def ngsolve_vector_array_factory(length, dim, seed):
if dim not in NGSOLVE_spaces:
mesh = ngmsh.Mesh(dim=1)
if dim > 0:
pids = []
for i in range(dim + 1):
pids.append(
mesh.Add(ngmsh.MeshPoint(ngmsh.Pnt(i / dim, 0, 0))))
for i in range(dim):
mesh.Add(ngmsh.Element1D([pids[i], pids[i + 1]], index=1))
NGSOLVE_spaces[dim] = NGSolveVectorSpace(
ngs.L2(ngs.Mesh(mesh), order=0))
U = NGSOLVE_spaces[dim].zeros(length)
np.random.seed(seed)
for v, a in zip(U._list, np.random.random((length, dim))):
v.to_numpy()[:] = a
if np.random.randint(2):
UU = NGSOLVE_spaces[dim].zeros(length)
for v, a in zip(UU._list, np.random.random((length, dim))):
v.real_part.to_numpy()[:] = a
for u, uu in zip(U._list, UU._list):
u.imag_part = uu.real_part
return U
def _create_ngsolve_space(dim):
if dim not in _NGSOLVE_spaces:
mesh = ngmsh.Mesh(dim=1)
if dim > 0:
pids = []
for i in range(dim + 1):
pids.append(mesh.Add(ngmsh.MeshPoint(ngmsh.Pnt(i / dim, 0, 0))))
for i in range(dim):
mesh.Add(ngmsh.Element1D([pids[i], pids[i + 1]], index=1))
_NGSOLVE_spaces[dim] = NGSolveVectorSpace(ngs.L2(ngs.Mesh(mesh), order=0))
return _NGSOLVE_spaces[dim]
def discretize_ngsolve():
from ngsolve import (ngsglobals, Mesh, H1, CoefficientFunction, LinearForm,
SymbolicLFI, BilinearForm, SymbolicBFI, grad,
TaskManager)
from netgen.csg import CSGeometry, OrthoBrick, Pnt
import numpy as np
ngsglobals.msg_level = 1
geo = CSGeometry()
obox = OrthoBrick(Pnt(-1, -1, -1), Pnt(1, 1, 1)).bc("outer")
b = []
b.append(
OrthoBrick(Pnt(-1, -1, -1), Pnt(0.0, 0.0,
0.0)).mat("mat1").bc("inner"))
b.append(
OrthoBrick(Pnt(-1, 0, -1), Pnt(0.0, 1.0, 0.0)).mat("mat2").bc("inner"))
b.append(
OrthoBrick(Pnt(0, -1, -1), Pnt(1.0, 0.0, 0.0)).mat("mat3").bc("inner"))
b.append(
OrthoBrick(Pnt(0, 0, -1), Pnt(1.0, 1.0, 0.0)).mat("mat4").bc("inner"))
b.append(
OrthoBrick(Pnt(-1, -1, 0), Pnt(0.0, 0.0, 1.0)).mat("mat5").bc("inner"))
b.append(
OrthoBrick(Pnt(-1, 0, 0), Pnt(0.0, 1.0, 1.0)).mat("mat6").bc("inner"))
b.append(
OrthoBrick(Pnt(0, -1, 0), Pnt(1.0, 0.0, 1.0)).mat("mat7").bc("inner"))
b.append(
OrthoBrick(Pnt(0, 0, 0), Pnt(1.0, 1.0, 1.0)).mat("mat8").bc("inner"))
box = (obox - b[0] - b[1] - b[2] - b[3] - b[4] - b[5] - b[6] - b[7])
geo.Add(box)
for bi in b:
geo.Add(bi)
# domain 0 is empty!
mesh = Mesh(geo.GenerateMesh(maxh=0.3))
# H1-conforming finite element space
V = H1(mesh, order=NGS_ORDER, dirichlet="outer")
v = V.TestFunction()
u = V.TrialFunction()
# Coeff as array: variable coefficient function (one CoefFct. per domain):
sourcefct = CoefficientFunction([1 for i in range(9)])
with TaskManager():
# the right hand side
f = LinearForm(V)
f += SymbolicLFI(sourcefct * v)
f.Assemble()
# the bilinear-form
mats = []
coeffs = [[0, 1, 0, 0, 0, 0, 0, 0, 1], [0, 0, 1, 0, 0, 0, 0, 1, 0],
[0, 0, 0, 1, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 1, 0, 0, 0]]
for c in coeffs:
diffusion = CoefficientFunction(c)
a = BilinearForm(V, symmetric=False)
a += SymbolicBFI(diffusion * grad(u) * grad(v),
definedon=(np.where(np.array(c) == 1)[0] +
1).tolist())
a.Assemble()
mats.append(a.mat)
from pymor.bindings.ngsolve import NGSolveVectorSpace, NGSolveMatrixOperator, NGSolveVisualizer
space = NGSolveVectorSpace(V)
op = LincombOperator(
[NGSolveMatrixOperator(m, space, space) for m in mats], [
ProjectionParameterFunctional('diffusion', (len(coeffs), ), (i, ))
for i in range(len(coeffs))
])
h1_0_op = op.assemble([1] * len(coeffs)).with_(name='h1_0_semi')
F = space.zeros()
F._list[0].real_part.impl.vec.data = f.vec
F = VectorOperator(F)
return StationaryModel(op,
F,
visualizer=NGSolveVisualizer(mesh, V),
products={'h1_0_semi': h1_0_op},
parameter_space=CubicParameterSpace(
op.parameter_type, 0.1, 1.))
def discretize_ngsolve():
from ngsolve import (ngsglobals, Mesh, H1, CoefficientFunction, LinearForm, SymbolicLFI,
BilinearForm, SymbolicBFI, grad, TaskManager)
from netgen.csg import CSGeometry, OrthoBrick, Pnt
import numpy as np
ngsglobals.msg_level = 1
geo = CSGeometry()
obox = OrthoBrick(Pnt(-1, -1, -1), Pnt(1, 1, 1)).bc("outer")
b = []
b.append(OrthoBrick(Pnt(-1, -1, -1), Pnt(0.0, 0.0, 0.0)).mat("mat1").bc("inner"))
b.append(OrthoBrick(Pnt(-1, 0, -1), Pnt(0.0, 1.0, 0.0)).mat("mat2").bc("inner"))
b.append(OrthoBrick(Pnt(0, -1, -1), Pnt(1.0, 0.0, 0.0)).mat("mat3").bc("inner"))
b.append(OrthoBrick(Pnt(0, 0, -1), Pnt(1.0, 1.0, 0.0)).mat("mat4").bc("inner"))
b.append(OrthoBrick(Pnt(-1, -1, 0), Pnt(0.0, 0.0, 1.0)).mat("mat5").bc("inner"))
b.append(OrthoBrick(Pnt(-1, 0, 0), Pnt(0.0, 1.0, 1.0)).mat("mat6").bc("inner"))
b.append(OrthoBrick(Pnt(0, -1, 0), Pnt(1.0, 0.0, 1.0)).mat("mat7").bc("inner"))
b.append(OrthoBrick(Pnt(0, 0, 0), Pnt(1.0, 1.0, 1.0)).mat("mat8").bc("inner"))
box = (obox - b[0] - b[1] - b[2] - b[3] - b[4] - b[5] - b[6] - b[7])
geo.Add(box)
for bi in b:
geo.Add(bi)
# domain 0 is empty!
mesh = Mesh(geo.GenerateMesh(maxh=0.3))
# H1-conforming finite element space
V = H1(mesh, order=NGS_ORDER, dirichlet="outer")
v = V.TestFunction()
u = V.TrialFunction()
# Coeff as array: variable coefficient function (one CoefFct. per domain):
sourcefct = CoefficientFunction([1 for i in range(9)])
with TaskManager():
# the right hand side
f = LinearForm(V)
f += SymbolicLFI(sourcefct * v)
f.Assemble()
# the bilinear-form
mats = []
coeffs = [[0, 1, 0, 0, 0, 0, 0, 0, 1],
[0, 0, 1, 0, 0, 0, 0, 1, 0],
[0, 0, 0, 1, 0, 0, 1, 0, 0],
[0, 0, 0, 0, 1, 1, 0, 0, 0]]
for c in coeffs:
diffusion = CoefficientFunction(c)
a = BilinearForm(V, symmetric=False)
a += SymbolicBFI(diffusion * grad(u) * grad(v), definedon=(np.where(np.array(c) == 1)[0] + 1).tolist())
a.Assemble()
mats.append(a.mat)
from pymor.bindings.ngsolve import NGSolveVectorSpace, NGSolveMatrixOperator, NGSolveVisualizer
space = NGSolveVectorSpace(V)
op = LincombOperator([NGSolveMatrixOperator(m, space, space) for m in mats],
[ProjectionParameterFunctional('diffusion', (len(coeffs),), (i,)) for i in range(len(coeffs))])
h1_0_op = op.assemble([1] * len(coeffs)).with_(name='h1_0_semi')
F = space.zeros()
F._list[0].impl.vec.data = f.vec
F = VectorFunctional(F)
return StationaryDiscretization(op, F, visualizer=NGSolveVisualizer(mesh, V),
products={'h1_0_semi': h1_0_op},
parameter_space=CubicParameterSpace(op.parameter_type, 0.1, 1.))