 =  nan
Newton iteration  11energy =              nan<A u 11 , A u 11 >_{-1}^0.5 =  nan
Newton iteration  12energy =              nan<A u 12 , A u 12 >_{-1}^0.5 =  nan
Newton iteration  13energy =              nan<A u 13 , A u 13 >_{-1}^0.5 =  nan
Newton iteration  14energy =              nan<A u 14 , A u 14 >_{-1}^0.5 =  nan
Newton iteration  15energy =              nan<A u 15 , A u 15 >_{-1}^0.5 =  nan
Newton iteration  16energy =              nan<A u 16 , A u 16 >_{-1}^0.5 =  nan
Newton iteration  17energy =              nan<A u 17 , A u 17 >_{-1}^0.5 =  nan
Newton iteration  18energy =              nan<A u 18 , A u 18 >_{-1}^0.5 =  nan
Newton iteration  19energy =              nan<A u 19 , A u 19 >_{-1}^0.5 =  nan
Newton iteration  20energy =              nan<A u 20 , A u 20 >_{-1}^0.5 =  nan
Newton iteration  21energy =              nan<A u 21 , A u 21 >_{-1}^0.5 =  nan
Newton iteration  22energy =              nan<A u 22 , A u 22 >_{-1}^0.5 =  nan
Newton iteration  23energy =              nan<A u 23 , A u 23 >_{-1}^0.5 =  nan
Newton iteration  24energy =              nan<A u 24 , A u 24 >_{-1}^0.5 =  nan
loadstep 32
Newton iteration   0energy =              nan<A u 0 , A u 0 >_{-1}^0.5 =  nan
Newton iteration   1energy =              nan<A u 1 , A u 1 >_{-1}^0.5 =  nan
Newton iteration   2energy =              nan<A u 2 , A u 2 >_{-1}^0.5 =  nan
Newton iteration   3energy =              nan<A u 3 , A u 3 >_{-1}^0.5 =  nan
Newton iteration   4energy =              nan<A u 4 , A u 4 >_{-1}^0.5 =  nan
Newton iteration   5energy =              nan<A u 5 , A u 5 >_{-1}^0.5 =  nan
Newton iteration   6energy =              nan<A u 6 , A u 6 >_{-1}^0.5 =  nan
Newton iteration   7energy =              nan<A u 7 , A u 7 >_{-1}^0.5 =  nan
Newton iteration   8energy =              nan<A u 8 , A u 8 >_{-1}^0.5 =  nan
Newton iteration   9energy =              nan<A u 9 , A u 9 >_{-1}^0.5 =  nan
Newton iteration  10energy =              nan<A u 10 , A u 10 >_{-1}^0.5 =  nan
Newton iteration  11energy =              nan<A u 11 , A u 11 >_{-1}^0.5 =  nan
Newton iteration  12energy =              nan<A u 12 , A u 12 >_{-1}^0.5 =  nan
Newton iteration  13energy =              nan<A u 13 , A u 13 >_{-1}^0.5 =  nan
Newton iteration  14energy =              nan<A u 14 , A u 14 >_{-1}^0.5 =  nan
Newton iteration  15energy =              nan<A u 15 , A u 15 >_{-1}^0.5 =  nan
Newton iteration  16energy =              nan<A u 16 , A u 16 >_{-1}^0.5 =  nan
Newton iteration  17energy =              nan<A u 17 , A u 17 >_{-1}^0.5 =  nan
Newton iteration  18energy =              nan<A u 18 , A u 18 >_{-1}^0.5 =  nan
Newton iteration  19energy =              nan<A u 19 , A u 19 >_{-1}^0.5 =  nan
Newton iteration  20energy =              nan<A u 20 , A u 20 >_{-1}^0.5 =  nan
Newton iteration  21energy =              nan<A u 21 , A u 21 >_{-1}^0.5 =  nan
Newton iteration  22energy =              nan<A u 22 , A u 22 >_{-1}^0.5 =  nan
Newton iteration  23energy =              nan<A u 23 , A u 23 >_{-1}^0.5 =  nan
Newton iteration  24energy =              nan<A u 24 , A u 24 >_{-1}^0.5 =  nan
loadstep 33
Newton iteration   0energy =              nan<A u 0 , A u 0 >_{-1}^0.5 =  nan
Newton iteration   1energy =              nan<A u 1 , A u 1 >_{-1}^0.5 =  nan
Newton iteration   2energy =              nan<A u 2 , A u 2 >_{-1}^0.5 =  nan
Newton iteration   3energy =              nan<A u 3 , A u 3 >_{-1}^0.5 =  nan
Newton iteration   4energy =              nan<A u 4 , A u 4 >_{-1}^0.5 =  nan
Newton iteration   5energy =              nan<A u 5 , A u 5 >_{-1}^0.5 =  nan
Newton iteration   6energy =              nan<A u 6 , A u 6 >_{-1}^0.5 =  nan
Newton iteration   7energy =              nan<A u 7 , A u 7 >_{-1}^0.5 =  nan
Newton iteration   8energy =              nan<A u 8 , A u 8 >_{-1}^0.5 =  nan
Newton iteration   9energy =              nan<A u 9 , A u 9 >_{-1}^0.5 =  nan
Newton iteration  10energy =              nan<A u 10 , A u 10 >_{-1}^0.5 =  nan
Newton iteration  11energy =              nan<A u 11 , A u 11 >_{-1}^0.5 =  nan
Newton iteration  12energy =              nan<A u 12 , A u 12 >_{-1}^0.5 =  nan
Newton iteration  13energy =              nan<A u 13 , A u 13 >_{-1}^0.5 =  nan
Newton iteration  14energy =              nan<A u 14 , A u 14 >_{-1}^0.5 =  nan
Newton iteration  15energy =              nan<A u 15 , A u 15 >_{-1}^0.5 =  nan
Newton iteration  16energy =              nan<A u 16 , A u 16 >_{-1}^0.5 =  nan
Newton iteration  17energy =              nan<A u 17 , A u 17 >_{-1}^0.5 =  nan
Newton iteration  18energy =              nan<A u 18 , A u 18 >_{-1}^0.5 =  nan
Newton iteration  19energy =              nan<A u 19 , A u 19 >_{-1}^0.5 =  nan
Newton iteration  20energy =              nan<A u 20 , A u 20 >_{-1}^0.5 =  nan
Newton iteration  21energy =              nan<A u 21 , A u 21 >_{-1}^0.5 =  nan
Newton iteration  22energy =              nan<A u 22 , A u 22 >_{-1}^0.5 =  nan
Newton iteration  23energy =              nan<A u 23 , A u 23 >_{-1}^0.5 =  nan
Newton iteration  24energy =              nan<A u 24 , A u 24 >_{-1}^0.5 =  nan
loadstep 34
Newton iteration   0energy =              nan<A u 0 , A u 0 >_{-1}^0.5 =  nan
Newton iteration   1energy =              nan<A u 1 , A u 1 >_{-1}^0.5 =  nan
Newton iteration   2energy =              nan<A u 2 , A u 2 >_{-1}^0.5 =  nan
Newton iteration   3energy =              nan<A u 3 , A u 3 >_{-1}^0.5 =  nan
Newton iteration   4energy =              nan<A u 4 , A u 4 >_{-1}^0.5 =  nan
Newton iteration   5energy =              nan<A u 5 , A u 5 >_{-1}^0.5 =  nan
Newton iteration   6energy =              nan<A u 6 , A u 6 >_{-1}^0.5 =  nan
Newton iteration   7energy =              nan<A u 7 , A u 7 >_{-1}^0.5 =  nan
Newton iteration   8energy =              nan<A u 8 , A u 8 >_{-1}^0.5 =  nan
Newton iteration   9energy =              nan<A u 9 , A u 9 >_{-1}^0.5 =  nan
Newton iteration  10energy =              nan<A u 10 , A u 10 >_{-1}^0.5 =  nan
Newton iteration  11energy =              nan<A u 11 , A u 11 >_{-1}^0.5 =  nan
Newton iteration  12energy =              nan<A u 12 , A u 12 >_{-1}^0.5 =  nan
Newton iteration  13energy =              nan<A u 13 , A u 13 >_{-1}^0.5 =  nan
Newton iteration  14energy =              nan<A u 14 , A u 14 >_{-1}^0.5 =  nan
Newton iteration  15energy =              nan<A u 15 , A u 15 >_{-1}^0.5 =  nan
Newton iteration  16energy =              nan<A u 16 , A u 16 >_{-1}^0.5 =  nan
Newton iteration  17energy =              nan<A u 17 , A u 17 >_{-1}^0.5 =  nan
Newton iteration  18energy =              nan<A u 18 , A u 18 >_{-1}^0.5 =  nan
Newton iteration  19energy =              nan<A u 19 , A u 19 >_{-1}^0.5 =  nan
Newton iteration  20energy =              nan<A u 20 , A u 20 >_{-1}^0.5 =  nan
Newton iteration  21energy =              nan<A u 21 , A u 21 >_{-1}^0.5 =  nan
Newton iteration  22energy =              nan<A u 22 , A u 22 >_{-1}^0.5 =  nan
Newton iteration  23energy =              nan<A u 23 , A u 23 >_{-1}^0.5 =  nan
Newton iteration  24energy =              nan<A u 24 , A u 24 >_{-1}^0.5 =  nan
loadstep 35
Newton iteration   0energy =              nan<A u 0 , A u 0 >_{-1}^0.5 =  nan
Newton iteration   1energy =              nan<A u 1 , A u 1 >_{-1}^0.5 =  nan
Newton iteration   2energy =              nan<A u 2 , A u 2 >_{-1}^0.5 =  nan
Newton iteration   3energy =              nan<A u 3 , A u 3 >_{-1}^0.5 =  nan
Newton iteration   4energy =              nan<A u 4 , A u 4 >_{-1}^0.5 =  nan
Newton iteration   5energy =              nan<A u 5 , A u 5 >_{-1}^0.5 =  nan
Newton iteration   6energy =              nan<A u 6 , A u 6 >_{-1}^0.5 =  nan
Newton iteration   7energy =              nan<A u 7 , A u 7 >_{-1}^0.5 =  nan
Newton iteration   8energy =              nan<A u 8 , A u 8 >_{-1}^0.5 =  nan
Newton iteration   9energy =              nan<A u 9 , A u 9 >_{-1}^0.5 =  nan
Newton iteration  10energy =              nan<A u 10 , A u 10 >_{-1}^0.5 =  nan
Newton iteration  11energy =              nan<A u 11 , A u 11 >_{-1}^0.5 =  nan
Newton iteration  12energy =              nan<A u 12 , A u 12 >_{-1}^0.5 =  nan
Newton iteration  13energy =              nan<A u 13 , A u 13 >_{-1}^0.5 =  nan
Newton iteration  14energy =              nan<A u 14 , A u 14 >_{-1}^0.5 =  nan
Newton iteration  15energy =              nan<A u 15 , A u 15 >_{-1}^0.5 =  nan
Newton iteration  16energy =              nan<A u 16 , A u 16 >_{-1}^0.5 =  nan
Newton iteration  17energy =              nan<A u 17 , A u 17 >_{-1}^0.5 =  nan
Newton iteration  18energy =              nan<A u 18 , A u 18 >_{-1}^0.5 =  nan
Newton iteration  19energy =              nan<A u 19 , A u 19 >_{-1}^0.5 =  nan
Newton iteration  20energy =              nan<A u 20 , A u 20 >_{-1}^0.5 =  nan
Newton iteration  21energy =              nan<A u 21 , A u 21 >_{-1}^0.5 =  nan
Newton iteration  22energy =              nan<A u 22 , A u 22 >_{-1}^0.5 =  nan
Newton iteration  23energy =              nan<A u 23 , A u 23 >_{-1}^0.5 =  nan
Newton iteration  24energy =              nan<A u 24 , A u 24 >_{-1}^0.5 =  nan
loadstep 36
Newton iteration   0energy =              nan<A u 0 , A u 0 >_{-1}^0.5 =  nan
Newton iteration   1energy =              nan<A u 1 , A u 1 >_{-1}^0.5 =  nan
Newton iteration   2energy =              nan<A u 2 , A u 2 >_{-1}^0.5 =  nan
Newton iteration   3energy =              nan<A u 3 , A u 3 >_{-1}^0.5 =  nan
Newton iteration   4energy =              nan<A u 4 , A u 4 >_{-1}^0.5 =  nan
Newton iteration   5energy =              nan<A u 5 , A u 5 >_{-1}^0.5 =  nan
Newton iteration   6energy =              nan<A u 6 , A u 6 >_{-1}^0.5 =  nan
Newton iteration   7energy =              nan<A u 7 , A u 7 >_{-1}^0.5 =  nan
Newton iteration   8energy =              nan<A u 8 , A u 8 >_{-1}^0.5 =  nan
Newton iteration   9energy =              nan<A u 9 , A u 9 >_{-1}^0.5 =  nan
Newton iteration  10energy =              nan<A u 10 , A u 10 >_{-1}^0.5 =  nan
Newton iteration  11energy =              nan<A u 11 , A u 11 >_{-1}^0.5 =  nan
Newton iteration  12energy =              nan<A u 12 , A u 12 >_{-1}^0.5 =  nan
Newton iteration  13energy =              nan<A u 13 , A u 13 >_{-1}^0.5 =  nan
Newton iteration  14energy =              nan<A u 14 , A u 14 >_{-1}^0.5 =  nan
Newton iteration  15energy =              nan<A u 15 , A u 15 >_{-1}^0.5 =  nan
Newton iteration  16energy =              nan<A u 16 , A u 16 >_{-1}^0.5 =  nan
Newton iteration  17energy =              nan<A u 17 , A u 17 >_{-1}^0.5 =  nan
Newton iteration  18energy =              nan<A u 18 , A u 18 >_{-1}^0.5 =  nan
Newton iteration  19energy =              nan<A u 19 , A u 19 >_{-1}^0.5 =  nan
Newton iteration  20energy =              nan<A u 20 , A u 20 >_{-1}^0.5 =  nan
Newton iteration  21energy =              nan<A u 21 , A u 21 >_{-1}^0.5 =  nan
Newton iteration  22energy =              nan<A u 22 , A u 22 >_{-1}^0.5 =  nan
Newton iteration  23energy =              nan<A u 23 , A u 23 >_{-1}^0.5 =  nan
Newton iteration  24energy =              nan<A u 24 , A u 24 >_{-1}^0.5 =  nan
loadstep 37
Newton iteration   0energy =              nan<A u 0 , A u 0 >_{-1}^0.5 =  nan
Newton iteration   1energy =              nan<A u 1 , A u 1 >_{-1}^0.5 =  nan
Newton iteration   2energy =              nan<A u 2 , A u 2 >_{-1}^0.5 =  nan
Newton iteration   3energy =              nan<A u 3 , A u 3 >_{-1}^0.5 =  nan
Newton iteration   4energy =              nan<A u 4 , A u 4 >_{-1}^0.5 =  nan
Newton iteration   5energy =              nan<A u 5 , A u 5 >_{-1}^0.5 =  nan
Newton iteration   6energy =              nan<A u 6 , A u 6 >_{-1}^0.5 =  nan
Newton iteration   7energy =              nan<A u 7 , A u 7 >_{-1}^0.5 =  nan
Newton iteration   8energy =              nan<A u 8 , A u 8 >_{-1}^0.5 =  nan
Newton iteration   9energy =              nan<A u 9 , A u 9 >_{-1}^0.5 =  nan
Newton iteration  10energy =              nan<A u 10 , A u 10 >_{-1}^0.5 =  nan
Newton iteration  11energy =              nan<A u 11 , A u 11 >_{-1}^0.5 =  nan
Newton iteration  12energy =              nan<A u 12 , A u 12 >_{-1}^0.5 =  nan
Newton iteration  13energy =              nan<A u 13 , A u 13 >_{-1}^0.5 =  nan
Newton iteration  14energy =              nan<A u 14 , A u 14 >_{-1}^0.5 =  nan
Newton iteration  15energy =              nan<A u 15 , A u 15 >_{-1}^0.5 =  nan
Newton iteration  16energy =              nan<A u 16 , A u 16 >_{-1}^0.5 =  nan
Newton iteration  17energy =              nan<A u 17 , A u 17 >_{-1}^0.5 =  nan
Newton iteration  18energy =              nan<A u 18 , A u 18 >_{-1}^0.5 =  nan
Newton iteration  19energy =              nan<A u 19 , A u 19 >_{-1}^0.5 =  nan
Newton iteration  20energy =              nan<A u 20 , A u 20 >_{-1}^0.5 =  nan
Newton iteration  21energy =              nan<A u 21 , A u 21 >_{-1}^0.5 =  nan
Newton iteration  22energy =              nan<A u 22 , A u 22 >_{-1}^0.5 =  nan
Newton iteration  23energy =              nan<A u 23 , A u 23 >_{-1}^0.5 =  nan
Newton iteration  24energy =              nan<A u 24 , A u 24 >_{-1}^0.5 =  nan
loadstep 38
Newton iteration   0energy =              nan<A u 0 , A u 0 >_{-1}^0.5 =  nan
Newton iteration   1energy =              nan<A u 1 , A u 1 >_{-1}^0.5 =  nan
Newton iteration   2energy =              nan<A u 2 , A u 2 >_{-1}^0.5 =  nan
Newton iteration   3energy =              nan<A u 3 , A u 3 >_{-1}^0.5 =  nan
Newton iteration   4energy =              nan<A u 4 , A u 4 >_{-1}^0.5 =  nan
Newton iteration   5energy =              nan<A u 5 , A u 5 >_{-1}^0.5 =  nan
Newton iteration   6energy =              nan<A u 6 , A u 6 >_{-1}^0.5 =  nan
Newton iteration   7energy =              nan<A u 7 , A u 7 >_{-1}^0.5 =  nan
Newton iteration   8energy =              nan<A u 8 , A u 8 >_{-1}^0.5 =  nan
Newton iteration   9energy =              nan<A u 9 , A u 9 >_{-1}^0.5 =  nan
Newton iteration  10energy =              nan<A u 10 , A u 10 >_{-1}^0.5 =  nan
Newton iteration  11energy =              nan<A u 11 , A u 11 >_{-1}^0.5 =  nan
Newton iteration  12energy =              nan<A u 12 , A u 12 >_{-1}^0.5 =  nan
Newton iteration  13energy =              nan<A u 13 , A u 13 >_{-1}^0.5 =  nan
Newton iteration  14energy =              nan<A u 14 , A u 14 >_{-1}^0.5 =  nan
Newton iteration  15energy =              nan<A u 15 , A u 15 >_{-1}^0.5 =  nan
Newton iteration  16energy =              nan<A u 16 , A u 16 >_{-1}^0.5 =  nan
Newton iteration  17energy =              nan<A u 17 , A u 17 >_{-1}^0.5 =  nan
Newton iteration  18energy =              nan<A u 18 , A u 18 >_{-1}^0.5 =  nan
Newton iteration  19energy =              nan<A u 19 , A u 19 >_{-1}^0.5 =  nan
Newton iteration  20energy =              nan<A u 20 , A u 20 >_{-1}^0.5 =  nan
Newton iteration  21energy =              nan<A u 21 , A u 21 >_{-1}^0.5 =  nan
Newton iteration  22energy =              nan<A u 22 , A u 22 >_{-1}^0.5 =  nan
Newton iteration  23energy =              nan<A u 23 , A u 23 >_{-1}^0.5 =  nan
Newton iteration  24energy =              nan<A u 24 , A u 24 >_{-1}^0.5 =  nan
loadstep 39
Newton iteration   0energy =              nan<A u 0 , A u 0 >_{-1}^0.5 =  nan
Newton iteration   1energy =              nan<A u 1 , A u 1 >_{-1}^0.5 =  nan
Newton iteration   2energy =              nan<A u 2 , A u 2 >_{-1}^0.5 =  nan
Newton iteration   3energy =              nan<A u 3 , A u 3 >_{-1}^0.5 =  nan
Newton iteration   4energy =              nan<A u 4 , A u 4 >_{-1}^0.5 =  nan
Newton iteration   5energy =              nan<A u 5 , A u 5 >_{-1}^0.5 =  nan
Newton iteration   6energy =              nan<A u 6 , A u 6 >_{-1}^0.5 =  nan
Newton iteration   7energy =              nan<A u 7 , A u 7 >_{-1}^0.5 =  nan
Newton iteration   8energy =              nan<A u 8 , A u 8 >_{-1}^0.5 =  nan
Newton iteration   9energy =              nan<A u 9 , A u 9 >_{-1}^0.5 =  nan
Newton iteration  10energy =              nan<A u 10 , A u 10 >_{-1}^0.5 =  nan
Newton iteration  11energy =              nan<A u 11 , A u 11 >_{-1}^0.5 =  nan
Newton iteration  12energy =              nan<A u 12 , A u 12 >_{-1}^0.5 =  nan
Newton iteration  13energy =              nan<A u 13 , A u 13 >_{-1}^0.5 =  nan
Newton iteration  14energy =              nan<A u 14 , A u 14 >_{-1}^0.5 =  nan
Newton iteration  15energy =              nan<A u 15 , A u 15 >_{-1}^0.5 =  nan
Newton iteration  16energy =              nan<A u 16 , A u 16 >_{-1}^0.5 =  nan
Newton iteration  17energy =              nan<A u 17 , A u 17 >_{-1}^0.5 =  nan
Newton iteration  18energy =              nan<A u 18 , A u 18 >_{-1}^0.5 =  nan
Newton iteration  19energy =              nan<A u 19 , A u 19 >_{-1}^0.5 =  nan
Newton iteration  20energy =              nan<A u 20 , A u 20 >_{-1}^0.5 =  nan
Newton iteration  21energy =              nan<A u 21 , A u 21 >_{-1}^0.5 =  nan
Newton iteration  22energy =              nan<A u 22 , A u 22 >_{-1}^0.5 =  nan
Newton iteration  23energy =              nan<A u 23 , A u 23 >_{-1}^0.5 =  nan
Newton iteration  24energy =              nan<A u 24 , A u 24 >_{-1}^0.5 =  nan
loadstep 40
Newton iteration   0energy =              nan<A u 0 , A u 0 >_{-1}^0.5 =  nan
Newton iteration   1energy =              nan<A u 1 , A u 1 >_{-1}^0.5 =  nan
Newton iteration   2energy =              nan<A u 2 , A u 2 >_{-1}^0.5 =  nan
Newton iteration   3energy =              nan<A u 3 , A u 3 >_{-1}^0.5 =  nan
Newton iteration   4energy =              nan<A u 4 , A u 4 >_{-1}^0.5 =  nan
Newton iteration   5energy =              nan<A u 5 , A u 5 >_{-1}^0.5 =  nan
Newton iteration   6energy =              nan<A u 6 , A u 6 >_{-1}^0.5 =  nan
Newton iteration   7energy =              nan<A u 7 , A u 7 >_{-1}^0.5 =  nan
Newton iteration   8energy =              nan<A u 8 , A u 8 >_{-1}^0.5 =  nan
Newton iteration   9energy =              nan<A u 9 , A u 9 >_{-1}^0.5 =  nan
Newton iteration  10energy =              nan<A u 10 , A u 10 >_{-1}^0.5 =  nan
Newton iteration  11energy =              nan<A u 11 , A u 11 >_{-1}^0.5 =  nan
Newton iteration  12energy =              nan<A u 12 , A u 12 >_{-1}^0.5 =  nan
Newton iteration  13energy =              nan<A u 13 , A u 13 >_{-1}^0.5 =  nan
Newton iteration  14energy =              nan<A u 14 , A u 14 >_{-1}^0.5 =  nan
Newton iteration  15energy =              nan<A u 15 , A u 15 >_{-1}^0.5 =  nan
Newton iteration  16energy =              nan<A u 16 , A u 16 >_{-1}^0.5 =  nan
Newton iteration  17energy =              nan<A u 17 , A u 17 >_{-1}^0.5 =  nan
Newton iteration  18energy =              nan<A u 18 , A u 18 >_{-1}^0.5 =  nan
Newton iteration  19energy =              nan<A u 19 , A u 19 >_{-1}^0.5 =  nan
Newton iteration  20energy =              nan<A u 20 , A u 20 >_{-1}^0.5 =  nan
Newton iteration  21energy =              nan<A u 21 , A u 21 >_{-1}^0.5 =  nan
Newton iteration  22energy =              nan<A u 22 , A u 22 >_{-1}^0.5 =  nan
Newton iteration  23energy =              nan<A u 23 , A u 23 >_{-1}^0.5 =  nan
Newton iteration  24energy =              nan<A u 24 , A u 24 >_{-1}^0.5 =  nan
loadstep 41
Newton iteration   0energy =              nan<A u 0 , A u 0 >_{-1}^0.5 =  nan
Newton iteration   1energy =              nan<A u 1 , A u 1 >_{-1}^0.5 =  nan
Newton iteration   2energy =              nan<A u 2 , A u 2 >_{-1}^0.5 =  nan
Newton iteration   3energy =              nan<A u 3 , A u 3 >_{-1}^0.5 =  nan
Newton iteration   4energy =              nan<A u 4 , A u 4 >_{-1}^0.5 =  nan
Newton iteration   5energy =              nan<A u 5 , A u 5 >_{-1}^0.5 =  nan
Newton iteration   6energy =              nan<A u 6 , A u 6 >_{-1}^0.5 =  nan
Newton iteration   7energy =              nan<A u 7 , A u 7 >_{-1}^0.5 =  nan
Newton iteration   8energy =              nan<A u 8 , A u 8 >_{-1}^0.5 =  nan
Newton iteration   9energy =              nan<A u 9 , A u 9 >_{-1}^0.5 =  nan
Newton iteration  10energy =              nan<A u 10 , A u 10 >_{-1}^0.5 =  nan
Newton iteration  11energy =              nan<A u 11 , A u 11 >_{-1}^0.5 =  nan
Newton iteration  12energy =              nan<A u 12 , A u 12 >_{-1}^0.5 =  nan
Newton iteration  13energy =              nan<A u 13 , A u 13 >_{-1}^0.5 =  nan
Newton iteration  14energy =              nan<A u 14 , A u 14 >_{-1}^0.5 =  nan
Newton iteration  15energy =              nan<A u 15 , A u 15 >_{-1}^0.5 =  nan
Newton iteration  16energy =              nan<A u 16 , A u 16 >_{-1}^0.5 =  nan
Newton iteration  17energy =              nan<A u 17 , A u 17 >_{-1}^0.5 =  nan
Newton iteration  18energy =              nan<A u 18 , A u 18 >_{-1}^0.5 =  nan
Newton iteration  19energy =              nan<A u 19 , A u 19 >_{-1}^0.5 =  nan
Newton iteration  20energy =              nan<A u 20 , A u 20 >_{-1}^0.5 =  nan
Newton iteration  21energy =              nan<A u 21 , A u 21 >_{-1}^0.5 =  nan
Newton iteration  22energy =              nan<A u 22 , A u 22 >_{-1}^0.5 =  nan
Newton iteration  23energy =              nan<A u 23 , A u 23 >_{-1}^0.5 =  nan
Newton iteration  24energy =              nan<A u 24 , A u 24 >_{-1}^0.5 =  nan
loadstep 42
Newton iteration   0energy =              nan<A u 0 , A u 0 >_{-1}^0.5 =  nan
Newton iteration   1energy =              nan<A u 1 , A u 1 >_{-1}^0.5 =  nan
Newton iteration   2energy =              nan<A u 2 , A u 2 >_{-1}^0.5 =  nan
Newton iteration   3energy =              nan<A u 3 , A u 3 >_{-1}^0.5 =  nan
Newton iteration   4energy =              nan<A u 4 , A u 4 >_{-1}^0.5 =  nan
Newton iteration   5energy =              nan<A u 5 , A u 5 >_{-1}^0.5 =  nan
Newton iteration   6energy =              nan<A u 6 , A u 6 >_{-1}^0.5 =  nan
Newton iteration   7energy =              nan<A u 7 , A u 7 >_{-1}^0.5 =  nan
Newton iteration   8energy =              nan<A u 8 , A u 8 >_{-1}^0.5 =  nan
Newton iteration   9energy =              nan<A u 9 , A u 9 >_{-1}^0.5 =  nan
Newton iteration  10energy =              nan<A u 10 , A u 10 >_{-1}^0.5 =  nan
Newton iteration  11energy =              nan<A u 11 , A u 11 >_{-1}^0.5 =  nan
Newton iteration  12energy =              nan<A u 12 , A u 12 >_{-1}^0.5 =  nan
Newton iteration  13energy =              nan<A u 13 , A u 13 >_{-1}^0.5 =  nan
Newton iteration  14energy =              nan<A u 14 , A u 14 >_{-1}^0.5 =  nan
Newton iteration  15energy =              nan<A u 15 , A u 15 >_{-1}^0.5 =  nan
Newton iteration  16energy =              nan<A u 16 , A u 16 >_{-1}^0.5 =  nan
Newton iteration  17energy =              nan<A u 17 , A u 17 >_{-1}^0.5 =  nan
Newton iteration  18energy =              nan<A u 18 , A u 18 >_{-1}^0.5 =  nan
Newton iteration  19energy =              nan<A u 19 , A u 19 >_{-1}^0.5 =  nan
Newton iteration  20energy =              nan<A u 20 , A u 20 >_{-1}^0.5 =  nan
Newton iteration  21energy =              nan<A u 21 , A u 21 >_{-1}^0.5 =  nan
Newton iteration  22energy =              nan<A u 22 , A u 22 >_{-1}^0.5 =  nan
Newton iteration  23energy =              nan<A u 23 , A u 23 >_{-1}^0.5 =  nan
Newton iteration  24energy =              nan<A u 24 , A u 24 >_{-1}^0.5 =  nan
loadstep 43
Newton iteration   0energy =              nan<A u 0 , A u 0 >_{-1}^0.5 =  nan
Newton iteration   1energy =              nan<A u 1 , A u 1 >_{-1}^0.5 =  nan
Newton iteration   2energy =              nan<A u 2 , A u 2 >_{-1}^0.5 =  nan
Newton iteration   3energy =              nan<A u 3 , A u 3 >_{-1}^0.5 =  nan
Newton iteration   4energy =              nan<A u 4 , A u 4 >_{-1}^0.5 =  nan
Newton iteration   5energy =              nan<A u 5 , A u 5 >_{-1}^0.5 =  nan
Newton iteration   6energy =              nan<A u 6 , A u 6 >_{-1}^0.5 =  nan
Newton iteration   7energy =              nan<A u 7 , A u 7 >_{-1}^0.5 =  nan
Newton iteration   8energy =              nan<A u 8 , A u 8 >_{-1}^0.5 =  nan
Newton iteration   9energy =              nan<A u 9 , A u 9 >_{-1}^0.5 =  nan
Newton iteration  10energy =              nan<A u 10 , A u 10 >_{-1}^0.5 =  nan
Newton iteration  11energy =              nan<A u 11 , A u 11 >_{-1}^0.5 =  nan
Newton iteration  12energy =              nan<A u 12 , A u 12 >_{-1}^0.5 =  nan
Newton iteration  13energy =              nan<A u 13 , A u 13 >_{-1}^0.5 =  nan
Newton iteration  14energy =              nan<A u 14 , A u 14 >_{-1}^0.5 =  nan
Newton iteration  15energy =              nan<A u 15 , A u 15 >_{-1}^0.5 =  nan
Newton iteration  16energy =              nan<A u 16 , A u 16 >_{-1}^0.5 =  nan
Newton iteration  17energy =              nan<A u 17 , A u 17 >_{-1}^0.5 =  nan
Newton iteration  18energy =              nan<A u 18 , A u 18 >_{-1}^0.5 =  nan
Newton iteration  19energy =              nan<A u 19 , A u 19 >_{-1}^0.5 =  nan
Newton iteration  20energy =              nan<A u 20 , A u 20 >_{-1}^0.5 =  nan
Newton iteration  21energy =              nan<A u 21 , A u 21 >_{-1}^0.5 =  nan
Newton iteration  22energy =              nan<A u 22 , A u 22 >_{-1}^0.5 =  nan
Newton iteration  23energy =              nan<A u 23 , A u 23 >_{-1}^0.5 =  nan
Newton iteration  24energy =              nan<A u 24 , A u 24 >_{-1}^0.5 =  nan
loadstep 44
Newton iteration   0energy =              nan<A u 0 , A u 0 >_{-1}^0.5 =  nan
Newton iteration   1energy =              nan<A u 1 , A u 1 >_{-1}^0.5 =  nan
Newton iteration   2energy =              nan<A u 2 , A u 2 >_{-1}^0.5 =  nan
Newton iteration   3energy =              nan<A u 3 , A u 3 >_{-1}^0.5 =  nan
Newton iteration   4energy =              nan<A u 4 , A u 4 >_{-1}^0.5 =  nan
Newton iteration   5energy =              nan<A u 5 , A u 5 >_{-1}^0.5 =  nan
Newton iteration   6energy =              nan<A u 6 , A u 6 >_{-1}^0.5 =  nan
Newton iteration   7energy =              nan<A u 7 , A u 7 >_{-1}^0.5 =  nan
Newton iteration   8energy =              nan<A u 8 , A u 8 >_{-1}^0.5 =  nan
Newton iteration   9energy =              nan<A u 9 , A u 9 >_{-1}^0.5 =  nan
Newton iteration  10energy =              nan<A u 10 , A u 10 >_{-1}^0.5 =  nan
Newton iteration  11energy =              nan<A u 11 , A u 11 >_{-1}^0.5 =  nan
Newton iteration  12energy =              nan<A u 12 , A u 12 >_{-1}^0.5 =  nan
Newton iteration  13energy =              nan<A u 13 , A u 13 >_{-1}^0.5 =  nan
Newton iteration  14energy =              nan<A u 14 , A u 14 >_{-1}^0.5 =  nan
Newton iteration  15energy =              nan<A u 15 , A u 15 >_{-1}^0.5 =  nan
Newton iteration  16energy =              nan<A u 16 , A u 16 >_{-1}^0.5 =  nan
Newton iteration  17energy =              nan<A u 17 , A u 17 >_{-1}^0.5 =  nan
Newton iteration  18energy =              nan<A u 18 , A u 18 >_{-1}^0.5 =  nan
Newton iteration  19energy =              nan<A u 19 , A u 19 >_{-1}^0.5 =  nan
Newton iteration  20energy =              nan<A u 20 , A u 20 >_{-1}^0.5 =  nan
Newton iteration  21energy =              nan<A u 21 , A u 21 >_{-1}^0.5 =  nan
Newton iteration  22energy =              nan<A u 22 , A u 22 >_{-1}^0.5 =  nan
Newton iteration  23energy =              nan<A u 23 , A u 23 >_{-1}^0.5 =  nan
Newton iteration  24energy =              nan<A u 24 , A u 24 >_{-1}^0.5 =  nan
loadstep 45
Newton iteration   0energy =              nan<A u 0 , A u 0 >_{-1}^0.5 =  nan
Newton iteration   1energy =              nan<A u 1 , A u 1 >_{-1}^0.5 =  nan
Newton iteration   2energy =              nan<A u 2 , A u 2 >_{-1}^0.5 =  nan
Newton iteration   3energy =              nan<A u 3 , A u 3 >_{-1}^0.5 =  nan
Newton iteration   4energy =              nan<A u 4 , A u 4 >_{-1}^0.5 =  nan
Newton iteration   5energy =              nan<A u 5 , A u 5 >_{-1}^0.5 =  nan
Newton iteration   6energy =              nan<A u 6 , A u 6 >_{-1}^0.5 =  nan
Newton iteration   7energy =              nan<A u 7 , A u 7 >_{-1}^0.5 =  nan
Newton iteration   8energy =              nan<A u 8 , A u 8 >_{-1}^0.5 =  nan
Newton iteration   9energy =              nan<A u 9 , A u 9 >_{-1}^0.5 =  nan
Newton iteration  10energy =              nan<A u 10 , A u 10 >_{-1}^0.5 =  nan
Newton iteration  11energy =              nan<A u 11 , A u 11 >_{-1}^0.5 =  nan
Newton iteration  12energy =              nan<A u 12 , A u 12 >_{-1}^0.5 =  nan
Newton iteration  13energy =              nan<A u 13 , A u 13 >_{-1}^0.5 =  nan
Newton iteration  14energy =              nan<A u 14 , A u 14 >_{-1}^0.5 =  nan
Newton iteration  15energy =              nan<A u 15 , A u 15 >_{-1}^0.5 =  nan
Newton iteration  16energy =              nan<A u 16 , A u 16 >_{-1}^0.5 =  nan
Newton iteration  17energy =              nan<A u 17 , A u 17 >_{-1}^0.5 =  nan
Newton iteration  18energy =              nan<A u 18 , A u 18 >_{-1}^0.5 =  nan
Newton iteration  19energy =              nan<A u 19 , A u 19 >_{-1}^0.5 =  nan
Newton iteration  20energy =              nan<A u 20 , A u 20 >_{-1}^0.5 =  nan
Newton iteration  21energy =              nan<A u 21 , A u 21 >_{-1}^0.5 =  nan
Newton iteration  22energy =              nan<A u 22 , A u 22 >_{-1}^0.5 =  nan
Newton iteration  23energy =              nan<A u 23 , A u 23 >_{-1}^0.5 =  nan
Newton iteration  24energy =              nan<A u 24 , A u 24 >_{-1}^0.5 =  nan
loadstep 46
Newton iteration   0energy =              nan<A u 0 , A u 0 >_{-1}^0.5 =  nan
Newton iteration   1energy =              nan<A u 1 , A u 1 >_{-1}^0.5 =  nan
Newton iteration   2energy =              nan<A u 2 , A u 2 >_{-1}^0.5 =  nan
Newton iteration   3energy =              nan<A u 3 , A u 3 >_{-1}^0.5 =  nan
Newton iteration   4energy =              nan<A u 4 , A u 4 >_{-1}^0.5 =  nan
Newton iteration   5energy =              nan<A u 5 , A u 5 >_{-1}^0.5 =  nan
Newton iteration   6energy =              nan<A u 6 , A u 6 >_{-1}^0.5 =  nan
Newton iteration   7energy =              nan<A u 7 , A u 7 >_{-1}^0.5 =  nan
Newton iteration   8energy =              nan<A u 8 , A u 8 >_{-1}^0.5 =  nan
Newton iteration   9energy =              nan<A u 9 , A u 9 >_{-1}^0.5 =  nan
Newton iteration  10energy =              nan<A u 10 , A u 10 >_{-1}^0.5 =  nan
Newton iteration  11energy =              nan<A u 11 , A u 11 >_{-1}^0.5 =  nan
Newton iteration  12energy =              nan<A u 12 , A u 12 >_{-1}^0.5 =  nan
Newton iteration  13energy =              nan<A u 13 , A u 13 >_{-1}^0.5 =  nan
Newton iteration  14energy =              nan<A u 14 , A u 14 >_{-1}^0.5 =  nan
Newton iteration  15energy =              nan<A u 15 , A u 15 >_{-1}^0.5 =  nan
Newton iteration  16energy =              nan<A u 16 , A u 16 >_{-1}^0.5 =  nan
Newton iteration  17energy =              nan<A u 17 , A u 17 >_{-1}^0.5 =  nan
Newton iteration  18energy =              nan<A u 18 , A u 18 >_{-1}^0.5 =  nan
Newton iteration  19energy =              nan<A u 19 , A u 19 >_{-1}^0.5 =  nan
Newton iteration  20energy =              nan<A u 20 , A u 20 >_{-1}^0.5 =  nan
Newton iteration  21energy =              nan<A u 21 , A u 21 >_{-1}^0.5 =  nan
Newton iteration  22energy =              nan<A u 22 , A u 22 >_{-1}^0.5 =  nan
Newton iteration  23energy =              nan<A u 23 , A u 23 >_{-1}^0.5 =  nan
Newton iteration  24energy =              nan<A u 24 , A u 24 >_{-1}^0.5 =  nan
loadstep 47
Newton iteration   0energy =              nan<A u 0 , A u 0 >_{-1}^0.5 =  nan
Newton iteration   1energy =              nan<A u 1 , A u 1 >_{-1}^0.5 =  nan
Newton iteration   2energy =              nan<A u 2 , A u 2 >_{-1}^0.5 =  nan
Newton iteration   3energy =              nan<A u 3 , A u 3 >_{-1}^0.5 =  nan
Newton iteration   4energy =              nan<A u 4 , A u 4 >_{-1}^0.5 =  nan
Newton iteration   5energy =              nan<A u 5 , A u 5 >_{-1}^0.5 =  nan
Newton iteration   6energy =              nan<A u 6 , A u 6 >_{-1}^0.5 =  nan
Newton iteration   7energy =              nan<A u 7 , A u 7 >_{-1}^0.5 =  nan
Newton iteration   8energy =              nan<A u 8 , A u 8 >_{-1}^0.5 =  nan
Newton iteration   9energy =              nan<A u 9 , A u 9 >_{-1}^0.5 =  nan
Newton iteration  10energy =              nan<A u 10 , A u 10 >_{-1}^0.5 =  nan
Newton iteration  11energy =              nan<A u 11 , A u 11 >_{-1}^0.5 =  nan
Newton iteration  12energy =              nan<A u 12 , A u 12 >_{-1}^0.5 =  nan
Newton iteration  13energy =              nan<A u 13 , A u 13 >_{-1}^0.5 =  nan
Newton iteration  14energy =              nan<A u 14 , A u 14 >_{-1}^0.5 =  nan
Newton iteration  15energy =              nan<A u 15 , A u 15 >_{-1}^0.5 =  nan
Newton iteration  16energy =              nan<A u 16 , A u 16 >_{-1}^0.5 =  nan
Newton iteration  17energy =              nan<A u 17 , A u 17 >_{-1}^0.5 =  nan
Newton iteration  18energy =              nan<A u 18 , A u 18 >_{-1}^0.5 =  nan
Newton iteration  19energy =              nan<A u 19 , A u 19 >_{-1}^0.5 =  nan
Newton iteration  20energy =              nan<A u 20 , A u 20 >_{-1}^0.5 =  nan
Newton iteration  21energy =              nan<A u 21 , A u 21 >_{-1}^0.5 =  nan
Newton iteration  22energy =              nan<A u 22 , A u 22 >_{-1}^0.5 =  nan
Newton iteration  23energy =              nan<A u 23 , A u 23 >_{-1}^0.5 =  nan
Newton iteration  24energy =              nan<A u 24 , A u 24 >_{-1}^0.5 =  nan
loadstep 48
Newton iteration   0energy =              nan<A u 0 , A u 0 >_{-1}^0.5 =  nan
Newton iteration   1energy =              nan<A u 1 , A u 1 >_{-1}^0.5 =  nan
Newton iteration   2energy =              nan<A u 2 , A u 2 >_{-1}^0.5 =  nan
Newton iteration   3energy =              nan<A u 3 , A u 3 >_{-1}^0.5 =  nan
Newton iteration   4energy =              nan<A u 4 , A u 4 >_{-1}^0.5 =  nan
Newton iteration   5energy =              nan<A u 5 , A u 5 >_{-1}^0.5 =  nan
Newton iteration   6energy =              nan<A u 6 , A u 6 >_{-1}^0.5 =  nan
Newton iteration   7energy =              nan<A u 7 , A u 7 >_{-1}^0.5 =  nan
Newton iteration   8energy =              nan<A u 8 , A u 8 >_{-1}^0.5 =  nan
Newton iteration   9energy =              nan<A u 9 , A u 9 >_{-1}^0.5 =  nan
Newton iteration  10energy =              nan<A u 10 , A u 10 >_{-1}^0.5 =  nan
Newton iteration  11energy =              nan<A u 11 , A u 11 >_{-1}^0.5 =  nan
Newton iteration  12energy =              nan<A u 12 , A u 12 >_{-1}^0.5 =  nan
Newton iteration  13energy =              nan<A u 13 , A u 13 >_{-1}^0.5 =  nan
Newton iteration  14energy =              nan<A u 14 , A u 14 >_{-1}^0.5 =  nan
Newton iteration  15energy =              nan<A u 15 , A u 15 >_{-1}^0.5 =  nan
Newton iteration  16energy =              nan<A u 16 , A u 16 >_{-1}^0.5 =  nan
Newton iteration  17energy =              nan<A u 17 , A u 17 >_{-1}^0.5 =  nan
Newton iteration  18energy =              nan<A u 18 , A u 18 >_{-1}^0.5 =  nan
Newton iteration  19energy =              nan<A u 19 , A u 19 >_{-1}^0.5 =  nan
Newton iteration  20energy =              nan<A u 20 , A u 20 >_{-1}^0.5 =  nan
Newton iteration  21energy =              nan<A u 21 , A u 21 >_{-1}^0.5 =  nan
Newton iteration  22energy =              nan<A u 22 , A u 22 >_{-1}^0.5 =  nan
Newton iteration  23energy =              nan<A u 23 , A u 23 >_{-1}^0.5 =  nan
Newton iteration  24energy =              nan<A u 24 , A u 24 >_{-1}^0.5 =  nan
loadstep 49
Newton iteration   0energy =              nan<A u 0 , A u 0 >_{-1}^0.5 =  nan
Newton iteration   1energy =              nan<A u 1 , A u 1 >_{-1}^0.5 =  nan
Newton iteration   2energy =              nan<A u 2 , A u 2 >_{-1}^0.5 =  nan
Newton iteration   3energy =              nan<A u 3 , A u 3 >_{-1}^0.5 =  nan
Newton iteration   4energy =              nan<A u 4 , A u 4 >_{-1}^0.5 =  nan
Newton iteration   5energy =              nan<A u 5 , A u 5 >_{-1}^0.5 =  nan
Newton iteration   6energy =              nan<A u 6 , A u 6 >_{-1}^0.5 =  nan
Newton iteration   7energy =              nan<A u 7 , A u 7 >_{-1}^0.5 =  nan
Newton iteration   8energy =              nan<A u 8 , A u 8 >_{-1}^0.5 =  nan
Newton iteration   9energy =              nan<A u 9 , A u 9 >_{-1}^0.5 =  nan
Newton iteration  10energy =              nan<A u 10 , A u 10 >_{-1}^0.5 =  nan
Newton iteration  11energy =              nan<A u 11 , A u 11 >_{-1}^0.5 =  nan
Newton iteration  12energy =              nan<A u 12 , A u 12 >_{-1}^0.5 =  nan
Newton iteration  13energy =              nan<A u 13 , A u 13 >_{-1}^0.5 =  nan
Newton iteration  14energy =              nan<A u 14 , A u 14 >_{-1}^0.5 =  nan
Newton iteration  15energy =              nan<A u 15 , A u 15 >_{-1}^0.5 =  nan
Newton iteration  16energy =              nan<A u 16 , A u 16 >_{-1}^0.5 =  nan
Newton iteration  17energy =              nan<A u 17 , A u 17 >_{-1}^0.5 =  nan
Newton iteration  18energy =              nan<A u 18 , A u 18 >_{-1}^0.5 =  nan
Newton iteration  19energy =              nan<A u 19 , A u 19 >_{-1}^0.5 =  nan
Newton iteration  20energy =              nan<A u 20 , A u 20 >_{-1}^0.5 =  nan
Newton iteration  21energy =              nan<A u 21 , A u 21 >_{-1}^0.5 =  nan
Newton iteration  22energy =              nan<A u 22 , A u 22 >_{-1}^0.5 =  nan
Newton iteration  23energy =              nan<A u 23 , A u 23 >_{-1}^0.5 =  nan
Newton iteration  24energy =              nan<A u 24 , A u 24 >_{-1}^0.5 =  nan

Allen-Cahn equation

The Allen-Cahn equations describe the process of phase separation and is the ($L^2$) gradient-flow equation to the energy

$$E(v) = \int_{\Omega} \varepsilon \vert \nabla v \vert^2~+~v^2(1-v^2) ~ dx$$

i.e. the solution to the Allen-Cahn equation solves

$$\partial_t u = \frac{\delta E}{\delta u}$$

The quantity $u$ is an indicator for a phase where $-1$ refers to one phase and $1$ to another phase.

The equation has two driving forces:

• $u$ is pulled into one of the two minima ($-1$ and $1$) of the nonlinear term $u^2(1-u^2)$ (separation of the phases)

• the diffusion term scaled with $\varepsilon$ enforces a smooth transition between the two phases. $\varepsilon$ determines the size of the transition layer

We use the “SymbolicEnergy” feature to formulate the energy minimization problem and combine it with an implicit Euler discretization:

$$M u^{n+1} - M u^n = \Delta t \underbrace{\frac{\delta E}{\delta u}}_{=:A(u)} (u^{n+1})$$

which we can interpreted as a nonlinear minimization problem again with the energy

$$E^{IE}(v) = \int_{\Omega} \frac{\varepsilon}{2} \vert \nabla v \vert^2~+~v^2(1-v^2) + \frac{1}{2\Delta t} \vert v - u^n \vert^2 ~ dx$$

To solve the nonlinear equation at every time step we again rely on Newton’s method.

from ngsolve import *

from netgen.geom2d import *

periodic = SplineGeometry()
pnts = [ (0,0), (1,0), (1,1), (0,1) ]
pnums = [periodic.AppendPoint(*p) for p in pnts]
lright = periodic.Append ( ["line", pnums[0], pnums[1]],bc="periodic")
btop = periodic.Append ( ["line", pnums[1], pnums[2]], bc="periodic")
periodic.Append ( ["line", pnums[3], pnums[2]], leftdomain=0, rightdomain=1, copy=lright, bc="periodic")
periodic.Append ( ["line", pnums[0], pnums[3]], leftdomain=0, rightdomain=1, copy=btop, bc="periodic")

mesh = Mesh (periodic.GenerateMesh(maxh=0.2))
V = Periodic(H1(mesh, order=4, dirichlet=[]))
u = V.TrialFunction()

eps = 4e-3
dt = 1e-1
gfu = GridFunction(V)
gfuold = GridFunction(V)
a = BilinearForm (V, symmetric=False)
a += Variation( (eps/2*grad(u)*grad(u) + ((1-u*u)*(1-u*u))
                     + 0.5/dt*(u-gfuold)*(u-gfuold)) * dx)

from math import pi
gfu = GridFunction(V)
gfu.Set(sin(2*pi*x))
#gfu.Set(sin(1e8*x)) #<- essentially a random function
Draw(gfu,mesh,"u")
SetVisualization (deformation=True)
t = 0

for timestep in range(50):
    gfuold.vec.data = gfu.vec
    SolveNonlinearMinProblem(a,gfu)
    Redraw()
    t += dt
    print("t = ", t)

Newton iteration   0energy = 0.4145019207496359<A u 0 , A u 0 >_{-1}^0.5 =  0.2809270463814763
Newton iteration   1energy = 0.37689785802772924<A u 1 , A u 1 >_{-1}^0.5 =  0.01917437047193973
Newton iteration   2energy = 0.3767134210404818<A u 2 , A u 2 >_{-1}^0.5 =  9.628937134602255e-05
Newton iteration   3energy = 0.37671341640458017<A u 3 , A u 3 >_{-1}^0.5 =  2.5054562992371867e-09
Newton iteration   4energy = 0.37671341640458006<A u 4 , A u 4 >_{-1}^0.5 =  3.003282889895448e-16
t =  0.1
Newton iteration   0energy = 0.3438812865238592<A u 0 , A u 0 >_{-1}^0.5 =  0.23603934740782906
Newton iteration   1energy = 0.31710944329874874<A u 1 , A u 1 >_{-1}^0.5 =  0.013442999343193882
Newton iteration   2energy = 0.3170188793463516<A u 2 , A u 2 >_{-1}^0.5 =  4.660092984275238e-05
Newton iteration   3energy = 0.31701887826051917<A u 3 , A u 3 >_{-1}^0.5 =  5.76804827520762e-10
Newton iteration   4energy = 0.3170188782605193<A u 4 , A u 4 >_{-1}^0.5 =  3.331991791505268e-16
t =  0.2
Newton iteration   0energy = 0.2954943565138458<A u 0 , A u 0 >_{-1}^0.5 =  0.18345925931027077
Newton iteration   1energy = 0.27916403033890114<A u 1 , A u 1 >_{-1}^0.5 =  0.008014651163108892
Newton iteration   2energy = 0.2791318699362322<A u 2 , A u 2 >_{-1}^0.5 =  1.6250158077627237e-05
Newton iteration   3energy = 0.279131869804198<A u 3 , A u 3 >_{-1}^0.5 =  6.857115501841529e-11
Newton iteration   4energy = 0.27913186980419785<A u 4 , A u 4 >_{-1}^0.5 =  3.416831081582394e-16
t =  0.30000000000000004
Newton iteration   0energy = 0.26692789507920534<A u 0 , A u 0 >_{-1}^0.5 =  0.13349658930568847
Newton iteration   1energy = 0.2582050355110707<A u 1 , A u 1 >_{-1}^0.5 =  0.0041885131065817005
Newton iteration   2energy = 0.2581962576290239<A u 2 , A u 2 >_{-1}^0.5 =  4.366756818971012e-06
Newton iteration   3energy = 0.25819625761948967<A u 3 , A u 3 >_{-1}^0.5 =  4.8506189386333065e-12
Newton iteration   4energy = 0.25819625761948944<A u 4 , A u 4 >_{-1}^0.5 =  3.588377772533667e-16
t =  0.4
Newton iteration   0energy = 0.2520431142368918<A u 0 , A u 0 >_{-1}^0.5 =  0.09236175483868561
Newton iteration   1energy = 0.24783887867786308<A u 1 , A u 1 >_{-1}^0.5 =  0.0019843467589302
Newton iteration   2energy = 0.2478369092241838<A u 2 , A u 2 >_{-1}^0.5 =  9.685217011892036e-07
Newton iteration   3energy = 0.2478369092237148<A u 3 , A u 3 >_{-1}^0.5 =  2.3476531523095486e-13
Newton iteration   4energy = 0.24783690922371485<A u 4 , A u 4 >_{-1}^0.5 =  3.7248806965135973e-16
t =  0.5
Newton iteration   0energy = 0.24499322447001137<A u 0 , A u 0 >_{-1}^0.5 =  0.061646841904519516
Newton iteration   1energy = 0.24311100787346115<A u 1 , A u 1 >_{-1}^0.5 =  0.0008779623506489409
Newton iteration   2energy = 0.2431106224096563<A u 2 , A u 2 >_{-1}^0.5 =  1.8822078760924155e-07
Newton iteration   3energy = 0.24311062240963854<A u 3 , A u 3 >_{-1}^0.5 =  8.81645854287601e-15
t =  0.6
Newton iteration   0energy = 0.2418735481479401<A u 0 , A u 0 >_{-1}^0.5 =  0.04016635875651366
Newton iteration   1energy = 0.24107181028212027<A u 1 , A u 1 >_{-1}^0.5 =  0.0003715367480243826
Newton iteration   2energy = 0.24107174125819192<A u 2 , A u 2 >_{-1}^0.5 =  3.3668941389797124e-08
Newton iteration   3energy = 0.2410717412581913<A u 3 , A u 3 >_{-1}^0.5 =  4.617523763320809e-16
t =  0.7
Newton iteration   0energy = 0.24055438873764584<A u 0 , A u 0 >_{-1}^0.5 =  0.025782033859246597
Newton iteration   1energy = 0.2402233339155409<A u 1 , A u 1 >_{-1}^0.5 =  0.00015331214259508866
Newton iteration   2energy = 0.2402233221629405<A u 2 , A u 2 >_{-1}^0.5 =  5.795968682048955e-09
Newton iteration   3energy = 0.24022332216294046<A u 3 , A u 3 >_{-1}^0.5 =  4.3395457490668377e-16
t =  0.7999999999999999
Newton iteration   0energy = 0.2400118618581594<A u 0 , A u 0 >_{-1}^0.5 =  0.016425332383409562
Newton iteration   1energy = 0.23987730469401888<A u 1 , A u 1 >_{-1}^0.5 =  6.283809116192321e-05
Newton iteration   2energy = 0.23987730271968516<A u 2 , A u 2 >_{-1}^0.5 =  1.0154930066600787e-09
Newton iteration   3energy = 0.2398773027196851<A u 3 , A u 3 >_{-1}^0.5 =  4.805333945709333e-16
t =  0.8999999999999999
Newton iteration   0energy = 0.23979158193635391<A u 0 , A u 0 >_{-1}^0.5 =  0.010464445156609924
Newton iteration   1energy = 0.23973691889059928<A u 1 , A u 1 >_{-1}^0.5 =  2.620620881241072e-05
Newton iteration   2energy = 0.23973691854721502<A u 2 , A u 2 >_{-1}^0.5 =  1.999460969185541e-10
Newton iteration   3energy = 0.23973691854721504<A u 3 , A u 3 >_{-1}^0.5 =  4.457911895517942e-16
t =  0.9999999999999999
Newton iteration   0energy = 0.2397018609405314<A u 0 , A u 0 >_{-1}^0.5 =  0.00673541582696503
Newton iteration   1energy = 0.23967920289205236<A u 1 , A u 1 >_{-1}^0.5 =  1.1556763084947155e-05
Newton iteration   2energy = 0.23967920282527283<A u 2 , A u 2 >_{-1}^0.5 =  5.0994587785631396e-11
Newton iteration   3energy = 0.2396792028252728<A u 3 , A u 3 >_{-1}^0.5 =  4.714110044332649e-16
t =  1.0999999999999999
Newton iteration   0energy = 0.23966435830447477<A u 0 , A u 0 >_{-1}^0.5 =  0.0044525423614036955
Newton iteration   1energy = 0.2396544535095991<A u 1 , A u 1 >_{-1}^0.5 =  5.694142646676037e-06
Newton iteration   2energy = 0.23965445349338746<A u 2 , A u 2 >_{-1}^0.5 =  1.7725040441281417e-11
Newton iteration   3energy = 0.2396544534933875<A u 3 , A u 3 >_{-1}^0.5 =  4.567722193531726e-16
t =  1.2
Newton iteration   0energy = 0.23964767142737942<A u 0 , A u 0 >_{-1}^0.5 =  0.0030979081418175307
Newton iteration   1energy = 0.23964287580252736<A u 1 , A u 1 >_{-1}^0.5 =  3.284053675981641e-06
Newton iteration   2energy = 0.2396428757971349<A u 2 , A u 2 >_{-1}^0.5 =  7.767210031814492e-12
Newton iteration   3energy = 0.23964287579713484<A u 3 , A u 3 >_{-1}^0.5 =  4.662852056770271e-16
t =  1.3
Newton iteration   0energy = 0.23963934988363764<A u 0 , A u 0 >_{-1}^0.5 =  0.002326255780763496
Newton iteration   1energy = 0.2396366454535445<A u 1 , A u 1 >_{-1}^0.5 =  2.2181767038475607e-06
Newton iteration   2energy = 0.23963664545108435<A u 2 , A u 2 >_{-1}^0.5 =  3.983602113181903e-12
Newton iteration   3energy = 0.2396366454510843<A u 3 , A u 3 >_{-1}^0.5 =  4.444524444123482e-16
t =  1.4000000000000001
Newton iteration   0energy = 0.23963447926266948<A u 0 , A u 0 >_{-1}^0.5 =  0.0019006816819441919
Newton iteration   1energy = 0.23963267365152316<A u 1 , A u 1 >_{-1}^0.5 =  1.6879462608466211e-06
Newton iteration   2energy = 0.2396326736500986<A u 2 , A u 2 >_{-1}^0.5 =  2.298272966166801e-12
Newton iteration   3energy = 0.23963267365009866<A u 3 , A u 3 >_{-1}^0.5 =  4.578265035668924e-16
t =  1.5000000000000002
Newton iteration   0energy = 0.23963111549003374<A u 0 , A u 0 >_{-1}^0.5 =  0.0016629280504840886
Newton iteration   1energy = 0.23962973322336584<A u 1 , A u 1 >_{-1}^0.5 =  1.3855651852362916e-06
Newton iteration   2energy = 0.23962973322240586<A u 2 , A u 2 >_{-1}^0.5 =  1.458620838855635e-12
Newton iteration   3energy = 0.239629733222406<A u 3 , A u 3 >_{-1}^0.5 =  4.518386193786961e-16
t =  1.6000000000000003
Newton iteration   0energy = 0.23962848049094237<A u 0 , A u 0 >_{-1}^0.5 =  0.0015187632040498532
Newton iteration   1energy = 0.23962732741809964<A u 1 , A u 1 >_{-1}^0.5 =  1.1887244240849515e-06
Newton iteration   2energy = 0.23962732741739326<A u 2 , A u 2 >_{-1}^0.5 =  1.0010923706915846e-12
Newton iteration   3energy = 0.2396273274173932<A u 3 , A u 3 >_{-1}^0.5 =  4.2566588833671387e-16
t =  1.7000000000000004
Newton iteration   0energy = 0.23962625398674228<A u 0 , A u 0 >_{-1}^0.5 =  0.0014193843873493643
Newton iteration   1energy = 0.23962524682330952<A u 1 , A u 1 >_{-1}^0.5 =  1.0456329093933632e-06
Newton iteration   2energy = 0.23962524682276293<A u 2 , A u 2 >_{-1}^0.5 =  7.300993583012621e-13
Newton iteration   3energy = 0.2396252468227629<A u 3 , A u 3 >_{-1}^0.5 =  4.534110875500262e-16
t =  1.8000000000000005
Newton iteration   0energy = 0.23962429644294805<A u 0 , A u 0 >_{-1}^0.5 =  0.0013419591604952315
Newton iteration   1energy = 0.23962339612718114<A u 1 , A u 1 >_{-1}^0.5 =  9.330532164753765e-07
Newton iteration   2energy = 0.23962339612674582<A u 2 , A u 2 >_{-1}^0.5 =  5.563574228766939e-13
Newton iteration   3energy = 0.23962339612674577<A u 3 , A u 3 >_{-1}^0.5 =  4.0237775990779104e-16
t =  1.9000000000000006
Newton iteration   0energy = 0.23962254072403272<A u 0 , A u 0 >_{-1}^0.5 =  0.0012763226584932732
Newton iteration   1energy = 0.23962172630379305<A u 1 , A u 1 >_{-1}^0.5 =  8.399033658821723e-07
Newton iteration   2energy = 0.23962172630344042<A u 2 , A u 2 >_{-1}^0.5 =  4.3694470025439145e-13
Newton iteration   3energy = 0.23962172630344036<A u 3 , A u 3 >_{-1}^0.5 =  4.3805270472932427e-16
t =  2.0000000000000004
Newton iteration   0energy = 0.2396209495967649<A u 0 , A u 0 >_{-1}^0.5 =  0.001217971596189921
Newton iteration   1energy = 0.2396202079282432<A u 1 , A u 1 >_{-1}^0.5 =  7.604668960370086e-07
Newton iteration   2energy = 0.23962020792795408<A u 2 , A u 2 >_{-1}^0.5 =  3.503108574361001e-13
Newton iteration   3energy = 0.2396202079279541<A u 3 , A u 3 >_{-1}^0.5 =  4.2155579625369558e-16
t =  2.1000000000000005
Newton iteration   0energy = 0.2396194989264497<A u 0 , A u 0 >_{-1}^0.5 =  0.00116483587636887
Newton iteration   1energy = 0.23961882055016812<A u 1 , A u 1 >_{-1}^0.5 =  6.914942047786559e-07
Newton iteration   2energy = 0.23961882054992897<A u 2 , A u 2 >_{-1}^0.5 =  2.8492948852230904e-13
Newton iteration   3energy = 0.23961882054992895<A u 3 , A u 3 >_{-1}^0.5 =  4.041623035830586e-16
t =  2.2000000000000006
Newton iteration   0energy = 0.23961817091741788<A u 0 , A u 0 >_{-1}^0.5 =  0.0011158806899792928
Newton iteration   1energy = 0.23961754835794213<A u 1 , A u 1 >_{-1}^0.5 =  6.309368258451742e-07
Newton iteration   2energy = 0.2396175483577431<A u 2 , A u 2 >_{-1}^0.5 =  2.342551544364737e-13
Newton iteration   3energy = 0.23961754835774307<A u 3 , A u 3 >_{-1}^0.5 =  3.7659915046707365e-16
t =  2.3000000000000007
Newton iteration   0energy = 0.23961695130021213<A u 0 , A u 0 >_{-1}^0.5 =  0.001070516865471795
Newton iteration   1energy = 0.23961637832545668<A u 1 , A u 1 >_{-1}^0.5 =  5.773776869002892e-07
Newton iteration   2energy = 0.23961637832529<A u 2 , A u 2 >_{-1}^0.5 =  1.941499345816214e-13
Newton iteration   3energy = 0.23961637832529<A u 3 , A u 3 >_{-1}^0.5 =  4.188228630245016e-16
t =  2.400000000000001
Newton iteration   0energy = 0.23961582808585102<A u 0 , A u 0 >_{-1}^0.5 =  0.0010283540627855198
Newton iteration   1energy = 0.23961529935305356<A u 1 , A u 1 >_{-1}^0.5 =  5.297627567252096e-07
Newton iteration   2energy = 0.23961529935291329<A u 2 , A u 2 >_{-1}^0.5 =  1.6202966695387348e-13
Newton iteration   3energy = 0.23961529935291334<A u 3 , A u 3 >_{-1}^0.5 =  3.999392740516295e-16
t =  2.500000000000001
Newton iteration   0energy = 0.23961479095503746<A u 0 , A u 0 >_{-1}^0.5 =  0.0009890970729079993
Newton iteration   1energy = 0.23961430181779786<A u 1 , A u 1 >_{-1}^0.5 =  4.872666035427371e-07
Newton iteration   2energy = 0.23961430181767918<A u 2 , A u 2 >_{-1}^0.5 =  1.3597696579476573e-13
Newton iteration   3energy = 0.23961430181767918<A u 3 , A u 3 >_{-1}^0.5 =  3.8936866568800425e-16
t =  2.600000000000001
Newton iteration   0energy = 0.2396138309145451<A u 0 , A u 0 >_{-1}^0.5 =  0.0009525015914657539
Newton iteration   1energy = 0.23961337730105753<A u 1 , A u 1 >_{-1}^0.5 =  4.4921981867275515e-07
Newton iteration   2energy = 0.2396133773009566<A u 2 , A u 2 >_{-1}^0.5 =  1.1472689377689044e-13
Newton iteration   3energy = 0.2396133773009566<A u 3 , A u 3 >_{-1}^0.5 =  4.0613019318331927e-16
t =  2.700000000000001
Newton iteration   0energy = 0.23961294007376774<A u 0 , A u 0 >_{-1}^0.5 =  0.0009183547757921597
Newton iteration   1energy = 0.23961251839967962<A u 1 , A u 1 >_{-1}^0.5 =  4.150665658147821e-07
Newton iteration   2energy = 0.2396125183995934<A u 2 , A u 2 >_{-1}^0.5 =  9.723092503762368e-14
t =  2.800000000000001
Newton iteration   0energy = 0.2396121114812304<A u 0 , A u 0 >_{-1}^0.5 =  0.0008864662194052564
Newton iteration   1energy = 0.23961171858168256<A u 1 , A u 1 >_{-1}^0.5 =  3.8433776208680404e-07
Newton iteration   2energy = 0.23961171858160873<A u 2 , A u 2 >_{-1}^0.5 =  8.284192585188487e-14
t =  2.9000000000000012
Newton iteration   0energy = 0.2396113389953494<A u 0 , A u 0 >_{-1}^0.5 =  0.0008566633749442762
Newton iteration   1energy = 0.2396109720692427<A u 1 , A u 1 >_{-1}^0.5 =  3.56632954760139e-07
Newton iteration   2energy = 0.2396109720691791<A u 2 , A u 2 >_{-1}^0.5 =  7.08144198455852e-14
t =  3.0000000000000013
Newton iteration   0energy = 0.23961061717765086<A u 0 , A u 0 >_{-1}^0.5 =  0.0008287889263646279
Newton iteration   1energy = 0.2396102737406834<A u 1 , A u 1 >_{-1}^0.5 =  3.3160737847372484e-07
Newton iteration   2energy = 0.23961027374062843<A u 2 , A u 2 >_{-1}^0.5 =  6.083862558389641e-14
t =  3.1000000000000014
Newton iteration   0energy = 0.23960994120243972<A u 0 , A u 0 >_{-1}^0.5 =  0.0008026990506789688
Newton iteration   1energy = 0.2396096190469689<A u 1 , A u 1 >_{-1}^0.5 =  3.089623021042399e-07
Newton iteration   2energy = 0.23960961904692127<A u 2 , A u 2 >_{-1}^0.5 =  5.243570434427366e-14
t =  3.2000000000000015
Newton iteration   0energy = 0.2396093067794342<A u 0 , A u 0 >_{-1}^0.5 =  0.0007782621114843857
Newton iteration   1energy = 0.23960900393990864<A u 1 , A u 1 >_{-1}^0.5 =  2.884375804322967e-07
Newton iteration   2energy = 0.23960900393986703<A u 2 , A u 2 >_{-1}^0.5 =  4.5379186834519644e-14
t =  3.3000000000000016
Newton iteration   0energy = 0.23960871008705956<A u 0 , A u 0 >_{-1}^0.5 =  0.0007553575814402258
Newton iteration   1energy = 0.23960842481012126<A u 1 , A u 1 >_{-1}^0.5 =  2.698057545765207e-07
Newton iteration   2energy = 0.23960842481008499<A u 2 , A u 2 >_{-1}^0.5 =  3.942665697811389e-14
t =  3.4000000000000017
Newton iteration   0energy = 0.239608147714714<A u 0 , A u 0 >_{-1}^0.5 =  0.0007338751008235229
Newton iteration   1energy = 0.2396078784332731<A u 1 , A u 1 >_{-1}^0.5 =  2.528672818893669e-07
Newton iteration   2energy = 0.23960787843324122<A u 2 , A u 2 >_{-1}^0.5 =  3.4403333422175943e-14
t =  3.5000000000000018
Newton iteration   0energy = 0.23960761661268348<A u 0 , A u 0 >_{-1}^0.5 =  0.0007137136279143401
Newton iteration   1energy = 0.2396073619233964<A u 1 , A u 1 >_{-1}^0.5 =  2.374466157006292e-07
Newton iteration   2energy = 0.23960736192336823<A u 2 , A u 2 >_{-1}^0.5 =  3.0137895183934865e-14
t =  3.600000000000002
Newton iteration   0energy = 0.23960711404861687<A u 0 , A u 0 >_{-1}^0.5 =  0.0006947806591328947
Newton iteration   1energy = 0.23960687269229808<A u 1 , A u 1 >_{-1}^0.5 =  2.2338894227617265e-07
Newton iteration   2energy = 0.23960687269227304<A u 2 , A u 2 >_{-1}^0.5 =  2.6475425404173353e-14
t =  3.700000000000002
Newton iteration   0energy = 0.23960663756966025<A u 0 , A u 0 >_{-1}^0.5 =  0.0006769915073033545
Newton iteration   1energy = 0.23960640841422393<A u 1 , A u 1 >_{-1}^0.5 =  2.1055743624529568e-07
Newton iteration   2energy = 0.2396064084142018<A u 2 , A u 2 >_{-1}^0.5 =  2.3313036877749828e-14
t =  3.800000000000002
Newton iteration   0energy = 0.2396061849694749<A u 0 , A u 0 >_{-1}^0.5 =  0.000660268631502265
Newton iteration   1energy = 0.239605966995068<A u 1 , A u 1 >_{-1}^0.5 =  1.9883093309711906e-07
Newton iteration   2energy = 0.23960596699504824<A u 2 , A u 2 >_{-1}^0.5 =  2.065902890547247e-14
t =  3.900000000000002
Newton iteration   0energy = 0.23960575425948316<A u 0 , A u 0 >_{-1}^0.5 =  0.0006445410144723969
Newton iteration   1energy = 0.2396055465455128<A u 1 , A u 1 >_{-1}^0.5 =  1.8810194233256467e-07
Newton iteration   2energy = 0.23960554654549515<A u 2 , A u 2 >_{-1}^0.5 =  1.8347648711839195e-14
t =  4.000000000000002
Newton iteration   0energy = 0.23960534364377498<A u 0 , A u 0 >_{-1}^0.5 =  0.000629743584834913
Newton iteration   1energy = 0.2396051453575804<A u 1 , A u 1 >_{-1}^0.5 =  1.7827494164831928e-07
Newton iteration   2energy = 0.23960514535756444<A u 2 , A u 2 >_{-1}^0.5 =  1.636304282394239e-14
t =  4.100000000000001
Newton iteration   0energy = 0.239604951497189<A u 0 , A u 0 >_{-1}^0.5 =  0.0006158166819322605
Newton iteration   1energy = 0.23960476188413732<A u 1 , A u 1 >_{-1}^0.5 =  1.692649062807602e-07
Newton iteration   2energy = 0.23960476188412316<A u 2 , A u 2 >_{-1}^0.5 =  1.4662402859105416e-14
t =  4.200000000000001
Newton iteration   0energy = 0.23960457634614438<A u 0 , A u 0 >_{-1}^0.5 =  0.0006027055613937356
Newton iteration   1energy = 0.23960439472096592<A u 1 , A u 1 >_{-1}^0.5 =  1.6099603650454517e-07
Newton iteration   2energy = 0.23960439472095302<A u 2 , A u 2 >_{-1}^0.5 =  1.3206294622538514e-14
t =  4.300000000000001
Newton iteration   0energy = 0.23960421685186575<A u 0 , A u 0 >_{-1}^0.5 =  0.0005903599395996152
Newton iteration   1energy = 0.23960404259105963<A u 1 , A u 1 >_{-1}^0.5 =  1.5340065262841853e-07
Newton iteration   2energy = 0.23960404259104776<A u 2 , A u 2 >_{-1}^0.5 =  1.1852161151991052e-14
t =  4.4
Newton iteration   0energy = 0.2396038717956791<A u 0 , A u 0 >_{-1}^0.5 =  0.0005787335752183923
Newton iteration   1energy = 0.239603704330855<A u 1 , A u 1 >_{-1}^0.5 =  1.46418233678702e-07
Newton iteration   2energy = 0.23960370433084424<A u 2 , A u 2 >_{-1}^0.5 =  1.0748221722086695e-14
t =  4.5
Newton iteration   0energy = 0.23960354006611378<A u 0 , A u 0 >_{-1}^0.5 =  0.0005677838859552262
Newton iteration   1energy = 0.2396033788781438<A u 1 , A u 1 >_{-1}^0.5 =  1.3999457887557826e-07
Newton iteration   2energy = 0.2396033788781339<A u 2 , A u 2 >_{-1}^0.5 =  9.755204030558368e-15
t =  4.6
Newton iteration   0energy = 0.2396032206475711<A u 0 , A u 0 >_{-1}^0.5 =  0.0005574715986071908
Newton iteration   1energy = 0.23960306526144695<A u 1 , A u 1 >_{-1}^0.5 =  1.3408107468246175e-07
Newton iteration   2energy = 0.23960306526143796<A u 2 , A u 2 >_{-1}^0.5 =  8.937102320550931e-15
t =  4.699999999999999
Newton iteration   0energy = 0.23960291261035707<A u 0 , A u 0 >_{-1}^0.5 =  0.0005477604304859817
Newton iteration   1energy = 0.2396027625906625<A u 1 , A u 1 >_{-1}^0.5 =  1.2863405340373862e-07
Newton iteration   2energy = 0.2396027625906542<A u 2 , A u 2 >_{-1}^0.5 =  8.133917206458277e-15
t =  4.799999999999999
Newton iteration   0energy = 0.23960261510190292<A u 0 , A u 0 >_{-1}^0.5 =  0.0005386168002506194
Newton iteration   1energy = 0.2396024700488202<A u 1 , A u 1 >_{-1}^0.5 =  1.2361423086153643e-07
Newton iteration   2energy = 0.23960247004881263<A u 2 , A u 2 >_{-1}^0.5 =  7.475563372220586e-15
t =  4.899999999999999
Newton iteration   0energy = 0.23960232733902043<A u 0 , A u 0 >_{-1}^0.5 =  0.0005300095661919587
Newton iteration   1energy = 0.2396021868848042<A u 1 , A u 1 >_{-1}^0.5 =  1.1898621269510796e-07
Newton iteration   2energy = 0.23960218688479706<A u 2 , A u 2 >_{-1}^0.5 =  6.923928011706675e-15
t =  4.999999999999998

Minimal energy extension (postscript in unit-2.1.3 )

$$u \in V^{ho,disc}, \quad u^{lo,cont} \in V^{lo,cont}, \quad \lambda \in V^{lo,disc},$$

from netgen.geom2d import unit_square
mesh = Mesh(unit_square.GenerateMesh(maxh=0.1))
fes_ho = Discontinuous(H1(mesh, order=10))
fes_lo = H1(mesh, order=1, dirichlet=".*")
fes_lam = Discontinuous(H1(mesh, order=1))
fes = FESpace([fes_ho, fes_lo, fes_lam])
uho, ulo, lam = fes.TrialFunction()

$$\int_{\Omega} \frac12 \Vert \nabla u \Vert^2 - u + \sum_T \sum_{V \in V(T)} ((u-u^{lo})\cdot \lambda)|_{V} \longrightarrow \operatorname{min}!$$

a = BilinearForm(fes)
a += Variation(0.5 * grad(uho)*grad(uho)*dx
               - 1*uho*dx
               + (uho-ulo)*lam*dx(element_vb=BBND))
gfu = GridFunction(fes)
solvers.Newton(a=a, u=gfu)
Draw(gfu.components[0])

Newton iteration  0
err =  0.3939295546929309
Newton iteration  1
err =  3.930938818539888e-15

The minimization problem is solved by the solution of the PDE:

$$\int_{\Omega} \nabla u \cdot \nabla v = \int_{\Omega} 1 \cdot v \quad \forall ~ v \in V^{ho,disc}$$

under the constraint

$$u(v) = u^{lo}(v) \quad \text{ for all vertices } v \in V(T) \text{ for all } T.$$