def kappa(mesh,lset_approx, subdivlvl=0):
"""
Tuple of ratios between negative/positive and full
part of an element (deprecated).
"""
print("kappa-function is deprecated - use CutRatioGF instead")
kappa1 = GridFunction(L2(mesh,order=0))
lset_neg = { "levelset" : lset_approx, "domain_type" : NEG, "subdivlvl" : subdivlvl}
kappa_f = LinearForm(kappa1.space)
kappa_f += SymbolicLFI(levelset_domain = lset_neg, form = kappa1.space.TestFunction() )
kappa_f.Assemble();
kappa1.space.SolveM(CoefficientFunction(1.0),kappa_f.vec)
kappa1.vec.data = kappa_f.vec
kappa2 = 1.0 - kappa1
return (kappa1,kappa2)
def single_iteration(self, a: ngs.BilinearForm, L: ngs.LinearForm,
precond: ngs.Preconditioner,
gfu: ngs.GridFunction) -> None:
if self.linearize == 'Oseen':
self.construct_and_run_solver(a, L, precond, gfu)
component = self.model_components['u']
err = norm("l2_norm",
self.W[0],
gfu.components[0],
self.mesh,
self.fes.components[component],
average=False)
gfu_norm = mean(gfu.components[0], self.mesh)
numit = 1
if self.verbose > 0:
print(numit, err)
while (err > self.abs_nonlinear_tolerance +
self.rel_nonlinear_tolerance * gfu_norm) and (
numit < self.nonlinear_max_iters):
self.W[0].vec.data = gfu.components[0].vec
self.apply_dirichlet_bcs_to(gfu)
a.Assemble()
L.Assemble()
precond.Update()
self.construct_and_run_solver(a, L, precond, gfu)
err = norm("l2_norm",
self.W[0],
gfu.components[0],
self.mesh,
self.fes.components[component],
average=False)
gfu_norm = mean(gfu.components[0], self.mesh)
numit += 1
if self.verbose > 0:
print(numit, err)
self.W[0].vec.data = gfu.components[0].vec
elif self.linearize == 'IMEX':
self.construct_and_run_solver(a, L, precond, gfu)
# H1-conforming finite element space
fes = H1(mesh, order=3, dirichlet=[1,2,3,4])
# define trial- and test-functions
u = fes.TrialFunction()
v = fes.TestFunction()
# the right hand side
f = LinearForm(fes)
f += 32 * (y*(1-y)+x*(1-x)) * v * dx
# the bilinear-form
a = BilinearForm(fes, symmetric=True)
a += grad(u)*grad(v)*dx
a.Assemble()
f.Assemble()
# the solution field
gfu = GridFunction(fes)
gfu.vec.data = a.mat.Inverse(fes.FreeDofs(), inverse="sparsecholesky") * f.vec
# print (u.vec)
# plot the solution (netgen-gui only)
Draw (gfu)
Draw (-grad(gfu), mesh, "Flux")
exact = 16*x*(1-x)*y*(1-y)
print ("L2-error:", sqrt (Integrate ( (gfu-exact)*(gfu-exact), mesh)))
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 Heat1DFEM(N=8,
order=1,
k1=1,
k2=1,
Q1=0,
Q2=10,
boundary_condition_left="Robin",
boundary_condition_right="Dirichlet",
value_left=0,
value_right=1,
q_value_left=0,
q_value_right=1,
r_value_left=0,
r_value_right=1,
intervalsize=0.14):
if (boundary_condition_left == "Neumann" or
(boundary_condition_left == "Robin" and r_value_left == 0)) and (
boundary_condition_right == "Neumann" or
(boundary_condition_right == "Robin" and r_value_right == 0)):
print("Temperatur ist nicht eindeutig bestimmt.")
#return
mesh1D = Mesh1D(N, interval=(0, intervalsize))
dbnds = []
if boundary_condition_left == "Dirichlet":
dbnds.append(1)
# print(True)
if boundary_condition_right == "Dirichlet":
dbnds.append(2)
fes = H1(mesh1D, order=order, dirichlet=dbnds)
gf = GridFunction(fes)
if boundary_condition_left == "Dirichlet":
gf.vec[0] = value_left
if boundary_condition_right == "Dirichlet":
gf.vec[N] = value_right
Q = IfPos(X - 0.5 * intervalsize, Q2, Q1)
k = IfPos(X - 0.5 * intervalsize, k2, k1)
u, v = fes.TnT()
a = BilinearForm(fes)
a += SymbolicBFI(k * grad(u) * grad(v))
if boundary_condition_left == "Robin":
a += SymbolicBFI(r_value_left * u * v,
definedon=mesh1D.Boundaries("left"))
if boundary_condition_right == "Robin":
a += SymbolicBFI(r_value_right * u * v,
definedon=mesh1D.Boundaries("right"))
a.Assemble()
f = LinearForm(fes)
f += SymbolicLFI(Q * v)
f.Assemble()
if boundary_condition_left == "Neumann":
f.vec[0] += q_value_left
elif boundary_condition_left == "Robin":
f.vec[0] += r_value_left * value_left
if boundary_condition_right == "Neumann":
f.vec[N] += q_value_right
elif boundary_condition_right == "Robin":
f.vec[N] += r_value_right * value_right
f.vec.data -= a.mat * gf.vec
gf.vec.data += a.mat.Inverse(fes.FreeDofs()) * f.vec
Draw1D(mesh1D, [(gf, "u_h")], n_p=5 * order**2)