def test_2(self, presets_load_coefficientfunction_into_gridfunction):
"""
Check that coefficientfunctions can be loaded into different component of a gridfunction correctly. Check 2D and
3D. Also check scalar and vector coefficientfunctions.
"""
mesh_2d, fes_scalar_2d, fes_vector_2d, fes_mixed_2d, mesh_3d, fes_scalar_3d, fes_vector_3d, fes_mixed_3d = presets_load_coefficientfunction_into_gridfunction
cfu_scalar = ngs.CoefficientFunction(ngs.x + ngs.y)
gfu_mixed_2d = ngs.GridFunction(fes_mixed_2d)
cfu_vector_2d = ngs.CoefficientFunction((ngs.x, ngs.y))
coef_dict_2d = {0: cfu_vector_2d, 1: cfu_scalar}
gfu_mixed_3d = ngs.GridFunction(fes_mixed_3d)
cfu_vector_3d = ngs.CoefficientFunction((ngs.x, ngs.y, ngs.z))
coef_dict_3d = {0: cfu_vector_3d, 1: cfu_scalar}
# Check 2D
load_coefficientfunction_into_gridfunction(gfu_mixed_2d, coef_dict_2d)
err_scalar_2d = ngs.Integrate((cfu_scalar - gfu_mixed_2d.components[1]) * (cfu_scalar - gfu_mixed_2d.components[1]), mesh_2d)
err_vector_2d = ngs.Integrate((cfu_vector_2d - gfu_mixed_2d.components[0]) * (cfu_vector_2d - gfu_mixed_2d.components[0]), mesh_2d)
assert math.isclose(err_scalar_2d, 0.0, abs_tol=1e-16)
assert math.isclose(err_vector_2d, 0.0, abs_tol=1e-16)
# Check 3D
load_coefficientfunction_into_gridfunction(gfu_mixed_3d, coef_dict_3d)
err_scalar_3d = ngs.Integrate((cfu_scalar - gfu_mixed_3d.components[1]) * (cfu_scalar - gfu_mixed_3d.components[1]), mesh_3d)
err_vector_3d = ngs.Integrate((cfu_vector_3d - gfu_mixed_3d.components[0]) * (cfu_vector_3d - gfu_mixed_3d.components[0]), mesh_3d)
assert math.isclose(err_scalar_3d, 0.0, abs_tol=1e-16)
assert math.isclose(err_vector_3d, 0.0, abs_tol=1e-16)
def test_4(self, presets_load_coefficientfunction_into_gridfunction):
""" Check that the coefficientfunction and gridfunction dimensions must agree. Check 2D and 3D. """
mesh_2d, fes_scalar_2d, fes_vector_2d, fes_mixed_2d, mesh_3d, fes_scalar_3d, fes_vector_3d, fes_mixed_3d = presets_load_coefficientfunction_into_gridfunction
cfu_scalar = ngs.CoefficientFunction(ngs.x + ngs.y)
gfu_mixed_2d = ngs.GridFunction(fes_mixed_2d)
cfu_vector_2d = ngs.CoefficientFunction((ngs.x, ngs.y))
gfu_mixed_3d = ngs.GridFunction(fes_mixed_3d)
cfu_vector_3d = ngs.CoefficientFunction((ngs.x, ngs.y, ngs.z))
# Check 2D.
with pytest.raises(netgen.libngpy._meshing.NgException):
coef_dict = {1: cfu_vector_2d} # Vector coefficientfunction but scalar gridfunction.
load_coefficientfunction_into_gridfunction(gfu_mixed_2d, coef_dict)
with pytest.raises(netgen.libngpy._meshing.NgException):
coef_dict = {0: cfu_scalar} # Scalar coefficientfunction but vector gridfunction.
load_coefficientfunction_into_gridfunction(gfu_mixed_2d, coef_dict)
# Check 3D.
with pytest.raises(netgen.libngpy._meshing.NgException):
coef_dict = {1: cfu_vector_3d} # Vector coefficientfunction but scalar gridfunction.
load_coefficientfunction_into_gridfunction(gfu_mixed_3d, coef_dict)
with pytest.raises(netgen.libngpy._meshing.NgException):
coef_dict = {0: cfu_scalar} # Scalar coefficientfunction but vector gridfunction.
load_coefficientfunction_into_gridfunction(gfu_mixed_3d, coef_dict)
def test_3(self, presets_load_coefficientfunction_into_gridfunction):
""" Check that passing in a coef_dict with multiple keys, one of which is None raises an error. """
mesh_2d, fes_scalar_2d, fes_vector_2d, fes_mixed_2d, mesh_3d, fes_scalar_3d, fes_vector_3d, fes_mixed_3d = presets_load_coefficientfunction_into_gridfunction
gfu = ngs.GridFunction(fes_scalar_2d)
cfu_1 = ngs.CoefficientFunction(ngs.x + ngs.y)
cfu_2 = ngs.CoefficientFunction(ngs.x * ngs.y)
coef_dict = {None: cfu_1, 0: cfu_2}
with pytest.raises(AssertionError):
load_coefficientfunction_into_gridfunction(gfu, coef_dict)
def test_evaluate():
from netgen.geom2d import unit_square
import ngsolve as ngs
import numpy as np
mesh = ngs.Mesh(unit_square.GenerateMesh(maxh=0.2))
pnts = np.linspace(0.1, 0.9, 9)
cf = ngs.CoefficientFunction((ngs.x, ngs.y))
cf2 = ngs.CoefficientFunction((ngs.y, ngs.x * 1J))
mips = mesh(pnts, 0.5)
vals = cf(mips)
vals2 = cf2(mips)
assert np.linalg.norm(vals - np.array(list(zip(pnts, [0.5] * 10)))) < 1e-10
assert np.linalg.norm(
vals2 - np.array(list(zip([0.5 + 0J] * 10, pnts * 1J)))) < 1e-10
assert ngs.x(mesh(0.5, 0.5)) - 0.5 < 1e-10
def do_test(rots, reo, ms=50):
print('======= test 3d, lo, rots =', rots, ', reorder=', reo)
sys.stdout.flush()
geo, mesh = gen_beam(dim=3,
maxh=0.2,
lens=[7, 1, 1],
nref=0,
comm=ngsolve.mpi_world)
V, a, f = setup_elast(mesh,
rotations=rots,
f_vol=ngsolve.CoefficientFunction((0, -0.005, 0)),
diri="left",
multidim=False,
reorder=reo)
print('V ndof', V.ndof)
ngsolve.ngsglobals.msg_level = 5
pc_opts = {"ngs_amg_max_coarse_size": 10}
if reo == "sep":
pc_opts["ngs_amg_dof_blocks"] = [3, 3] if rots else [3]
elif reo is not False:
pc_opts["ngs_amg_dof_blocks"] = [6] if rots else [3]
if rots:
pc_opts["ngs_amg_rots"] = True
c = ngsolve.Preconditioner(a, "ngs_amg.elast_3d", **pc_opts)
Solve(a, f, c, ms=ms)
print('======= completed test 3d, lo, rots =', rots, ', reorder=', reo,
'\n\n')
sys.stdout.flush()
def do_ho_smooth(rots, ms, pc_opts):
print('test 2d, rots = ', rots)
geo, mesh = gen_beam(dim = 2, maxh = 0.2, lens = [10,1], nref = 0, comm = ngsolve.mpi_world)
V, a, f = setup_elast(mesh, order = 4, rotations = rots, f_vol = ngsolve.CoefficientFunction( (0, -0.005) ), diri = "left")
print('V ndof', V.ndof)
pc_opts["ngs_amg_rots"] = rots
c = ngsolve.Preconditioner(a, "ngs_amg.elast_2d", **pc_opts)
Solve(a, f, c, ms = ms)
def do_test_2d_lo(jump, rots, ms=40):
geo, mesh = gen_sq_with_sqs(maxh=0.1, nref=0, comm=ngsolve.mpi_world)
a0 = 1
mu = {"mat_a": a0, "mat_b": jump * a0}
V, a, f = setup_elast(mesh,
rotations=rots,
f_vol=ngsolve.CoefficientFunction((0, -0.005)),
diri="outer_left",
mu=ngsolve.CoefficientFunction(
[mu[name] for name in mesh.GetMaterials()]))
print('V ndof', V.ndof)
pc_opts = {
"ngs_amg_max_coarse_size": 10,
"ngs_amg_log_level": "extra",
"ngs_amg_print_log": True
}
if rots:
pc_opts["ngs_amg_rots"] = True
c = ngsolve.Preconditioner(a, "ngs_amg.elast_2d", **pc_opts)
Solve(a, f, c, ms=50)
def set_initial_conditions(self, gfu_IC: ngs.GridFunction, mesh: ngs.Mesh, model_name: str,
model_components: Dict[str, int]) -> None:
"""
Function to load the initial conditions from their configfile into a gridfunction.
Args:
mesh: The model's mesh.
model_name: Sometimes several models will use the same IC configfile. This identifies which model's ICs
should be loaded.
gfu_IC: A gridfunction to hold the initial conditions.
model_components: Maps between variable names and their component in the model's finite element space.
"""
coef_dict = {}
file_dict = {}
for var, marker_dict in self.ic_dict[model_name].items():
# Determine which component of the gridfunction the initial condition is for
if var == 'all':
component = None
else:
component = model_components[var]
# Check if the initial condition is specified as a file, a coefficientfunction, or a dict of material
# markers and coefficientfunctions.
if len(marker_dict) == 1:
# One single file or coefficientfunction.
assert next(iter(marker_dict.keys())) == 'all'
val = next(iter(marker_dict.values()))
if val is None:
# No initial condition needed so just keep the zeroed out gridfunction.
return
if isinstance(val, str):
# Check that the file exists.
val = self._find_rel_path_for_file(val)
file_dict[component] = val
else:
coef_dict[component] = val
else:
# Need to construct a coefficientfunction from a set of material markers.
coef = ngs.CoefficientFunction([marker_dict[mat] for mat in mesh.GetMaterials()])
coef_dict[component] = coef
if coef_dict:
load_coefficientfunction_into_gridfunction(gfu_IC, coef_dict)
if file_dict:
update_gridfunction_from_files(gfu_IC, file_dict)
def do_ho_smooth(rots, ms, pc_opts):
print('test 3d, rots = ', rots)
sys.stdout.flush()
geo, mesh = gen_beam(dim = 3, maxh = 0.35, lens = [5,1,1], nref = 0, comm = ngsolve.mpi_world)
V, a, f = setup_elast(mesh, order = 2, rotations = rots, f_vol = ngsolve.CoefficientFunction( (0, -0.005, 0) ), diri = "left")
pc_opts["ngs_amg_rots"] = rots
if not rots:
pc_opts["ngs_amg_reg_mats"] = True
pc_opts["ngs_amg_reg_rmats"] = True
c = ngs_amg.elast_3d(a, **pc_opts)
Solve(a, f, c, ms = ms)
def inital_span(X):
# Coefficient funtions in the span.
coeffs = (ng.CoefficientFunction([1]), ng.x, ng.y)
# The span as a list.
span = [ng.GridFunction(X) for k in range(len(coeffs))]
# Set the values of each GridFunction.
for k in range(len(coeffs)):
span[k].Set(coeffs[k])
return span
def rbms(dim, V, rots):
if rots:
tups = [(1, 0, 0), (0, 1, 0), (y, -x, 1)]
else:
tups = [(1, 0), (0, 1), (y, -x)]
cfs = [ngsolve.CoefficientFunction(x) for x in tups]
gf = ngsolve.GridFunction(V)
kvecs = [gf.vec.CreateVector() for c in cfs]
for vec, cf in zip(kvecs, cfs):
gf.Set(cf)
vec.data = gf.vec
return kvecs
def test_2d_lo_R():
geo, mesh = gen_beam(dim=2,
maxh=0.1,
lens=[10, 1],
nref=0,
comm=ngsolve.mpi_world)
V, a, f = setup_elast(mesh,
rotations=True,
f_vol=ngsolve.CoefficientFunction((0, -0.005)),
diri="left")
pc_opts = {"ngs_amg_rots": True, "ngs_amg_max_coarse_size": 20}
c = ngsolve.Preconditioner(a, "ngs_amg.elast_2d", **pc_opts)
Solve(a, f, c, ms=50)
def test_3d_lo():
geo, mesh = gen_beam(dim=3,
maxh=0.25,
lens=[10, 1, 1],
nref=0,
comm=ngsolve.mpi_world)
V, a, f = setup_elast(mesh,
rotations=False,
f_vol=ngsolve.CoefficientFunction(
(0, -0.005, 0.002)),
diri="left")
pc_opts = {"ngs_amg_reg_rmats": True, "ngs_amg_max_coarse_size": 10}
c = ngsolve.Preconditioner(a, "ngs_amg.elast_3d", **pc_opts)
Solve(a, f, c, ms=40)
def do_test_2d_ho(jump):
print('test sq_with_sqs, jump =', jump)
sys.stdout.flush()
geo, mesh = gen_sq_with_sqs(maxh=0.1, nref=0, comm=ngsolve.mpi_world)
a0 = 1
alpha = {"mat_a": a0, "mat_b": jump * a0}
V, a, f = setup_poisson(mesh,
order=3,
diri="outer_.*",
alpha=ngsolve.CoefficientFunction(
[alpha[name] for name in mesh.GetMaterials()]))
pc_opts = {
"ngs_amg_max_coarse_size": 5,
"ngs_amg_log_level": "extra",
"ngs_amg_print_hog": True
}
c = ngsolve.Preconditioner(a, "ngs_amg.h1_scal", **pc_opts)
Solve(a, f, c, ms=100, tol=1e-6, nocb=False)
def test_1(self, presets_load_coefficientfunction_into_gridfunction):
""" Check that a coefficientfunction can be loaded into a full gridfunction correctly. Check 2D and 3D. """
mesh_2d, fes_scalar_2d, fes_vector_2d, fes_mixed_2d, mesh_3d, fes_scalar_3d, fes_vector_3d, fes_mixed_3d = presets_load_coefficientfunction_into_gridfunction
gfu_scalar_2d = ngs.GridFunction(fes_scalar_2d)
gfu_scalar_3d = ngs.GridFunction(fes_scalar_3d)
cfu_scalar = ngs.CoefficientFunction(ngs.x + ngs.y)
coef_dict = {None: cfu_scalar}
# Check 2D
load_coefficientfunction_into_gridfunction(gfu_scalar_2d, coef_dict)
err_2d = ngs.Integrate((cfu_scalar - gfu_scalar_2d) * (cfu_scalar - gfu_scalar_2d), mesh_2d)
assert math.isclose(err_2d, 0.0, abs_tol=1e-16)
# Check 3D
load_coefficientfunction_into_gridfunction(gfu_scalar_3d, coef_dict)
err_3d = ngs.Integrate((cfu_scalar - gfu_scalar_3d) * (cfu_scalar - gfu_scalar_3d), mesh_3d)
assert math.isclose(err_3d, 0.0, abs_tol=1e-16)
def do_test_2d_lo_fiber(jump, ms=25):
print('\n\n---\ntest 2d fibers, jump =', jump, '\n---')
sys.stdout.flush()
geo, mesh = gen_fibers_2d(maxh=0.1, nref=1, comm=ngsolve.mpi_world)
a0 = 1
alpha = {"mat_a": a0, "mat_b": jump * a0}
V, a, f = setup_poisson(mesh,
order=1,
diri="outer_top|outer_bot",
alpha=ngsolve.CoefficientFunction(
[alpha[name] for name in mesh.GetMaterials()]))
pc_opts = {
"ngs_amg_max_coarse_size": 5,
"ngs_amg_sm_type": "bgs",
"ngs_amg_log_level": "extra",
"ngs_amg_print_log": True
}
c = ngsolve.Preconditioner(a, "ngs_amg.h1_scal", **pc_opts)
Solve(a, f, c, ms=ms, tol=1e-6)
def __init__(self, cf, mesh, order, min_, max_, draw_vol, draw_surf,
autoscale, deformation, interpolate_multidim, animate):
from IPython.display import display, Javascript
import threading
self.cf = cf
self.mesh = mesh
self.order = order
self.min = min_
self.max = max_
self.draw_vol = draw_vol
self.draw_surf = draw_surf
self.autoscale = autoscale
self.interpolate_multidim = interpolate_multidim
self.animate = animate
if isinstance(deformation, ngs.CoefficientFunction):
if deformation.dim == 2:
deformation = ngs.CoefficientFunction((deformation, 0.0))
self.deformation = deformation
def do_ho_smooth_nodalp2(rots, ms, pc_opts, order = 3):
print('test 3d with nodalp2, order = ', order, 'rots = ', rots)
sys.stdout.flush()
geo, mesh = gen_beam(dim = 3, maxh = 0.35, lens = [5,1,1], nref = 0, comm = ngsolve.mpi_world)
V, a, f = setup_elast(mesh, order = order, rotations = rots, f_vol = ngsolve.CoefficientFunction( (0, -0.005, 0) ), diri = "left",
fes_opts = {"nodalp2" : True} )
print('V ndof', V.ndof)
pc_opts["ngs_amg_rots"] = rots
pc_opts["ngs_amg_first_aaf"] = 0.1
if order == 2:
pc_opts["ngs_amg_lo"] = False
else:
pc_opts["ngs_amg_on_dofs"] = "select"
pc_opts["ngs_amg_subset"] = "nodalp2"
if rots is False:
pc_opts["ngs_amg_reg_mats"] = True
pc_opts["ngs_amg_reg_rmats"] = True
c = ngs_amg.elast_3d(a, **pc_opts)
Solve(a, f, c, ms = ms)
def setup_norot_elast(mesh,
mu=1,
lam=0,
f_vol=None,
multidim=True,
reorder=False,
diri=".*",
order=1,
fes_opts=dict(),
blf_opts=dict(),
lf_opts=dict()):
dim = mesh.dim
if multidim:
V = ngs.H1(mesh, order=order, dirichlet=diri, **fes_opts, dim=mesh.dim)
else:
V = ngs.VectorH1(mesh, order=order, dirichlet=diri, **fes_opts)
if reorder:
raise Exception(
"reordered does not work anymore (now ordered by elements)!!")
V = ngs.comp.Reorder(V)
u, v = V.TnT()
sym = lambda X: 0.5 * (X + X.trans)
grd = lambda X: ngs.CoefficientFunction(tuple(
ngs.grad(X)[i, j] for i in range(dim) for j in range(dim)),
dims=(dim, dim))
eps = lambda X: sym(grd(X))
a = ngs.BilinearForm(V, symmetric=False, **blf_opts)
a += mu * ngs.InnerProduct(eps(u), eps(v)) * ngs.dx
if lam != 0:
div = lambda U: sum([ngs.grad(U)[i, i] for i in range(1, dim)],
start=ngs.grad(U)[0, 0])
a += lam * div(u) * div(v) * ngs.dx
lf = ngs.LinearForm(V)
lf += f_vol * v * ngs.dx
return V, a, lf
def do_test_2d_lo(jump, ms=25):
print('\n\n---\ntest sq_with_sqs, jump =', jump, '\n---')
sys.stdout.flush()
geo, mesh = gen_sq_with_sqs(maxh=0.05, nref=1, comm=ngsolve.mpi_world)
a0 = 1
alpha = {"mat_a": a0, "mat_b": jump * a0}
V, a, f = setup_poisson(mesh, order=1, diri="outer_bot|outer_top|outer_left|outer_right", \
alpha = ngsolve.CoefficientFunction([alpha[name] for name in mesh.GetMaterials()]) )
pc_opts = {
"ngs_amg_max_coarse_size": 5,
"ngs_amg_log_level": "extra",
"ngs_amg_crs_alg": "agg",
"ngs_amg_agg_wt_geom": True,
"ngs_amg_enable_disc": False,
#"ngs_amg_max_levels" : 4,
"ngs_amg_enable_sp": True,
"ngs_amg_print_log": True
}
c = ngsolve.Preconditioner(a, "ngs_amg.h1_scal", **pc_opts)
Solve(a, f, c, ms=ms, tol=1e-6)
def _eval(self, diff, differentiate=False):
# Assemble Bilinearform
self.gfu_integrator.vec.FV().NumPy()[:] = diff
self.gfu_integrator_codomain.Set(self.gfu_integrator)
self.a.Assemble()
# Assemble Linearform, boundary term
self.gfu_b.Set(self.g)
self.b.Assemble()
# Solve system
self.gfu.vec.data = self._solve(self.a, self.b.vec)
# res=sco.minimize((lambda u: self._target(u, self.b.vec)), np.zeros(self.fes_codomain.ndof), constraints={"fun": self._constraint, "type": "eq"})
if differentiate:
sigma = ngs.CoefficientFunction(self.gfu_integrator)
self.gfu_bdr.Set(self.g / sigma)
# self.gfu.vec.FV().NumPy()[:]=res.x
return self._get_boundary_values(self.gfu)
def linear_combo(v, W):
"""
Method that multiplies the list v containing the span of our vectors
to the matrix W that solved the eigenproblem
vAv*W = vBv*W*E,
where E is the diagonal matrix of eigenvalues.
"""
# Create an array of new eigenfunctions.
q = []
for k in range(len(v)):
q += [ng.GridFunction(v[k].space)]
q[k].Set(ng.CoefficientFunction(0))
# Now set the values of each new grid function.
for k in range(len(q)):
for m in range(len(v)):
q[k].vec.data += np.complex(W[m, k]) * v[m].vec
return q
def Solve(a, f, c, ms=100):
ngs.ngsglobals.msg_level = 5
gfu = ngs.GridFunction(a.space)
with ngs.TaskManager():
a.Assemble()
f.Assemble()
ngs.ngsglobals.msg_level = 5
if c is None:
c = a.mat.Inverse(V.FreeDofs())
else:
c.Test()
cb = None if a.space.mesh.comm.rank != 0 else lambda k, x: print(
"it =", k, ", err =", x)
cg = ngs.krylovspace.CGSolver(mat=a.mat,
pre=c,
callback=cb,
maxsteps=ms,
tol=1e-6)
cg.Solve(sol=gfu.vec, rhs=f.vec)
print("used nits = ", cg.iterations)
ngsolve.Draw(mesh,
deformation=ngsolve.CoefficientFunction(
(gfu[0], gfu[1], 0)))
# PARAMETERS:
p = 3 # polynomial degree
h0 = 1 # coarse mesh size for unit square domain
markprm = 0.5 # percentage of max total error for marking
# SET UP:
mesh = Mesh(unit_square.GenerateMesh(maxh=h0))
q_zero = 'bottom' # Mesh boundary parts where q and
mu_zero = 'bottom|right|left' # mu has essential b.c
u00 = exp(-1000 * ((x - 0.5) * (x - 0.5))) # Nonzero initial condition
cwave = 1. # wave speed
F = ngs.CoefficientFunction((0, 0)) # Zero source
a, f, X, sep = makeforms(mesh, p, F, q_zero, mu_zero, cwave, epsil=1.e-10)
euz = GridFunction(X) # Contains solution at each adaptive step
q = euz.components[sep[0]] # Volume (L2) components
mu = euz.components[sep[0]+1]
zq = euz.components[sep[1]] # Interface components
zmu = euz.components[sep[1]+1]
zq.Set(u00, definedon='bottom')
zmu.Set(-u00, definedon='bottom')
ngs.Draw(mu, autoscale=False, # draw only one of the solution components
min=-1.0, max=1.0)
landweber = Landweber(setting, data, init_solution, stepsize=1)
stoprule = (rules.CountIterations(1000) +
rules.Discrepancy(setting.Hcodomain.norm,
data,
noiselevel=setting.Hcodomain.norm(noise),
tau=1.1))
reco, reco_data = landweber.run(stoprule)
ngs.Draw(exact_solution_coeff, op.fes_domain.mesh, "exact")
ngs.Draw(init, op.fes_domain.mesh, "init")
# Draw recondtructed solution
gfu_reco = ngs.GridFunction(op.fes_domain)
gfu_reco.vec.FV().NumPy()[:] = reco
coeff_reco = ngs.CoefficientFunction(gfu_reco)
ngs.Draw(coeff_reco, op.fes_domain.mesh, "reco")
# Draw data space
gfu_data = ngs.GridFunction(op.fes_codomain)
gfu_reco_data = ngs.GridFunction(op.fes_codomain)
gfu_data.vec.FV().NumPy()[:] = data
coeff_data = ngs.CoefficientFunction(gfu_data)
gfu_reco_data.vec.FV().NumPy()[:] = reco_data
coeff_reco_data = ngs.CoefficientFunction(gfu_reco_data)
ngs.Draw(coeff_data, op.fes_codomain.mesh, "data")
ngs.Draw(coeff_reco_data, op.fes_codomain.mesh, "reco_data")
import ngsolve, ngs_amg
from amg_utils import *
maxh = 0.25
geo, mesh = gen_beam(dim=3,
maxh=maxh,
lens=[10, 1, 1],
nref=0,
comm=ngsolve.mpi_world)
V, a, f = setup_elast(mesh,
rotations=False,
f_vol=ngsolve.CoefficientFunction((0, -1e-5, -1e-5)),
diri="left")
#pc_opts = { "ngs_amg_reg_rmats" : True }
pc_opts = {
"ngs_amg_reg_rmats": True,
"ngs_amg_rots": False,
"mgs_amg_max_levels": 2,
#"ngs_amg_aaf" : 0.25,
"ngs_amg_max_coarse_size": 20,
#"ngs_amg_max_levels" : 4,
"ngs_amg_log_level": "extra",
"ngs_amg_enable_sp": True,
"ngs_amg_sp_max_per_row": 4,
"ngs_amg_enable_redist": True,
"ngs_amg_first_aaf": 0.025
}
gfu = ngsolve.GridFunction(V)
a.Assemble()
f.Assemble()
def BuildRenderData(mesh,
func,
order=2,
draw_surf=True,
draw_vol=True,
deformation=None):
timer.Start()
#TODO: handle quads and non-smooth functions
#TODO: subdivision
d = {}
d['ngsolve_version'] = ngs.__version__
d['mesh_dim'] = mesh.dim
# order = order or mesh.GetCurveOrder()
if (not func) and (mesh.GetCurveOrder() == 1):
order = 1
order2d = min(order, 3)
order3d = min(order, 2)
d['order2d'] = order2d
d['order3d'] = order3d
d['draw_vol'] = func and mesh.dim == 3 and draw_vol
d['draw_surf'] = func and draw_surf
if isinstance(deformation, bool):
d['deformation'] = deformation
deformation = None
func2 = None
if func and func.is_complex:
d['is_complex'] = True
func1 = func[0].real
func2 = ngs.CoefficientFunction((func[0].imag, 0.0))
d['funcdim'] = 2
elif func and func.dim > 1:
func1 = func[0]
func2 = ngs.CoefficientFunction(
tuple(func[i] if i < func.dim else 0.0
for i in range(1, 3))) # max 3-dimensional functions
d['funcdim'] = func.dim
elif func:
func1 = func
d['funcdim'] = 1
else:
func1 = ngs.CoefficientFunction(0.0)
d['funcdim'] = 0
func1 = ngs.CoefficientFunction((ngs.x, ngs.y, ngs.z, func1))
func0 = ngs.CoefficientFunction((ngs.x, ngs.y, ngs.z, 0.0))
if deformation is not None:
func1 += ngs.CoefficientFunction((deformation, 0.0))
func0 += ngs.CoefficientFunction((deformation, 0.0))
d['show_wireframe'] = False
d['show_mesh'] = False
if order2d > 0:
og = order2d
d['show_wireframe'] = True
d['show_mesh'] = True
timer2.Start()
timer3Bvals.Start()
# transform point-values to Bernsteinbasis
def Binomial(n, i):
return math.factorial(n) / math.factorial(i) / math.factorial(n -
i)
def Bernstein(x, i, n):
return Binomial(n, i) * x**i * (1 - x)**(n - i)
Bvals = ngs.Matrix(og + 1, og + 1)
for i in range(og + 1):
for j in range(og + 1):
Bvals[i, j] = Bernstein(i / og, j, og)
iBvals = Bvals.I
timer3Bvals.Stop()
# print (Bvals)
# print (iBvals)
Bezier_points = []
# TODO: Quads
ipts = [(i / og, 0) for i in range(og + 1)] + [
(0, i / og) for i in range(og + 1)
] + [(i / og, 1.0 - i / og) for i in range(og + 1)]
ir = ngs.IntegrationRule(ipts, [
0,
] * len(ipts))
vb = [ngs.VOL, ngs.BND][mesh.dim - 2]
pts = mesh.MapToAllElements(ir, vb)
cf = func1 if draw_surf else func0
pmat = cf(pts)
timermult.Start()
pmat = pmat.reshape(-1, og + 1, 4)
BezierPnts = np.tensordot(iBvals.NumPy(), pmat, axes=(1, 1))
timermult.Stop()
timer2list.Start()
for i in range(og + 1):
Bezier_points.append(encodeData(BezierPnts[i]))
timer2list.Stop()
if func2 and draw_surf:
pmat = func2(pts)
pmat = pmat.reshape(-1, og + 1, 2)
timermult.Start()
BezierPnts = np.tensordot(iBvals.NumPy(), pmat, axes=(1, 1))
timermult.Stop()
timer2list.Start()
for i in range(og + 1):
Bezier_points.append(encodeData(BezierPnts[i]))
timer2list.Stop()
d['Bezier_points'] = Bezier_points
timer2.Stop()
timer3.Start()
ndtrig = int((og + 1) * (og + 2) / 2)
if og in bezier_trig_trafos.keys():
iBvals_trig = bezier_trig_trafos[og]
else:
def BernsteinTrig(x, y, i, j, n):
return math.factorial(n)/math.factorial(i)/math.factorial(j)/math.factorial(n-i-j) \
* x**i*y**j*(1-x-y)**(n-i-j)
Bvals = ngs.Matrix(ndtrig, ndtrig)
ii = 0
for ix in range(og + 1):
for iy in range(og + 1 - ix):
jj = 0
for jx in range(og + 1):
for jy in range(og + 1 - jx):
Bvals[ii,
jj] = BernsteinTrig(ix / og, iy / og, jx, jy,
og)
jj += 1
ii += 1
iBvals_trig = Bvals.I
bezier_trig_trafos[og] = iBvals_trig
# Bezier_points = [ [] for i in range(ndtrig) ]
Bezier_points = []
ir = ngs.IntegrationRule([(i / og, j / og) for j in range(og + 1)
for i in range(og + 1 - j)], [
0,
] * (ndtrig))
vb = [ngs.VOL, ngs.BND][mesh.dim - 2]
pts = mesh.MapToAllElements(ir, vb)
pmat = ngs.CoefficientFunction(func1 if draw_surf else func0)(pts)
timer3minmax.Start()
funcmin = np.min(pmat[:, 3])
funcmax = np.max(pmat[:, 3])
pmin = np.min(pmat[:, 0:3], axis=0)
pmax = np.max(pmat[:, 0:3], axis=0)
mesh_center = (pmin + pmax) / 2
mesh_radius = np.linalg.norm(pmax - pmin) / 2
timer3minmax.Stop()
pmat = pmat.reshape(mesh.GetNE(vb), len(ir), 4)
BezierPnts = np.tensordot(iBvals_trig.NumPy(), pmat, axes=(1, 1))
timer3list.Start()
for i in range(ndtrig):
Bezier_points.append(encodeData(BezierPnts[i]))
timer3list.Stop()
if func2 and draw_surf:
pmat = ngs.CoefficientFunction(func2)(pts)
pmat = pmat.reshape(mesh.GetNE(vb), len(ir), 2)
funcmin = min(funcmin, np.min(pmat))
funcmax = max(funcmax, np.max(pmat))
BezierPnts = np.tensordot(iBvals_trig.NumPy(), pmat, axes=(1, 1))
if og == 1:
for i in range(ndtrig):
Bezier_points.append(encodeData(BezierPnts[i]))
else:
BezierPnts = BezierPnts.transpose(
(1, 0, 2)).reshape(mesh.GetNE(vb),
len(ir) // 2, 4).transpose((1, 0, 2))
for i in range(ndtrig // 2):
Bezier_points.append(encodeData(BezierPnts[i]))
d['Bezier_trig_points'] = Bezier_points
d['mesh_center'] = list(mesh_center)
d['mesh_radius'] = mesh_radius
timer3.Stop()
timer4.Start()
if mesh.dim == 3 and draw_vol:
p0 = []
p1 = []
p2 = []
p3 = []
values = []
tets = []
if order3d == 1:
ir = ngs.IntegrationRule([(1, 0, 0), (0, 1, 0), (0, 0, 1),
(0, 0, 0)], [0] * 4)
else:
ir = ngs.IntegrationRule([(1, 0, 0), (0, 1, 0),
(0, 0, 1), (0, 0, 0), (0.5, 0, 0),
(0, 0.5, 0), (0, 0, 0.5), (0.5, 0.5, 0),
(0.5, 0, 0.5), (0, 0.5, 0.5)], [0] * 10)
pts = mesh.MapToAllElements(ir, ngs.VOL)
pmat = func1(pts) if draw_vol else func0(pts)
ne = mesh.GetNE(ngs.VOL)
pmat = pmat.reshape(ne, len(ir), 4)
funcmin = min(funcmin, np.min(pmat[:, :, 3]))
funcmax = max(funcmax, np.max(pmat[:, :, 3]))
points3d = []
for i in range(len(ir)):
points3d.append(encodeData(pmat[:, i, :]))
if func2 and draw_vol:
pmat = func2(pts).reshape(ne, len(ir) // 2, 4)
funcmin = min(funcmin, np.min(pmat))
funcmax = max(funcmax, np.max(pmat))
for i in range(len(ir) // 2):
points3d.append(encodeData(pmat[:, i, :]))
d['points3d'] = points3d
if func:
d['funcmin'] = funcmin
d['funcmax'] = funcmax
timer4.Stop()
timer.Stop()
return d
li_factor = sqrt(solubility_difference) * sqrt(concentration)
return F * reaction_rate * li_factor
mesh = ngs.Mesh('mesh.vol')
n_lithium_space = ngs.H1(mesh, order=1)
potential_space = ngs.H1(mesh, order=1, dirichlet='anode')
V = ngs.FESpace([n_lithium_space, potential_space])
print(V.ndof)
u, p = V.TrialFunction()
v, q = V.TestFunction()
# Coefficient functions
cf_diffusivity = ngs.CoefficientFunction([diffusivity[mat] for mat in mesh.GetMaterials()])
cf_conductivity = ngs.CoefficientFunction([conductivity[mat] for mat in mesh.GetMaterials()])
cf_valence = ngs.CoefficientFunction([valence[mat] for mat in mesh.GetMaterials()])
def material_overpotential_cathode(concentr, pot):
"""Return material overpotential for cathode Li_yMn2O4 particles"""
return pot - open_circuit_manganese(concentr) + ohmic_contact_pot # V
def material_overpotential_anode(concentr, pot):
"""Return material overpotential for Li_xC6 anode"""
return pot - open_circuit_carbon(concentr) + ohmic_contact_pot # V
mass = ngs.BilinearForm(V)
def BuildRenderData(mesh,
func,
order=2,
draw_surf=True,
draw_vol=True,
deformation=None,
region=True,
objects=[]):
timer.Start()
if isinstance(deformation,
ngs.CoefficientFunction) and deformation.dim == 2:
deformation = ngs.CoefficientFunction((deformation, 0.0))
#TODO: handle quads and non-smooth functions
#TODO: subdivision
d = {}
d['ngsolve_version'] = ngs.__version__
d['mesh_dim'] = mesh.dim
# order = order or mesh.GetCurveOrder()
if (not func) and (mesh.GetCurveOrder() == 1) and (mesh.nv == len(
mesh.ngmesh.Points())):
order = 1
order2d = min(order, 3)
order3d = min(order, 2)
d['order2d'] = order2d
d['order3d'] = order3d
d['draw_vol'] = func and mesh.dim == 3 and draw_vol and mesh.ne > 0
d['draw_surf'] = func and draw_surf
d['objects'] = []
for obj in objects:
if isinstance(obj, dict):
d['objects'].append(obj)
else:
d['objects'].append(obj._GetWebguiData())
if isinstance(deformation, bool):
d['deformation'] = deformation
deformation = None
func0 = None
func2 = None
if func and func.is_complex:
d['is_complex'] = True
func1 = func[0].real
func2 = ngs.CoefficientFunction((func[0].imag, 0.0))
d['funcdim'] = 2
elif func and func.dim > 1:
func1 = func[0]
func2 = ngs.CoefficientFunction(
tuple(func[i] if i < func.dim else 0.0
for i in range(1, 3))) # max 3-dimensional functions
d['funcdim'] = func.dim
elif func:
func1 = func
d['funcdim'] = 1
else:
# no function at all -> we are just drawing a mesh, eval mesh element index instead
mats = mesh.GetMaterials()
bnds = mesh.GetBoundaries()
bbnds = mesh.GetBBoundaries()
nmats = len(mesh.GetMaterials())
nbnds = len(mesh.GetBoundaries())
n = max(nmats, nbnds, len(bbnds))
func1 = ngs.CoefficientFunction(list(range(n)))
n_regions = [0, 0, nmats, nbnds]
d['mesh_regions_2d'] = n_regions[mesh.dim]
d['mesh_regions_3d'] = nmats if mesh.dim == 3 else 0
d['names'] = bnds if mesh.dim == 3 else mats
d['edge_names'] = bbnds if mesh.dim == 3 else bnds
d['funcdim'] = 0
func0 = func1
if func0 is None:
func0 = ngs.CoefficientFunction(0.0)
func1 = ngs.CoefficientFunction((ngs.x, ngs.y, ngs.z, func1))
func0 = ngs.CoefficientFunction((ngs.x, ngs.y, ngs.z, func0))
if deformation is not None:
func1 += ngs.CoefficientFunction((deformation, 0.0))
func0 += ngs.CoefficientFunction((deformation, 0.0))
d['show_wireframe'] = False
d['show_mesh'] = False
if order2d > 0:
og = order2d
d['show_wireframe'] = True
d['show_mesh'] = True
timer2.Start()
timer3Bvals.Start()
# transform point-values to Bernsteinbasis
def Binomial(n, i):
return math.factorial(n) / math.factorial(i) / math.factorial(n -
i)
def Bernstein(x, i, n):
return Binomial(n, i) * x**i * (1 - x)**(n - i)
Bvals = ngs.Matrix(og + 1, og + 1)
for i in range(og + 1):
for j in range(og + 1):
Bvals[i, j] = Bernstein(i / og, j, og)
iBvals = Bvals.I
timer3Bvals.Stop()
# print (Bvals)
# print (iBvals)
Bezier_points = []
# TODO: Quads
ipts = [(i / og, 0) for i in range(og + 1)] + [
(0, i / og) for i in range(og + 1)
] + [(i / og, 1.0 - i / og) for i in range(og + 1)]
ir_trig = ngs.IntegrationRule(ipts, [
0,
] * len(ipts))
ipts = [(i / og, 0) for i in range(og + 1)] + [
(0, i / og) for i in range(og + 1)
] + [(i / og, 1.0) for i in range(og + 1)] + [(1.0, i / og)
for i in range(og + 1)]
ir_quad = ngs.IntegrationRule(ipts, [
0,
] * len(ipts))
vb = [ngs.VOL, ngs.BND][mesh.dim - 2]
if region and region.VB() == vb:
vb = region
cf = func1 if draw_surf else func0
timer2map.Start()
pts = mesh.MapToAllElements(
{
ngs.ET.TRIG: ir_trig,
ngs.ET.QUAD: ir_quad
}, vb)
timer2map.Stop()
pmat = cf(pts)
pmima = updatePMinMax(pmat)
timermult.Start()
pmat = pmat.reshape(-1, og + 1, 4)
if False:
BezierPnts = np.tensordot(iBvals.NumPy(), pmat, axes=(1, 1))
else:
BezierPnts = np.zeros((og + 1, pmat.shape[0], 4))
for i in range(4):
ngsmat = ngs.Matrix(pmat[:, :, i].transpose())
BezierPnts[:, :, i] = iBvals * ngsmat
timermult.Stop()
timer2list.Start()
for i in range(og + 1):
Bezier_points.append(encodeData(BezierPnts[i]))
timer2list.Stop()
if func2 and draw_surf:
pmat = func2(pts)
pmat = pmat.reshape(-1, og + 1, 2)
timermult.Start()
BezierPnts = np.tensordot(iBvals.NumPy(), pmat, axes=(1, 1))
timermult.Stop()
timer2list.Start()
for i in range(og + 1):
Bezier_points.append(encodeData(BezierPnts[i]))
timer2list.Stop()
d['Bezier_points'] = Bezier_points
ipts = [(i / og, 0) for i in range(og + 1)]
ir_seg = ngs.IntegrationRule(ipts, [
0,
] * len(ipts))
vb = [ngs.VOL, ngs.BND, ngs.BBND][mesh.dim - 1]
if region and region.VB() == vb:
vb = region
pts = mesh.MapToAllElements(ir_seg, vb)
pmat = func0(pts)
pmima = updatePMinMax(pmat)
pmat = pmat.reshape(-1, og + 1, 4)
edge_data = np.tensordot(iBvals.NumPy(), pmat, axes=(1, 1))
edges = []
for i in range(og + 1):
edges.append(encodeData(edge_data[i]))
d['edges'] = edges
timer2.Stop()
timer3.Start()
ndtrig = int((og + 1) * (og + 2) / 2)
if og in bezier_trig_trafos.keys():
iBvals_trig = bezier_trig_trafos[og]
else:
def BernsteinTrig(x, y, i, j, n):
return math.factorial(n)/math.factorial(i)/math.factorial(j)/math.factorial(n-i-j) \
* x**i*y**j*(1-x-y)**(n-i-j)
Bvals = ngs.Matrix(ndtrig, ndtrig)
ii = 0
for ix in range(og + 1):
for iy in range(og + 1 - ix):
jj = 0
for jx in range(og + 1):
for jy in range(og + 1 - jx):
Bvals[ii,
jj] = BernsteinTrig(ix / og, iy / og, jx, jy,
og)
jj += 1
ii += 1
iBvals_trig = Bvals.I
bezier_trig_trafos[og] = iBvals_trig
# Bezier_points = [ [] for i in range(ndtrig) ]
Bezier_points = []
ipts = [(i / og, j / og) for j in range(og + 1)
for i in range(og + 1 - j)]
ir_trig = ngs.IntegrationRule(ipts, [
0,
] * len(ipts))
ipts = ([(i / og, j / og) for j in range(og + 1)
for i in range(og + 1 - j)] + [(1 - i / og, 1 - j / og)
for j in range(og + 1)
for i in range(og + 1 - j)])
ir_quad = ngs.IntegrationRule(ipts, [
0,
] * len(ipts))
vb = [ngs.VOL, ngs.BND][mesh.dim - 2]
if region and region.VB() == vb:
vb = region
pts = mesh.MapToAllElements(
{
ngs.ET.TRIG: ir_trig,
ngs.ET.QUAD: ir_quad
}, vb)
pmat = ngs.CoefficientFunction(func1 if draw_surf else func0)(pts)
timer3minmax.Start()
pmima = updatePMinMax(pmat, pmima)
funcmin, funcmax = getMinMax(pmat[:, 3])
timer3minmax.Stop()
pmin, pmax = [ngs.Vector(p) for p in zip(*pmima)]
mesh_center = 0.5 * (pmin + pmax)
mesh_radius = np.linalg.norm(pmax - pmin) / 2
pmat = pmat.reshape(-1, len(ir_trig), 4)
if False:
timer3multnumpy.Start()
BezierPnts = np.tensordot(iBvals_trig.NumPy(), pmat, axes=(1, 1))
timer3multnumpy.Stop()
else:
timer3multngs.Start()
BezierPnts = np.zeros((len(ir_trig), pmat.shape[0], 4))
for i in range(4):
ngsmat = ngs.Matrix(pmat[:, :, i].transpose())
BezierPnts[:, :, i] = iBvals_trig * ngsmat
timer3multngs.Stop()
timer3list.Start()
for i in range(ndtrig):
Bezier_points.append(encodeData(BezierPnts[i]))
timer3list.Stop()
if func2 and draw_surf:
pmat = ngs.CoefficientFunction(func2)(pts)
pmat = pmat.reshape(-1, len(ir_trig), 2)
funcmin, funcmax = getMinMax(pmat.flatten(), funcmin, funcmax)
BezierPnts = np.tensordot(iBvals_trig.NumPy(), pmat, axes=(1, 1))
if og == 1:
for i in range(ndtrig):
Bezier_points.append(encodeData(BezierPnts[i]))
else:
BezierPnts = BezierPnts.transpose(
(1, 0, 2)).reshape(-1,
len(ir_trig) // 2, 4).transpose(
(1, 0, 2))
for i in range(ndtrig // 2):
Bezier_points.append(encodeData(BezierPnts[i]))
d['Bezier_trig_points'] = Bezier_points
d['mesh_center'] = list(mesh_center)
d['mesh_radius'] = mesh_radius
timer3.Stop()
timer4.Start()
if d['draw_vol']:
p0 = []
p1 = []
p2 = []
p3 = []
values = []
tets = []
midpoint = lambda p0, p1: tuple(
(0.5 * (p0[i] + p1[i]) for i in range(3)))
def makeP2Tets(p1_tets):
p2_tets = []
for tet in p1_tets:
tet.append(midpoint(tet[0], tet[3]))
tet.append(midpoint(tet[1], tet[3]))
tet.append(midpoint(tet[2], tet[3]))
tet.append(midpoint(tet[0], tet[1]))
tet.append(midpoint(tet[0], tet[2]))
tet.append(midpoint(tet[1], tet[2]))
p2_tets.append(tet)
return p2_tets
# divide any element into tets
p1_tets = {}
p1_tets[ngs.ET.TET] = [[(1, 0, 0), (0, 1, 0), (0, 0, 1), (0, 0, 0)]]
p1_tets[ngs.ET.PYRAMID] = [[(1, 0, 0), (0, 1, 0), (0, 0, 1),
(0, 0, 0)],
[(1, 0, 0), (0, 1, 0), (0, 0, 1),
(1, 1, 0)]]
p1_tets[ngs.ET.PRISM] = [[(1, 0, 0), (0, 1, 0), (0, 0, 1), (0, 0, 0)],
[(0, 0, 1), (0, 1, 0), (0, 1, 1), (1, 0, 0)],
[(1, 0, 1), (0, 1, 1), (1, 0, 0), (0, 0, 1)]]
p1_tets[ngs.ET.HEX] = [[(1, 0, 0), (0, 1, 0), (0, 0, 1), (0, 0, 0)],
[(0, 1, 1), (1, 1, 1), (1, 1, 0), (1, 0, 1)],
[(1, 0, 1), (0, 1, 1), (1, 0, 0), (0, 0, 1)],
[(0, 1, 1), (1, 1, 0), (0, 1, 0), (1, 0, 0)],
[(0, 0, 1), (0, 1, 0), (0, 1, 1), (1, 0, 0)],
[(1, 0, 1), (1, 1, 0), (0, 1, 1), (1, 0, 0)]]
intrules = {}
for eltype in p1_tets:
points = p1_tets[eltype]
if order3d > 1:
points = makeP2Tets(points)
intrules[eltype] = ngs.IntegrationRule(sum(points, []))
pts = mesh.MapToAllElements(intrules, ngs.VOL)
pmat = func1(pts)
np_per_tet = len(intrules[ngs.ET.TET])
ne = mesh.GetNE(ngs.VOL)
pmat = pmat.reshape(-1, np_per_tet, 4)
funcmin, funcmax = getMinMax(pmat[:, :, 3].flatten(), funcmin, funcmax)
points3d = []
for i in range(np_per_tet):
points3d.append(encodeData(pmat[:, i, :]))
if func2:
pmat = func2(pts).reshape(-1, np_per_tet // 2, 4)
funcmin, funcmax = getMinMax(pmat.flatten(), funcmin, funcmax)
for i in range(np_per_tet // 2):
points3d.append(encodeData(pmat[:, i, :]))
d['points3d'] = points3d
if func:
d['funcmin'] = funcmin
d['funcmax'] = funcmax
timer4.Stop()
timer.Stop()
return d
def setup_rot_elast(mesh,
mu=1,
lam=0,
f_vol=None,
multidim=True,
reorder=False,
diri=".*",
order=1,
fes_opts=dict(),
blf_opts=dict(),
lf_opts=dict()):
dim = mesh.dim
mysum = lambda x: sum(x[1:], x[0])
if dim == 2:
to_skew = lambda x: ngs.CoefficientFunction(
(0, -x[0], x[0], 0), dims=(2, 2))
else:
# to_skew = lambda x : ngs.CoefficientFunction( ( 0 , x[2], -x[1], \
# -x[2], 0 , x[0], \
# x[1], -x[0], 0), dims = (3,3) )
to_skew = lambda x : ngs.CoefficientFunction( ( 0 , -x[2], x[1], \
x[2], 0 , -x[0], \
-x[1], x[0], 0), dims = (3,3) )
if multidim:
mdim = dim + ((dim - 1) * dim) // 2
V = ngs.H1(mesh, order=order, dirichlet=diri, **fes_opts, dim=mdim)
if reorder:
V = ngs.comp.Reorder(V)
trial, test = V.TnT()
u = ngs.CoefficientFunction(tuple(trial[x] for x in range(dim)))
gradu = ngs.CoefficientFunction(tuple(
ngs.Grad(trial)[i, j] for i in range(dim) for j in range(dim)),
dims=(dim, dim))
divu = mysum([ngs.Grad(trial)[i, i] for i in range(dim)])
w = to_skew([trial[x] for x in range(dim, mdim)])
ut = ngs.CoefficientFunction(tuple(test[x] for x in range(dim)))
gradut = ngs.CoefficientFunction(tuple(
ngs.Grad(test)[i, j] for i in range(dim) for j in range(dim)),
dims=(dim, dim))
divut = mysum([ngs.Grad(test)[i, i] for i in range(dim)])
wt = to_skew([test[x] for x in range(dim, mdim)])
else:
Vu = ngs.VectorH1(mesh, order=order, dirichlet=diri, **fes_opts)
if reorder == "sep":
Vu = ngs.comp.Reorder(Vu)
if dim == 3:
Vw = Vu
else:
Vw = ngs.H1(mesh, order=order, dirichlet=diri, **fes_opts)
if reorder == "sep":
Vw = ngs.comp.Reorder(Vw)
V = ngs.FESpace([Vu, Vw])
# print("free pre RO: ", V.FreeDofs())
if reorder is True:
V = ngs.comp.Reorder(V)
# print("free post RO: ", V.FreeDofs())
(u, w), (ut, wt) = V.TnT()
gradu = ngs.Grad(u)
divu = mysum([ngs.Grad(u)[i, i] for i in range(dim)])
w = to_skew(w)
gradut = ngs.Grad(ut)
divut = mysum([ngs.Grad(ut)[i, i] for i in range(dim)])
wt = to_skew(wt)
a = ngs.BilinearForm(V, **blf_opts)
a += (mu * ngs.InnerProduct(gradu - w, gradut - wt)) * ngs.dx
#a += ngs.InnerProduct(w,wt) * ngs.dx
#trial, test = V.TnT()
#a += 0.1 * ngs.InnerProduct(trial,test) * ngs.dx
if lam != 0:
a += lam * divu * divut * ngs.dx
lf = ngs.LinearForm(V)
lf += f_vol * ut * ngs.dx
return V, a, lf