This page was generated from unit-5a.3-petsc/PETSc_interface.ipynb.

5.3.2 NGSolve - PETSc interface

We use the ngs2petsc interface to map vectors and matrices between NGSolve and PETSc

from ipyparallel import Client
c = Client(profile='mpi')
c.ids

[0, 1, 2, 3]

%%px
from ngsolve import *
from netgen.geom2d import unit_square
comm = MPI.COMM_WORLD
if comm.rank == 0:
    ngmesh = unit_square.GenerateMesh(maxh=0.1).Distribute(comm)
else:
    ngmesh = netgen.meshing.Mesh.Receive(comm)

for l in range(2):
    ngmesh.Refine()
mesh = Mesh(ngmesh)

The Python-module ngsolve.ngs2petsc provides functionality to transfer vectors and matrices between NGSolve and Python.

Make sure that the ipyparallel server can import the module, e.g. by starting the cluster in the current directory.

%%px
import ngsolve.ngs2petsc as n2p
import petsc4py.PETSc as psc

%%px
fes = H1(mesh, order=1, dirichlet="left|bottom")
u,v = fes.TnT()
a = BilinearForm(grad(u)*grad(v)*dx+u*v*ds).Assemble()
f = LinearForm(x*v*dx).Assemble()
gfu = GridFunction(fes)

The function CreatePETScMatrix takes an NGSolve matrix, and creates a PETSc matrix from it. A VectorMapping object can map vectors between NGSolve and PETSc.

%%px
psc_mat = n2p.CreatePETScMatrix(a.mat, fes.FreeDofs())
vecmap = n2p.VectorMapping (a.mat.row_pardofs, fes.FreeDofs())

Create PETSc-vectors fitting to the matrix

%%px
psc_f, psc_u = psc_mat.createVecs()
pass

setting up the parallel Krylov-space solver ….

%%px
ksp = psc.KSP()
ksp.create()
ksp.setOperators(psc_mat)
ksp.setType(psc.KSP.Type.CG)
ksp.setNormType(psc.KSP.NormType.NORM_NATURAL)
ksp.getPC().setType("gamg")
ksp.setTolerances(rtol=1e-6, atol=0, divtol=1e16, max_it=400)

moving vectors between NGSolve and PETSc, and solve:

%%px
vecmap.N2P(f.vec, psc_f)
ksp.solve(psc_f, psc_u)
vecmap.P2N(psc_u, gfu.vec)
pass

gfu = c[:]["gfu"]
from ngsolve.webgui import Draw

Draw (gfu[0])

BaseWebGuiScene

PETSc preconditioner for NGSolve

Next we create a PETSc preconditioner, and wrap it into an NGSolve preconditioner:

%%px
a = BilinearForm(grad(u)*grad(v)*dx+u*v*ds)
pre = Preconditioner(a, "gamg")
a.Assemble()
pass

and use it in an NGSolve - CGSolver:

%%px
from ngsolve.krylovspace import CGSolver
inv = CGSolver(a.mat, pre, printing=comm.rank==0)
gfu.vec.data = inv * f.vec

[stdout:0]
WARNING: printing is deprecated, use printrates instead!
CG iteration 1, residual = 0.16186373090106865
CG iteration 2, residual = 0.03225633463475834
CG iteration 3, residual = 0.00418734333654368
CG iteration 4, residual = 0.0005968449121709168
CG iteration 5, residual = 8.46191898805545e-05
CG iteration 6, residual = 1.0980502894984626e-05
CG iteration 7, residual = 1.6480728786493365e-06
CG iteration 8, residual = 2.0479915322434306e-07
CG iteration 9, residual = 2.615215383748639e-08
CG iteration 10, residual = 3.3832956106055766e-09
CG iteration 11, residual = 4.183121870187323e-10
CG iteration 12, residual = 5.703654006011637e-11
CG iteration 13, residual = 7.79793339014583e-12
CG iteration 14, residual = 9.331741996768944e-13
CG iteration 15, residual = 1.2343443410749943e-13

gfu = c[:]["gfu"]
Draw (gfu[0])

BaseWebGuiScene