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]:
(39, 56)
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]:
133
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'
| dirichlet_bbnd: regexpr
| Regular expression string defining the dirichlet bboundary,
| i.e. points in 2D and edges in 3D.
| More than one boundary can be combined by the | operator,
| i.e.: dirichlet_bbnd = '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
|
| loembedding
|
| 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
0.00888574
0.00633333
0.00074628
0.00399953
0.00769352
0.0104008
0.0115294
0.0150217
0.0167909
0.015258
0.0182768
0.0211091
0.0106045
0.00711336
0.00320035
0.000735854
0.000876249
0.000529403
0.00282218
0.0124495
0.0182096
0.0224435
0.0204234
0.0317338
0.0270543
0.0291603
0.0187131
0.0217393
0.00854715
0.00505989
0.0038006
0.00883394
0.0205505
0.0163797
0.0213793
0.0150785
0.0170279
0.0191555
-6.66667e-05
-3.33333e-05
-0.000526369
-0.000575033
-0.00109143
-0.0008
-0.000766667
-8.08556e-05
-2.24397e-05
-0.000120589
-0.000249038
-0.000218716
-0.000440093
-0.000380259
-0.000572665
-0.000711098
-0.000487162
-0.00080946
-0.000916707
-0.000914728
-0.000944161
-0.000759221
-0.00110619
-0.00127157
-0.000646306
-0.0014197
-0.00131979
-0.000648788
-0.00123697
-0.0012392
-0.0015957
-0.00146355
-0.000469258
-0.0014082
-0.00106589
-0.000437144
-0.000880349
-0.000856527
-0.000190932
-0.000699086
-0.000461922
-0.000315546
-0.000220954
-1.64401e-05
-9.82846e-05
-8.35917e-05
-2.64702e-05
-9.73025e-05
-0.000122662
-2.64702e-05
-0.000105881
-0.000353264
-0.00021487
-0.00066398
-0.000468351
-0.00059592
-0.000843865
-0.000796408
-0.000722285
-0.000922806
-0.00105484
-0.000955488
-0.00104202
-0.00117171
-0.00100951
-0.000963748
-0.00114996
-0.000965717
-0.00092025
-0.00104152
-0.00098591
-0.000825307
-0.000865806
-0.000574259
-0.000880372
-0.000710639
-0.000885225
-0.000308496
-0.000477574
-0.000191583
-0.00032424
-0.000250767
-0.000328592
-0.000559968
-0.00047995
-0.000773918
-0.00082872
-0.000774775
-0.000675938
-0.000761632
-0.000801479
-0.000841885
-0.000775647
-0.000743459
[9]:
print(a.mat)
Row 0: 0: 1
Row 1: 1: 0.828441
Row 2: 2: 1
Row 3: 3: 0.870927
Row 4: 0: -0.5 4: 1.88347
Row 5: 4: -0.397227 5: 1.77564
Row 6: 5: -0.326749 6: 1.7517
Row 7: 1: -0.208968 6: -0.273913 7: 1.82559
Row 8: 1: -0.209694 8: 1.8809
Row 9: 8: -0.350939 9: 1.74429
Row 10: 9: -0.262838 10: 1.77715
Row 11: 2: -0.5 10: -0.267845 11: 1.9829
Row 12: 2: -0.5 11: -0.115438 12: 1.81266
Row 13: 12: -0.253469 13: 1.79007
Row 14: 13: -0.404897 14: 1.83152
Row 15: 3: -0.344377 14: -0.218833 15: 1.78023
Row 16: 3: -0.336878 16: 1.81347
Row 17: 16: -0.20561 17: 1.94288
Row 18: 17: -0.368349 18: 2.04376
Row 19: 0: -0.5 4: -0.177276 18: -0.553239 19: 1.87497
Row 20: 4: -0.808965 5: -0.345183 19: -0.545937 20: 3.54246
Row 21: 5: -0.706484 6: -0.432506 20: -0.647227 21: 3.50609
Row 22: 6: -0.718531 7: -0.374026 21: -0.571505 22: 3.51428
Row 23: 1: -0.40978 7: -0.968685 8: -1.05698 22: -0.708085 23: 3.76596
Row 24: 8: -0.263291 9: -0.64648 22: -0.536887 23: -0.62243 24: 3.433
Row 25: 9: -0.484029 10: -0.84644 24: -0.459506 25: 3.57375
Row 26: 10: -0.400025 11: -1.09961 12: -0.239874 25: -0.517151 26: 3.71385
Row 27: 12: -0.703881 13: -0.775929 26: -0.788273 27: 3.68527
Row 28: 13: -0.355771 14: -0.309609 27: -0.733256 28: 3.48151
Row 29: 14: -0.898185 15: -0.432178 28: -0.790531 29: 3.74275
Row 30: 3: -0.189673 15: -0.784846 16: -0.908731 29: -0.98463 30: 3.81689
Row 31: 16: -0.36225 17: -1.16439 30: -0.851669 31: 3.85451
Row 32: 17: -0.204537 18: -1.12218 19: -0.098519 20: -0.584699 31: -0.517495 32: 3.69368
Row 33: 21: -0.714154 22: -0.60525 24: -0.354764 33: 3.57925
Row 34: 20: -0.610448 21: -0.43421 32: -0.800343 33: -0.624553 34: 3.5401
Row 35: 25: -0.379385 26: -0.66891 27: -0.683932 28: -0.449095 35: 3.53739
Row 36: 28: -0.434461 29: -0.637229 30: -0.0973365 31: -0.958711 32: -0.365907 34: -0.341534 36: 3.57061
Row 37: 24: -0.549644 25: -0.887236 33: -0.928035 35: -0.674877 37: 3.68681
Row 38: 28: -0.408789 33: -0.352491 34: -0.729009 35: -0.68119 36: -0.735427 37: -0.64702 38: 3.55392
Row 39: 0: -0.0833333 4: 0 19: 0.0833333 39: 0.0416667
Row 40: 0: -0.0833333 4: 0.0833333 19: 0 39: 1.73472e-18 40: 0.0416667
Row 41: 1: -0.0340869 7: -0.0835417 23: 0.117629 41: 0.0381141
Row 42: 1: -0.0342097 8: -0.0831255 23: 0.117335 42: 0.038071
Row 43: 1: -0.069777 7: 0.11837 8: 0.118074 23: -0.166667 41: -0.0208854 42: -0.0207814 43: 0.0761852
Row 44: 2: -0.0833333 11: 0 12: 0.0833333 44: 0.0416667
Row 45: 2: -0.0833333 11: 0.0833333 12: 0 44: 0 45: 0.0416667
Row 46: 3: -0.0173948 15: -0.0795022 30: 0.096897 46: 0.0385733
Row 47: 3: -0.0142173 16: -0.0873491 30: 0.101566 47: 0.0394282
Row 48: 3: -0.113542 15: 0.136898 16: 0.143495 30: -0.166851 46: -0.0198756 47: -0.0218373 48: 0.0780015
Row 49: 4: -0.0535736 5: -0.028366 20: 0.0819397 49: 0.037036
Row 50: 0: 0.166667 4: -0.164587 19: -0.124342 20: 0.122262 39: -0.0208333 40: -0.0208333 50: 0.0796187
Row 51: 4: -0.0957505 5: 0.0945705 19: 0.0705543 20: -0.0693744 49: -0.00709151 50: -0.0102521 51: 0.0749881
Row 52: 5: -0.0526905 6: -0.0380314 21: 0.0907219 52: 0.036295
Row 53: 4: 0.119778 5: -0.131261 20: -0.10714 21: 0.118623 49: -0.0133934 51: -0.0165511 53: 0.073983
Row 54: 5: -0.0836226 6: 0.0924896 20: 0.082731 21: -0.091598 52: -0.00950784 53: -0.0133916 54: 0.073242
Row 55: 6: -0.0573097 7: -0.0420363 22: 0.099346 55: 0.0362495
Row 56: 5: 0.107149 6: -0.116904 21: -0.102619 22: 0.112374 52: -0.0131726 54: -0.0136146 56: 0.0729017
Row 57: 6: -0.0797051 7: 0.0876885 21: 0.0839811 22: -0.0919644 55: -0.0105091 56: -0.012482 57: 0.0728562
Row 58: 6: 0.102962 7: -0.123558 22: -0.111917 23: 0.132513 55: -0.0143274 57: -0.011413 58: 0.0744532
Row 59: 1: 0.0689149 7: -0.0551294 22: 0.0749089 23: -0.0886944 41: -0.00852172 43: -0.008707 58: -0.0136519 59: 0.0763178
Row 60: 8: -0.0322109 9: -0.0557926 24: 0.0880035 60: 0.0366233
Row 61: 1: 0.0691587 8: -0.0466199 23: -0.0901615 24: 0.0676228 42: -0.00855243 43: -0.00873724 61: 0.078236
Row 62: 8: -0.151527 9: 0.114282 23: 0.148989 24: -0.111744 60: -0.0139482 61: -0.013988 62: 0.0767883
Row 63: 9: -0.0342301 10: -0.0697744 25: 0.104004 63: 0.0369527
Row 64: 8: 0.0907008 9: -0.104931 24: -0.0782661 25: 0.0924966 60: -0.00805273 62: -0.0146225 64: 0.072736
Row 65: 9: -0.0957605 10: 0.113581 24: 0.0980093 25: -0.11583 63: -0.0174436 64: -0.0115138 65: 0.0730654
Row 66: 10: -0.0327463 11: -0.0708467 26: 0.103593 66: 0.0370585
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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
0.0923044
0
0
0
0
0
0
0
0
0.0578972
0.0863393
0.0954128
0.0944891
0.0888235
0.0780439
0.059628
0.0330628
0.0374521
0.0370446
0.0317995
0.0185123
0.0383632
0.0427969
0.047351
0.0760518
0.0895602
0.0939297
0.0914143
0.0833171
0.0654761
0.0574569
0.0647326
0.0723792
0.0852186
0.0626708
0.0776805
0
-0.00576774
0
0
0.0208108
0
-0.0350847
0.00263379
-0.00729372
-0.0027615
0
-0.00993549
-0.00711876
0
-0.0174982
-0.0120617
0
-0.0150936
-0.0195578
-0.00638541
-0.0213554
0
-0.0254715
-0.00955261
0
-0.0381111
-0.0132127
0
-0.0262138
-0.0182002
-0.0333693
-0.0245117
-0.0242838
-0.00451911
-0.0119297
-0.014536
-0.00612786
-0.0105674
-0.00558557
-0.00891829
-0.00493114
-0.0051195
-0.00519767
-0.007602
0.00247896
-0.00133557
-0.00800354
0.00157024
-0.00177994
-0.00829596
0.00374357
0.00436653
-0.00759115
-0.00373981
-0.0120787
-0.0104187
-0.00708368
-0.0136752
-0.0120743
-0.00778966
-0.0256197
-0.0072408
-0.00331602
-0.00900117
-0.0206949
-0.0050238
-0.00300073
-0.0140407
-0.0179806
-0.0153171
-0.020859
-0.0164647
-0.00404961
-0.00810738
-0.0130797
-0.0135373
-0.00892006
-0.00206078
-0.00747051
-0.00532125
-0.00675915
-0.00966483
-0.00121964
-0.00276467
-0.0111685
-0.00868831
-0.0118313
-0.00814322
-0.0124053
-0.0120342
-0.00417412
-0.0154546
-0.00866456
-0.010265
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).