This page was generated from unit-1.1-poisson/poisson.ipynb.
1.1 First NGSolve example¶
Let us solve the Poisson problem of finding \(u\) satisfying
\[\begin{split}\begin{aligned}
-\Delta u & = f && \text { in the unit square},
\\
u & = 0 && \text{ on the bottom and right parts of the boundary},
\\
\frac{\partial u }{\partial n } & = 0
&& \text{ on the remaining boundary parts}.
\end{aligned}\end{split}\]
Quick steps to solution:¶
1. Import NGSolve and Netgen Python modules:¶
[1]:
import netgen.gui
from ngsolve import *
from netgen.geom2d import unit_square
2. Generate an unstructured mesh¶
[2]:
mesh = Mesh(unit_square.GenerateMesh(maxh=0.2))
mesh.nv, mesh.ne # number of vertices & elements
[2]:
(38, 54)
Here we prescribed a maximal mesh-size of 0.2 using the
maxhflag.The mesh can be viewed by switching to the
Meshtab in the Netgen GUI.
3. Declare a finite element space:¶
[3]:
fes = H1(mesh, order=2, dirichlet="bottom|right")
fes.ndof # number of unknowns in this space
[3]:
129
Python’s help system displays further documentation.
[4]:
help(fes)
Help on H1 in module ngsolve.comp object:
class H1(FESpace)
| An H1-conforming finite element space.
|
| The H1 finite element space consists of continuous and
| elemenet-wise polynomial functions. It uses a hierarchical (=modal)
| basis built from integrated Legendre polynomials on tensor-product elements,
| and Jaboci polynomials on simplicial elements.
|
| Boundary values are well defined. The function can be used directly on the
| boundary, using the trace operator is optional.
|
| The H1 space supports variable order, which can be set individually for edges,
| faces and cells.
|
| Internal degrees of freedom are declared as local dofs and are eliminated
| if static condensation is on.
|
| The wirebasket consists of all vertex dofs. Optionally, one can include the
| first (the quadratic bubble) edge basis function, or all edge basis functions
| into the wirebasket.
|
| Keyword arguments can be:
| order: int = 1
| order of finite element space
| complex: bool = False
| Set if FESpace should be complex
| dirichlet: regexpr
| Regular expression string defining the dirichlet boundary.
| More than one boundary can be combined by the | operator,
| i.e.: dirichlet = 'top|right'
| definedon: Region or regexpr
| FESpace is only defined on specific Region, created with mesh.Materials('regexpr')
| or mesh.Boundaries('regexpr'). If given a regexpr, the region is assumed to be
| mesh.Materials('regexpr').
| dim: int = 1
| Create multi dimensional FESpace (i.e. [H1]^3)
| dgjumps: bool = False
| Enable discontinuous space for DG methods, this flag is needed for DG methods,
| since the dofs have a different coupling then and this changes the sparsity
| pattern of matrices.
| low_order_space: bool = True
| Generate a lowest order space together with the high-order space,
| needed for some preconditioners.
| order_policy: ORDER_POLICY = ORDER_POLICY.OLDSTYLE
| CONSTANT .. use the same fixed order for all elements,
| NODAL ..... use the same order for nodes of same shape,
| VARIBLE ... use an individual order for each edge, face and cell,
| OLDSTYLE .. as it used to be for the last decade
| wb_withedges: bool = true(3D) / false(2D)
| use lowest-order edge dofs for BDDC wirebasket
| wb_fulledges: bool = false
| use all edge dofs for BDDC wirebasket
|
| Method resolution order:
| H1
| FESpace
| NGS_Object
| pybind11_builtins.pybind11_object
| builtins.object
|
| Methods defined here:
|
| __getstate__(...)
| __getstate__(self: ngsolve.comp.FESpace) -> tuple
|
| __init__(...)
| __init__(self: ngsolve.comp.H1, mesh: ngsolve.comp.Mesh, autoupdate: bool = False, **kwargs) -> None
|
| __setstate__(...)
| __setstate__(self: ngsolve.comp.H1, arg0: tuple) -> None
|
| ----------------------------------------------------------------------
| Static methods defined here:
|
| __flags_doc__(...) from builtins.PyCapsule
| __flags_doc__() -> dict
|
| ----------------------------------------------------------------------
| Data descriptors defined here:
|
| __dict__
|
| ----------------------------------------------------------------------
| Methods inherited from FESpace:
|
| ApplyM(...)
| ApplyM(self: ngsolve.comp.FESpace, vec: ngsolve.la.BaseVector, rho: ngsolve.fem.CoefficientFunction = None, definedon: ngsolve.comp.Region = None) -> None
|
| Apply mass-matrix. Available only for L2-like spaces
|
| ConvertL2Operator(...)
| ConvertL2Operator(self: ngsolve.comp.FESpace, l2space: ngsolve.comp.FESpace) -> ngsolve.la.BaseMatrix
|
| CouplingType(...)
| CouplingType(self: ngsolve.comp.FESpace, dofnr: int) -> ngsolve.comp.COUPLING_TYPE
|
|
| Get coupling type of a degree of freedom.
|
| Parameters:
|
| dofnr : int
| input dof number
|
| Elements(...)
| Elements(self: ngsolve.comp.FESpace, VOL_or_BND: ngsolve.comp.VorB = VorB.VOL) -> ngsolve.comp.FESpaceElementRange
|
|
| Returns an iterable range of elements.
|
| Parameters:
|
| VOL_or_BND : ngsolve.comp.VorB
| input VOL, BND, BBND,...
|
| FinalizeUpdate(...)
| FinalizeUpdate(self: ngsolve.comp.FESpace) -> None
|
| finalize update
|
| FreeDofs(...)
| FreeDofs(self: ngsolve.comp.FESpace, coupling: bool = False) -> pyngcore.BitArray
|
|
|
| Return BitArray of free (non-Dirichlet) dofs\n
| coupling=False ... all free dofs including local dofs\n
| coupling=True .... only element-boundary free dofs
|
| Parameters:
|
| coupling : bool
| input coupling
|
| GetDofNrs(...)
| GetDofNrs(*args, **kwargs)
| Overloaded function.
|
| 1. GetDofNrs(self: ngsolve.comp.FESpace, ei: ngsolve.comp.ElementId) -> tuple
|
|
|
| Parameters:
|
| ei : ngsolve.comp.ElementId
| input element id
|
|
|
| 2. GetDofNrs(self: ngsolve.comp.FESpace, ni: ngsolve.comp.NodeId) -> tuple
|
|
|
| Parameters:
|
| ni : ngsolve.comp.NodeId
| input node id
|
| GetDofs(...)
| GetDofs(self: ngsolve.comp.FESpace, region: ngsolve.comp.Region) -> pyngcore.BitArray
|
|
| Returns all degrees of freedom in given region.
|
| Parameters:
|
| region : ngsolve.comp.Region
| input region
|
| GetFE(...)
| GetFE(self: ngsolve.comp.FESpace, ei: ngsolve.comp.ElementId) -> object
|
|
| Get the finite element to corresponding element id.
|
| Parameters:
|
| ei : ngsolve.comp.ElementId
| input element id
|
| GetOrder(...)
| GetOrder(self: ngsolve.comp.FESpace, nodeid: ngsolve.comp.NodeId) -> int
|
| return order of node.
| by now, only isotropic order is supported here
|
| GetTrace(...)
| GetTrace(self: ngsolve.comp.FESpace, arg0: ngsolve.comp.FESpace, arg1: ngsolve.la.BaseVector, arg2: ngsolve.la.BaseVector, arg3: bool) -> None
|
| GetTraceTrans(...)
| GetTraceTrans(self: ngsolve.comp.FESpace, arg0: ngsolve.comp.FESpace, arg1: ngsolve.la.BaseVector, arg2: ngsolve.la.BaseVector, arg3: bool) -> None
|
| HideAllDofs(...)
| HideAllDofs(self: ngsolve.comp.FESpace, component: object = <ngsolve.ngstd.DummyArgument>) -> None
|
| set all visible coupling types to HIDDEN_DOFs (will be overwritten by any Update())
|
| InvM(...)
| InvM(self: ngsolve.comp.FESpace, rho: ngsolve.fem.CoefficientFunction = None) -> ngsolve.la.BaseMatrix
|
| Mass(...)
| Mass(self: ngsolve.comp.FESpace, rho: ngsolve.fem.CoefficientFunction = None, definedon: Optional[ngsolve.comp.Region] = None) -> ngsolve.la.BaseMatrix
|
| ParallelDofs(...)
| ParallelDofs(self: ngsolve.comp.FESpace) -> ngsolve.la.ParallelDofs
|
| Return dof-identification for MPI-distributed meshes
|
| Prolongation(...)
| Prolongation(self: ngsolve.comp.FESpace) -> ngmg::Prolongation
|
| Return prolongation operator for use in multi-grid
|
| Range(...)
| Range(self: ngsolve.comp.FESpace, component: int) -> ngsolve.ngstd.IntRange
|
|
| Return interval of dofs of a component of a product space.
|
| Parameters:
|
| component : int
| input component
|
| SetCouplingType(...)
| SetCouplingType(*args, **kwargs)
| Overloaded function.
|
| 1. SetCouplingType(self: ngsolve.comp.FESpace, dofnr: int, coupling_type: ngsolve.comp.COUPLING_TYPE) -> None
|
|
| Set coupling type of a degree of freedom.
|
| Parameters:
|
| dofnr : int
| input dof number
|
| coupling_type : ngsolve.comp.COUPLING_TYPE
| input coupling type
|
|
|
| 2. SetCouplingType(self: ngsolve.comp.FESpace, dofnrs: ngsolve.ngstd.IntRange, coupling_type: ngsolve.comp.COUPLING_TYPE) -> None
|
|
| Set coupling type for interval of dofs.
|
| Parameters:
|
| dofnrs : Range
| range of dofs
|
| coupling_type : ngsolve.comp.COUPLING_TYPE
| input coupling type
|
| SetDefinedOn(...)
| SetDefinedOn(self: ngsolve.comp.FESpace, region: ngsolve.comp.Region) -> None
|
|
| Set the regions on which the FESpace is defined.
|
| Parameters:
|
| region : ngsolve.comp.Region
| input region
|
| SetOrder(...)
| SetOrder(*args, **kwargs)
| Overloaded function.
|
| 1. SetOrder(self: ngsolve.comp.FESpace, element_type: ngsolve.fem.ET, order: int) -> None
|
|
|
| Parameters:
|
| element_type : ngsolve.fem.ET
| input element type
|
| order : object
| input polynomial order
|
|
| 2. SetOrder(self: ngsolve.comp.FESpace, nodeid: ngsolve.comp.NodeId, order: int) -> None
|
|
|
| Parameters:
|
| nodeid : ngsolve.comp.NodeId
| input node id
|
| order : int
| input polynomial order
|
| SolveM(...)
| SolveM(self: ngsolve.comp.FESpace, vec: ngsolve.la.BaseVector, rho: ngsolve.fem.CoefficientFunction = None, definedon: ngsolve.comp.Region = None) -> None
|
|
| Solve with the mass-matrix. Available only for L2-like spaces.
|
| Parameters:
|
| vec : ngsolve.la.BaseVector
| input right hand side vector
|
| rho : ngsolve.fem.CoefficientFunction
| input CF
|
| TestFunction(...)
| TestFunction(self: ngsolve.comp.FESpace) -> object
|
| Return a proxy to be used as a testfunction for :any:`Symbolic Integrators<symbolic-integrators>`
|
| TnT(...)
| TnT(self: ngsolve.comp.FESpace) -> Tuple[object, object]
|
| Return a tuple of trial and testfunction
|
| TraceOperator(...)
| TraceOperator(self: ngsolve.comp.FESpace, tracespace: ngsolve.comp.FESpace, average: bool) -> ngsolve.la.BaseMatrix
|
| TrialFunction(...)
| TrialFunction(self: ngsolve.comp.FESpace) -> object
|
| Return a proxy to be used as a trialfunction in :any:`Symbolic Integrators<symbolic-integrators>`
|
| Update(...)
| Update(self: ngsolve.comp.FESpace) -> None
|
| update space after mesh-refinement
|
| UpdateDofTables(...)
| UpdateDofTables(self: ngsolve.comp.FESpace) -> None
|
| update dof-tables after changing polynomial order distribution
|
| __eq__(...)
| __eq__(self: ngsolve.comp.FESpace, space: ngsolve.comp.FESpace) -> bool
|
| __str__(...)
| __str__(self: ngsolve.comp.FESpace) -> str
|
| __timing__(...)
| __timing__(self: ngsolve.comp.FESpace) -> object
|
| ----------------------------------------------------------------------
| Static methods inherited from FESpace:
|
| __special_treated_flags__(...) from builtins.PyCapsule
| __special_treated_flags__() -> dict
|
| ----------------------------------------------------------------------
| Data descriptors inherited from FESpace:
|
| components
| Return a list of the components of a product space
|
| couplingtype
|
| dim
| multi-dim of FESpace
|
| globalorder
| query global order of space
|
| is_complex
|
| lospace
|
| mesh
| mesh on which the FESpace is created
|
| ndof
| number of degrees of freedom
|
| ndofglobal
| global number of dofs on MPI-distributed mesh
|
| type
| type of finite element space
|
| ----------------------------------------------------------------------
| Data descriptors inherited from NGS_Object:
|
| __memory__
|
| name
|
| ----------------------------------------------------------------------
| Methods inherited from pybind11_builtins.pybind11_object:
|
| __new__(*args, **kwargs) from pybind11_builtins.pybind11_type
| Create and return a new object. See help(type) for accurate signature.
4. Declare test function, trial function, and grid function¶
Test and trial function are symbolic objects - called
ProxyFunctions- that help you construct bilinear forms (and have no space to hold solutions).GridFunctions, on the other hand, represent functions in the finite element space and contains memory to hold coefficient vectors.
[5]:
u = fes.TrialFunction() # symbolic object
v = fes.TestFunction() # symbolic object
gfu = GridFunction(fes) # solution
Alternately, you can get both the trial and test variables at once:
[6]:
u, v = fes.TnT()
5. Define and assemble linear and bilinear forms:¶
[7]:
a = BilinearForm(fes, symmetric=True)
a += grad(u)*grad(v)*dx
a.Assemble()
f = LinearForm(fes)
f += x*v*dx
f.Assemble()
You can examine the linear system in more detail:
[8]:
print(f.vec)
0.000333333
0.00896813
0.00633333
0.000801205
0.00384743
0.00745274
0.010402
0.0116458
0.0153532
0.0173012
0.0155111
0.0182062
0.0206364
0.00967366
0.00782633
0.00429241
0.000385723
0.00214091
0.000471409
0.00255107
0.0114933
0.0179248
0.0228051
0.0207208
0.0328187
0.0278923
0.0289917
0.0175791
0.0185541
0.0135822
0.0054952
0.00674838
0.0216669
0.0154523
0.0216449
0.0112586
0.0184036
0.0228345
-6.66667e-05
-3.33333e-05
-0.000530412
-0.000581324
-0.00110125
-0.0008
-0.000766667
-9.53866e-05
-1.92861e-05
-0.000125689
-0.000236921
-0.000212375
-0.000419804
-0.000376692
-0.000547145
-0.00069263
-0.000491432
-0.000804894
-0.000920196
-0.000924592
-0.000954328
-0.000780634
-0.0011262
-0.00130465
-0.000667812
-0.00146005
-0.00136067
-0.000648932
-0.00126658
-0.00124969
-0.00158695
-0.00145486
-0.000449393
-0.0013689
-0.00101734
-0.000393375
-0.000808082
-0.000765005
-0.000262255
-0.000715978
-0.00059172
-0.000443981
-0.000285588
-1.92861e-05
-7.71446e-05
-2.35704e-05
-0.000153523
-0.000170177
-0.000275715
-2.35704e-05
-9.42817e-05
-0.000315732
-0.000180311
-0.000634821
-0.000397348
-0.00054224
-0.000851315
-0.000796378
-0.000696661
-0.000936411
-0.00108382
-0.000981779
-0.00106254
-0.0012218
-0.00105316
-0.0010168
-0.0011697
-0.00099108
-0.000964265
-0.00101041
-0.000992376
-0.000739054
-0.000821161
-0.000709278
-0.000850196
-0.000854996
-0.000375107
-0.00053044
-0.000747141
-0.000343662
-0.000448901
-0.000381786
-0.000808027
-0.000909199
-0.000867983
-0.000572495
-0.000794308
-0.00086756
-0.000885566
-0.000705928
-0.000841344
[9]:
print(a.mat)
Row 0: 0: 1
Row 1: 1: 0.828659
Row 2: 2: 1
Row 3: 3: 0.927121
Row 4: 0: -0.5 4: 1.89564
Row 5: 4: -0.368222 5: 1.76675
Row 6: 5: -0.323989 6: 1.75371
Row 7: 1: -0.215377 6: -0.28107 7: 1.83079
Row 8: 1: -0.216995 8: 1.89633
Row 9: 8: -0.370903 9: 1.74923
Row 10: 9: -0.28503 10: 1.77374
Row 11: 2: -0.5 10: -0.2708 11: 1.98742
Row 12: 2: -0.5 11: -0.107953 12: 1.8314
Row 13: 12: -0.226615 13: 1.75649
Row 14: 13: -0.340475 14: 1.75841
Row 15: 3: -0.430464 14: -0.405649 15: 1.80397
Row 16: 3: -0.40524 16: 2.07708
Row 17: 16: -0.357165 17: 1.76574
Row 18: 17: -0.4411 18: 2.03144
Row 19: 0: -0.5 4: -0.162559 18: -0.401142 19: 1.79475
Row 20: 4: -0.864858 5: -0.363931 19: -0.445914 20: 3.55639
Row 21: 5: -0.710604 6: -0.421297 20: -0.63885 21: 3.50636
Row 22: 6: -0.727351 7: -0.354504 21: -0.590012 22: 3.51941
Row 23: 1: -0.396287 7: -0.979835 8: -1.07358 22: -0.708758 23: 3.77912
Row 24: 8: -0.234858 9: -0.642955 22: -0.575333 23: -0.620659 24: 3.43908
Row 25: 9: -0.450342 10: -0.827115 24: -0.519524 25: 3.55949
Row 26: 10: -0.390798 11: -1.10866 12: -0.229033 25: -0.551848 26: 3.72126
Row 27: 12: -0.767794 13: -0.694967 26: -0.795614 27: 3.68173
Row 28: 13: -0.494437 14: -0.423252 27: -0.768236 28: 3.58147
Row 29: 14: -0.58903 15: -0.280159 28: -0.925237 29: 3.64107
Row 30: 3: -0.0914169 15: -0.687702 16: -1.31467 17: -0.291354 29: -0.918013 30: 3.88347
Row 31: 17: -0.167863 18: -1.1892 19: -0.285134 20: -0.656359 31: 3.78758
Row 32: 21: -0.721448 22: -0.56345 24: -0.348528 32: 3.65403
Row 33: 20: -0.586481 21: -0.424154 31: -0.727336 32: -0.714696 33: 3.50962
Row 34: 25: -0.359375 26: -0.645303 27: -0.655116 28: -0.505535 34: 3.53735
Row 35: 17: -0.508263 29: -0.60229 30: -0.580311 31: -0.761684 33: -0.427885 35: 3.51679
Row 36: 24: -0.497222 25: -0.851288 32: -1.05767 34: -0.787214 36: 3.74238
Row 37: 28: -0.464771 29: -0.326346 32: -0.248246 33: -0.629064 34: -0.584808 35: -0.636353 36: -0.54899 37: 3.43858
Row 38: 0: -0.0833333 4: 0 19: 0.0833333 38: 0.0416667
Row 39: 0: -0.0833333 4: 0.0833333 19: 0 38: 1.73472e-18 39: 0.0416667
Row 40: 1: -0.0328806 7: -0.0838095 23: 0.11669 40: 0.0381466
Row 41: 1: -0.0331673 8: -0.0828599 23: 0.116027 41: 0.0380482
Row 42: 1: -0.072062 7: 0.119706 8: 0.119026 23: -0.166669 40: -0.0209524 41: -0.020715 42: 0.0761948
Row 43: 2: -0.0833333 11: 0 12: 0.0833333 43: 0.0416667
Row 44: 2: -0.0833333 11: 0.0833333 12: 0 43: 0 44: 0.0416667
Row 45: 3: -0.0192424 15: -0.0611511 30: 0.0803935 45: 0.0380344
Row 46: 3: 0.00400625 16: -0.113562 30: 0.109556 46: 0.044274
Row 47: 3: -0.139284 15: 0.132895 16: 0.181102 30: -0.174713 45: -0.0152878 46: -0.0283905 47: 0.0823083
Row 48: 4: -0.0567722 5: -0.0292894 20: 0.0860616 48: 0.036858
Row 49: 0: 0.166667 4: -0.170704 19: -0.123322 20: 0.12736 38: -0.0208333 39: -0.0208333 49: 0.0802799
Row 50: 4: -0.0884634 5: 0.0906596 19: 0.0670821 20: -0.0692783 48: -0.00732235 49: -0.00999723 50: 0.0754712
Row 51: 5: -0.0548556 6: -0.0365843 21: 0.0914399 51: 0.0363595
Row 52: 4: 0.118142 5: -0.124949 20: -0.108911 21: 0.115717 48: -0.014193 50: -0.0153426 52: 0.0736287
Row 53: 5: -0.0853641 6: 0.0905825 20: 0.0835044 21: -0.0887229 51: -0.00914608 52: -0.0130346 53: 0.0731302
Row 54: 6: -0.0583949 7: -0.0399938 22: 0.0983887 54: 0.0363084
Row 55: 5: 0.108854 6: -0.116829 21: -0.104941 22: 0.112916 51: -0.0137139 53: -0.0134996 55: 0.0729964
Row 56: 6: -0.0804768 7: 0.0868387 21: 0.0837172 22: -0.0900791 54: -0.00999844 55: -0.0125213 56: 0.0729453
Row 57: 6: 0.10524 7: -0.126341 22: -0.113441 23: 0.134543 54: -0.0145987 56: -0.0117112 57: 0.0747167
Row 58: 1: 0.0687769 7: -0.0549866 22: 0.0741367 23: -0.087927 40: -0.00822015 42: -0.00897406 57: -0.0137616 58: 0.0765548
Row 59: 8: -0.0298036 9: -0.0556868 24: 0.0854904 59: 0.0368269
Row 60: 1: 0.069333 8: -0.0455052 23: -0.0905362 24: 0.0667084 41: -0.00829182 42: -0.00904144 60: 0.0787427
Row 61: 8: -0.157887 9: 0.117504 23: 0.153439 24: -0.113056 59: -0.0139217 60: -0.0143422 61: 0.0775214
Row 62: 9: -0.0313276 10: -0.0692128 25: 0.10054 62: 0.0370114
Row 63: 8: 0.0916208 9: -0.105547 24: -0.079105 25: 0.0930309 59: -0.0074509 61: -0.0154543 63: 0.0729527
Row 64: 9: -0.0989773 10: 0.116718 24: 0.100774 25: -0.118514 62: -0.0173032 63: -0.0123254 64: 0.0731372
Row 65: 10: -0.0314963 11: -0.0720729 26: 0.103569 65: 0.0371756
Row 66: 9: 0.0788326 10: -0.0811417 25: -0.0766521 26: 0.0789612 62: -0.00783189 64: -0.0118763 66: 0.0739116
Row 67: 10: -0.113773 11: 0.117206 25: 0.113964 26: -0.117397 65: -0.0180182 66: -0.0113311 67: 0.0740759
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6. Solve the system:¶
[10]:
gfu.vec.data = \
a.mat.Inverse(freedofs=fes.FreeDofs()) * f.vec
Draw(gfu)
The Dirichlet boundary condition constrains some degrees of freedom. The argument fes.FreeDofs() indicates that only the remaining "free" degrees of freedom should participate in the linear solve.
You can examine the coefficient vector of solution if needed:
[11]:
print(gfu.vec)
0
0
0
0.0923002
0
0
0
0
0
0
0
0
0.0578974
0.0863383
0.0954046
0.0944886
0.088851
0.0779859
0.0596329
0.0330695
0.0358778
0.0367923
0.0321534
0.0187666
0.039323
0.0440006
0.0473955
0.0754942
0.089345
0.0924018
0.0900675
0.0609401
0.0584553
0.0636311
0.0735012
0.0808489
0.0646725
0.0806824
0
-0.005753
0
0
0.0210629
0
-0.035086
0.00263586
-0.00722906
-0.0053199
0
-0.00990601
-0.00627918
0
-0.016323
-0.0118361
0
-0.0149549
-0.0195579
-0.00642189
-0.0212263
0
-0.025571
-0.0101959
0
-0.0393962
-0.0141925
0
-0.0275764
-0.0181556
-0.033372
-0.0244469
-0.0242966
-0.00443999
-0.0108775
-0.0146141
-0.0063948
-0.00774334
-0.00565315
-0.00909429
-0.00785633
-0.00847728
-0.00755551
-0.00774445
0.00263616
-0.00823406
-0.00507479
-0.00539107
0.00395556
-0.00824646
0.00366889
0.00416289
-0.00432812
-0.00340091
-0.00931158
-0.0100027
-0.00716045
-0.0135339
-0.0116171
-0.00788447
-0.0251341
-0.00768871
-0.00317827
-0.00903235
-0.0216162
-0.00597072
-0.0032929
-0.0141649
-0.0192129
-0.014382
-0.0219207
-0.0142459
-0.0043319
-0.00964124
-0.0103001
-0.0100999
-0.00227504
-0.00914321
-0.0102146
-0.00700589
-0.00179493
-0.00840332
-0.00865067
-0.0115504
-0.0105298
-0.00906982
-0.0131517
-0.00454235
-0.01852
-0.00882419
-0.0126031
Ways to interact with NGSolve¶
A jupyter notebook (like this one) gives you one way to interact with NGSolve. When you have a complex sequence of tasks to perform, the notebook may not be adequate.
You can write an entire python module in a text editor and call python on the command line. (A script of the above is provided in
poisson.py.)python3 poisson.py
If you want the Netgen GUI, then use
netgenon the command line:netgen poisson.py
You can then ask for a python shell from the GUI’s menu options (
Solve -> Python shell).