def test_new_integrateX_via_straight_cutted_quad3D_polynomial(order, domain, quad_dominated, alpha, dim):
ngsglobals.msg_level = 0
if (quad_dominated):
mesh = MakeUniform3DGrid(quads = True, N=1, P1=(0,0,0),P2=(1,1,1))
else:
cube = OrthoBrick( Pnt(0,0,0), Pnt(1,1,1) ).bc(1)
geom = CSGeometry()
geom.Add (cube)
ngmesh = geom.GenerateMesh(maxh=1.3, quad_dominated=quad_dominated)
mesh = Mesh(ngmesh)
levelset = 1 - 2*x- 2*y - 2*z
val_pos = pow(2,-alpha-3)/(pow(alpha,3)+6*alpha*alpha + 11*alpha+6)
referencevals = {POS: val_pos, NEG: 1./(alpha+1) - val_pos}
lset_approx = GridFunction(H1(mesh,order=1))
InterpolateToP1(levelset,lset_approx)
f = dim**alpha
integral = Integrate(levelset_domain = { "levelset" : lset_approx, "domain_type" : domain},
cf=f, mesh=mesh, order = order)
error = abs(integral - referencevals[domain])
assert error < 5e-15*(order+1)*(order+1)
def test_new_integrateX_via_straight_cutted_quad3D(order, domain,
quad_dominated):
if (quad_dominated):
mesh = MakeUniform3DGrid(quads=True, N=1, P1=(0, 0, 0), P2=(1, 1, 1))
else:
cube = OrthoBrick(Pnt(0, 0, 0), Pnt(1, 1, 1)).bc(1)
geom = CSGeometry()
geom.Add(cube)
ngmesh = geom.GenerateMesh(maxh=1.3, quad_dominated=quad_dominated)
mesh = Mesh(ngmesh)
levelset = 1 - 2 * x - 2 * y - 2 * z
referencevals = {POS: 1. / 48, NEG: 47. / 48, IF: sqrt(3) / 8}
lset_approx = GridFunction(H1(mesh, order=1))
InterpolateToP1(levelset, lset_approx)
f = CoefficientFunction(1)
integral = Integrate(levelset_domain={
"levelset": lset_approx,
"domain_type": domain
},
cf=f,
mesh=mesh,
order=order)
print("Integral: ", integral)
error = abs(integral - referencevals[domain])
assert error < 5e-15 * (order + 1) * (order + 1)
def presets_load_coefficientfunction_into_gridfunction():
# 2D
mesh_2d = ngs.Mesh(unit_square.GenerateMesh(maxh=0.1))
fes_scalar_2d = ngs.H1(mesh_2d, order=2)
fes_vector_2d = ngs.HDiv(mesh_2d, order=2)
fes_mixed_2d = ngs.FESpace([fes_vector_2d, fes_scalar_2d])
# 3D
geo_3d = CSGeometry()
geo_3d.Add(OrthoBrick(Pnt(-1, 0, 0), Pnt(1, 1, 1)).bc('outer'))
mesh_3d = ngs.Mesh(geo_3d.GenerateMesh(maxh=0.3))
fes_scalar_3d = ngs.H1(mesh_3d, order=2)
fes_vector_3d = ngs.HDiv(mesh_3d, order=2)
fes_mixed_3d = ngs.FESpace([fes_vector_3d, fes_scalar_3d])
return mesh_2d, fes_scalar_2d, fes_vector_2d, fes_mixed_2d, mesh_3d, fes_scalar_3d, fes_vector_3d, fes_mixed_3d
def test_new_integrateX_TPMC_case_quad3D2(order, quad_dominated, high_order):
if quad_dominated:
mesh = MakeUniform3DGrid(quads=True, N=10, P1=(0, 0, 0), P2=(1, 1, 1))
else:
geom = CSGeometry()
geom.Add(OrthoBrick(Pnt(0, 0, 0), Pnt(1, 1, 1)).bc(1))
ngmesh = geom.GenerateMesh(maxh=0.2134981)
for i in range(4):
ngmesh.Refine()
mesh = Mesh(ngmesh)
#phi = -4*(1-x)*(1-y)*(1-z) + 4*(1-x)*(1-y)*z -1*(1-x)*y*(1-z) - 1*(1-x)*y*z + 2*x*(1-y)*(1-z) -3 *x*(1-y)*z + 5 * x * y * (1-z) -1 *x *y*z
phi = x * ((7 * y - 13) * z + 6) + y * (3 - 8 * z) + 8 * z - 4
if high_order:
print("Creating LevelSetMeshAdaptation class")
lsetmeshadap = LevelSetMeshAdaptation(mesh,
order=order,
threshold=0.2,
discontinuous_qn=True)
lsetp1 = lsetmeshadap.lset_p1
deformation = lsetmeshadap.CalcDeformation(phi)
mesh.SetDeformation(deformation)
else:
lsetp1 = GridFunction(H1(mesh, order=1))
lsetp1.Set(phi)
f = CoefficientFunction(1)
print("Doing integration")
for domain in [POS, NEG, IF]:
integral = Integrate(levelset_domain={
"levelset": lsetp1,
"domain_type": domain
},
cf=f,
mesh=mesh,
order=order)
print("Integral: ", integral, " ; domain = ", domain)
if domain == IF:
assert abs(integral - 1.82169) < 5e-3
elif domain == NEG:
assert abs(integral - 0.51681) < 1e-3
else:
assert abs(integral - 0.48319) < 1e-3
def _generateMesh(self, *args):
from netgen.csg import CSGeometry, Sphere, Pnt
from ngsolve import Mesh
r = self.getRadius()
geometry = CSGeometry()
sphere = Sphere(Pnt(0, 0, 0), r).bc("sphere")
geometry.Add(sphere)
self.geometry = geometry
self.mesh = Mesh(geometry.GenerateMesh(maxh=r / 5))
ngsolve.Draw(self.mesh)
def test_convection1d_dg():
m = meshing.Mesh()
m.dim = 1
nel = 20
pnums = []
for i in range(0, nel + 1):
pnums.append(m.Add(meshing.MeshPoint(Pnt(i / nel, 0, 0))))
for i in range(0, nel):
m.Add(meshing.Element1D([pnums[i], pnums[i + 1]], index=1))
m.Add(meshing.Element0D(pnums[0], index=1))
m.Add(meshing.Element0D(pnums[nel], index=2))
m.AddPointIdentification(pnums[0],
pnums[nel],
identnr=1,
type=meshing.IdentificationType.PERIODIC)
mesh = Mesh(m)
fes = L2(mesh, order=4)
u = fes.TrialFunction()
v = fes.TestFunction()
b = CoefficientFunction(1)
bn = b * specialcf.normal(1)
a = BilinearForm(fes)
a += SymbolicBFI(-u * b * grad(v))
a += SymbolicBFI(bn * IfPos(bn, u, u.Other()) * v, element_boundary=True)
u = GridFunction(fes)
pos = 0.5
u0 = exp(-100 * (x - pos) * (x - pos))
u.Set(u0)
w = u.vec.CreateVector()
t = 0
tau = 1e-4
tend = 1
with TaskManager():
while t < tend - tau / 2:
a.Apply(u.vec, w)
fes.SolveM(rho=CoefficientFunction(1), vec=w)
u.vec.data -= tau * w
t += tau
l2error = sqrt(Integrate((u - u0) * (u - u0), mesh))
print(l2error)
assert l2error < 1e-2
def test_new_integrateX_via_straight_cutted_quad3D(order, domain, quad):
cube = OrthoBrick(Pnt(0, 0, 0), Pnt(1, 1, 1)).bc(1)
geom = CSGeometry()
geom.Add(cube)
ngmesh = geom.GenerateMesh(maxh=1.3, quad_dominated=quad)
mesh = Mesh(ngmesh)
levelset = 1 - 2 * x - 2 * y - 2 * z
referencevals = {POS: 1. / 48, NEG: 47. / 48, IF: sqrt(3) / 8}
f = CoefficientFunction(1)
integral = Integrate(levelset_domain={
"levelset": levelset,
"domain_type": domain
},
cf=f,
mesh=mesh,
order=order)
error = abs(integral - referencevals[domain])
assert error < 5e-15 * (order + 1) * (order + 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].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.))
""" from math import pi # ngsolve stuff from ngsolve import * # visualization stuff from ngsolve.internal import * # basic xfem functionality from xfem import * from xfem.lsetcurv import * # from netgen.geom2d import SplineGeometry from netgen.csg import CSGeometry, OrthoBrick, Pnt # geometry cube = CSGeometry() cube.Add (OrthoBrick(Pnt(-1.41,-1.41,-1.41), Pnt(1.41,1.41,1.41))) mesh = Mesh (cube.GenerateMesh(maxh=0.6, quad_dominated=False)) levelset = sqrt(x*x+y*y+z*z)-1 for i in range(1): lsetp1 = GridFunction(H1(mesh,order=1)) InterpolateToP1(levelset,lsetp1) RefineAtLevelSet(lsetp1) mesh.Refine() order = 3 # class to compute the mesh transformation needed for higher order accuracy # * order: order of the mesh deformation function # * threshold: barrier for maximum deformation (to ensure shape regularity)
# integration on lset domains
from math import pi
# ngsolve stuff
from ngsolve import *
# basic xfem functionality
from xfem import *
from netgen.csg import CSGeometry, OrthoBrick, Pnt
cube = OrthoBrick(Pnt(0, 0, 0), Pnt(1, 1, 1)).bc(1)
geom = CSGeometry()
geom.Add(cube)
ngmesh = geom.GenerateMesh(maxh=1, quad_dominated=True)
mesh = Mesh(ngmesh)
def binary_pow(x, a):
if a == 0:
return 0 * x + 1
elif a == 1:
return x
else:
print("Invalid argument a")
#levelset coefficients
c = [[[1, -2], [-2, 0]], [[-2, 0], [0, 0]]]
#levelset = 1-2*x-2*y-2*z #(sqrt(x*x+y*y+z*z)-0.5)
levelset = sum([
c[alpha][beta][gamma] * binary_pow(x, alpha) * binary_pow(y, beta) *
from netgen.geom2d import unit_square, MakeCircle, SplineGeometry
from netgen.meshing import Element0D, Element1D, Element2D, MeshPoint, FaceDescriptor, Mesh
from netgen.csg import Pnt
quads = True
N = 5
mesh = Mesh()
mesh.SetGeometry(unit_square)
mesh.dim = 2
pnums = []
for i in range(N + 1):
for j in range(N + 1):
pnums.append(mesh.Add(MeshPoint(Pnt(i / N, j / N, 0))))
mesh.SetMaterial(1, "mat")
for j in range(N):
for i in range(N):
if quads:
mesh.Add(
Element2D(1, [
pnums[i + j * (N + 1)], pnums[i + (j + 1) * (N + 1)],
pnums[i + 1 + (j + 1) * (N + 1)], pnums[i + 1 + j *
(N + 1)]
]))
else:
mesh.Add(
Element2D(1, [
pnums[i + j * (N + 1)], pnums[i + (j + 1) * (N + 1)],
pnums[i + 1 + j * (N + 1)]
def MakeUniform3DGrid(quads = False, N=5, P1=(0,0,0),P2=(1,1,1)):
if not quads:
raise BaseException("Only hex cube so far...")
Lx = P2[0]-P1[0]
Ly = P2[1]-P1[1]
Lz = P2[2]-P1[2]
cube = OrthoBrick( Pnt(P1[0],P1[1],P1[2]), Pnt(P2[0],P2[1],P2[2]) ).bc(1)
geom = CSGeometry()
geom.Add (cube)
netmesh = NetMesh()
netmesh.SetGeometry(geom)
netmesh.dim = 3
pids = []
for i in range(N+1):
for j in range(N+1):
for k in range(N+1):
pids.append (netmesh.Add (MeshPoint(Pnt(P1[0] + Lx * i / N,
P1[1] + Ly * j / N,
P1[2] + Lz * k / N))))
for i in range(N):
for j in range(N):
for k in range(N):
base = i * (N+1)*(N+1) + j*(N+1) + k
baseup = base+(N+1)*(N+1)
pnum = [base,base+1,base+(N+1)+1,base+(N+1),
baseup, baseup+1, baseup+(N+1)+1, baseup+(N+1)]
elpids = [pids[p] for p in pnum]
netmesh.Add (Element3D(1,elpids))
def AddSurfEls (p1, dx, dy, facenr):
for i in range(N):
for j in range(N):
base = p1 + i*dx+j*dy
pnum = [base, base+dx, base+dx+dy, base+dy]
elpids = [pids[p] for p in pnum]
netmesh.Add (Element2D(facenr,elpids))
netmesh.Add (FaceDescriptor(surfnr=1,domin=1,bc=1))
AddSurfEls (0, 1, N+1, facenr=1)
netmesh.Add (FaceDescriptor(surfnr=2,domin=1,bc=1))
AddSurfEls (0, (N+1)*(N+1), 1, facenr=2)
netmesh.Add (FaceDescriptor(surfnr=3,domin=1,bc=1))
AddSurfEls (0, N+1, (N+1)*(N+1), facenr=3)
netmesh.Add (FaceDescriptor(surfnr=4,domin=1,bc=1))
AddSurfEls ((N+1)**3-1, -(N+1), -1, facenr=1)
netmesh.Add (FaceDescriptor(surfnr=5,domin=1,bc=1))
AddSurfEls ((N+1)**3-1, -(N+1)*(N+1), -(N+1), facenr=1)
netmesh.Add (FaceDescriptor(surfnr=6,domin=1,bc=1))
AddSurfEls ((N+1)**3-1, -1, -(N+1)*(N+1), facenr=1)
netmesh.Compress()
mesh = NGSMesh(netmesh)
mesh.ngmesh.Save("tmp.vol.gz")
mesh = NGSMesh("tmp.vol.gz")
return mesh
def MakeUniform2DGrid(quads=False, N=5, P1=(0, 0), P2=(1, 1)):
geom = SplineGeometry()
geom.AddRectangle(P1, P2, bc=1)
Lx = P2[0] - P1[0]
Ly = P2[1] - P1[1]
netmesh = NetMesh()
netmesh.SetGeometry(geom)
netmesh.dim = 2
pnums = []
for i in range(N + 1):
for j in range(N + 1):
pnums.append(
netmesh.Add(
MeshPoint(Pnt(P1[0] + Lx * i / N, P1[1] + Ly * j / N, 0))))
netmesh.Add(FaceDescriptor(surfnr=1, domin=1, bc=1))
netmesh.SetMaterial(1, "mat")
for j in range(N):
for i in range(N):
if quads:
netmesh.Add(
Element2D(1, [
pnums[i + j * (N + 1)], pnums[i + (j + 1) * (N + 1)],
pnums[i + 1 + (j + 1) * (N + 1)], pnums[i + 1 + j *
(N + 1)]
]))
else:
netmesh.Add(
Element2D(1, [
pnums[i + j * (N + 1)], pnums[i + (j + 1) * (N + 1)],
pnums[i + 1 + j * (N + 1)]
]))
netmesh.Add(
Element2D(1, [
pnums[i + (j + 1) * (N + 1)],
pnums[i + 1 + (j + 1) * (N + 1)], pnums[i + 1 + j *
(N + 1)]
]))
for j in range(N):
netmesh.Add(
Element1D([pnums[N + j * (N + 1)], pnums[N + (j + 1) * (N + 1)]],
index=1))
netmesh.Add(
Element1D([pnums[0 + j * (N + 1)], pnums[0 + (j + 1) * (N + 1)]],
index=1))
for i in range(N):
netmesh.Add(Element1D([pnums[i], pnums[i + 1]], index=1))
netmesh.Add(
Element1D([pnums[i + N * (N + 1)], pnums[i + 1 + N * (N + 1)]],
index=1))
netmesh.SetGeometry(geom)
netmesh.Compress()
mesh = NGSMesh(netmesh)
mesh.ngmesh.Save("tmp.vol.gz")
mesh = NGSMesh("tmp.vol.gz")
return mesh
(x * x + z * z - 4) * (x * x + z * z - 4) + (y * y + z * z - 4) *
(y * y + z * z - 4)) - 4).Compile(),
# geometry from 'Dziuk, Elliott, Finite element methods for surface PDEs, Acta Numerica, 2013', pp. 318-319:
"dziukelliott":
sqrt(0.25 * x * x + y * y + 4.0 * z * z / ((1 + 0.5 * sin(pi * x)) *
(1 + 0.5 * sin(pi * x)))) - 1.0,
# geometry from 'Dziuk, Finite elements for the beltrami operator on arbitrary surfaces':
"dziuk88":
sqrt((x - z * z) * (x - z * z) + y * y + z * z) - 1.0,
# the unit sphere
"sphere":
sqrt(x * x + y * y + z * z) - 1.0,
# torus with parameters as in 'Grande, Reusken, A higher order finite element method for partial differential euqations on surface, SINUM, 2016'
"torus":
sqrt(z * z + (sqrt(x * x + y * y) - 1.0) *
(sqrt(x * x + y * y) - 1.0)) - 0.6,
# gyroid from Lehrenfeld, CMAME, 2016
"gyroid":
cos(pi * x) * sin(pi * y) + cos(pi * y) * sin(pi * z) +
cos(pi * z) * sin(pi * x),
}
BoundingBoxes = {
"cheese": OrthoBrick(Pnt(-2.5, -2.5, -2.5), Pnt(2.5, 2.5, 2.5)),
"dziukelliott": OrthoBrick(Pnt(-2.5, -1.5, -1.5), Pnt(2.5, 1.5, 1.5)),
"dziuk88": OrthoBrick(Pnt(-2, -2, -2), Pnt(2, 2, 2)),
"sphere": OrthoBrick(Pnt(-1.5, -1.5, -1.5), Pnt(1.5, 1.5, 1.5)),
"torus": OrthoBrick(Pnt(-2, -2, -2), Pnt(2, 2, 2)),
"gyroid": OrthoBrick(Pnt(-1, -1, -1), Pnt(1, 1, 1)),
}
