def coarsen_form(form):
"""Return a coarse mesh version of a form
:arg form: The :class:`~ufl.classes.Form` to coarsen.
This maps over the form and replaces coefficients and arguments
with their coarse mesh equivalents."""
if form is None:
return None
assert isinstance(form, ufl.Form), \
"Don't know how to coarsen %r" % type(form)
mapper = CoarsenIntegrand()
forms = []
# Ugh, visitors can't deal with measures (they're not actual
# Exprs) so we need to map the transformer over the integrand and
# reconstruct the integral by building the measure by hand.
for it in form.integrals():
integrand = map_expr_dag(mapper, it.integrand())
mesh = it.ufl_domain()
hierarchy, level = utils.get_level(mesh)
new_mesh = hierarchy[level - 1]
measure = ufl.Measure(it.integral_type(),
domain=new_mesh,
subdomain_id=it.subdomain_id(),
subdomain_data=it.subdomain_data(),
metadata=it.metadata())
forms.append(integrand * measure)
return reduce(add, forms)
def test_interpolate_subset(order, dim, affine):
if dim == 2:
ct = CellType.triangle if affine else CellType.quadrilateral
mesh = create_unit_square(MPI.COMM_WORLD, 3, 4, ct)
elif dim == 3:
ct = CellType.tetrahedron if affine else CellType.hexahedron
mesh = create_unit_cube(MPI.COMM_WORLD, 3, 2, 2, ct)
V = FunctionSpace(mesh, ("DG", order))
u = Function(V)
cells = locate_entities(mesh, mesh.topology.dim,
lambda x: x[1] <= 0.5 + 1e-10)
num_local_cells = mesh.topology.index_map(mesh.topology.dim).size_local
cells_local = cells[cells < num_local_cells]
x = ufl.SpatialCoordinate(mesh)
f = x[1]**order
expr = Expression(f, V.element.interpolation_points)
u.interpolate(expr, cells_local)
mt = MeshTags(mesh, mesh.topology.dim, cells_local,
np.ones(cells_local.size, dtype=np.int32))
dx = ufl.Measure("dx", domain=mesh, subdomain_data=mt)
assert np.isclose(
np.abs(form(assemble_scalar(form(ufl.inner(u - f, u - f) * dx(1))))),
0)
integral = mesh.comm.allreduce(assemble_scalar(form(u * dx)), op=MPI.SUM)
assert np.isclose(integral, 1 / (order + 1) * 0.5**(order + 1), 0)
def test_assembly_dx_domains(mode):
mesh = dolfinx.generation.UnitSquareMesh(MPI.COMM_WORLD,
10,
10,
ghost_mode=mode)
V = dolfinx.FunctionSpace(mesh, ("CG", 1))
u, v = ufl.TrialFunction(V), ufl.TestFunction(V)
# Prepare a marking structures
# indices cover all cells
# values are [1, 2, 3, 3, ...]
cell_map = mesh.topology.index_map(mesh.topology.dim)
num_cells = cell_map.size_local + cell_map.num_ghosts
indices = numpy.arange(0, num_cells)
values = numpy.full(indices.shape, 3, dtype=numpy.intc)
values[0] = 1
values[1] = 2
marker = dolfinx.mesh.MeshTags(mesh, mesh.topology.dim, indices, values)
dx = ufl.Measure('dx', subdomain_data=marker, domain=mesh)
w = dolfinx.Function(V)
with w.vector.localForm() as w_local:
w_local.set(0.5)
bc = dolfinx.fem.DirichletBC(dolfinx.Function(V), range(30))
# Assemble matrix
a = w * ufl.inner(u, v) * (dx(1) + dx(2) + dx(3))
A = dolfinx.fem.assemble_matrix(a)
A.assemble()
a2 = w * ufl.inner(u, v) * dx
A2 = dolfinx.fem.assemble_matrix(a2)
A2.assemble()
assert (A - A2).norm() < 1.0e-12
# Assemble vector
L = ufl.inner(w, v) * (dx(1) + dx(2) + dx(3))
b = dolfinx.fem.assemble_vector(L)
dolfinx.fem.apply_lifting(b, [a], [[bc]])
b.ghostUpdate(addv=PETSc.InsertMode.ADD_VALUES,
mode=PETSc.ScatterMode.REVERSE)
dolfinx.fem.set_bc(b, [bc])
L2 = ufl.inner(w, v) * dx
b2 = dolfinx.fem.assemble_vector(L2)
dolfinx.fem.apply_lifting(b2, [a], [[bc]])
b2.ghostUpdate(addv=PETSc.InsertMode.ADD_VALUES,
mode=PETSc.ScatterMode.REVERSE)
dolfinx.fem.set_bc(b2, [bc])
assert (b - b2).norm() < 1.0e-12
# Assemble scalar
L = w * (dx(1) + dx(2) + dx(3))
s = dolfinx.fem.assemble_scalar(L)
s = mesh.mpi_comm().allreduce(s, op=MPI.SUM)
assert s == pytest.approx(0.5, 1.0e-12)
L2 = w * dx
s2 = dolfinx.fem.assemble_scalar(L2)
s2 = mesh.mpi_comm().allreduce(s2, op=MPI.SUM)
assert s == pytest.approx(s2, 1.0e-12)
def test_assembly_dx_domains(mesh):
V = dolfinx.FunctionSpace(mesh, ("CG", 1))
u, v = ufl.TrialFunction(V), ufl.TestFunction(V)
# Prepare a marking structures
# indices cover all cells
# values are [1, 2, 3, 3, ...]
imap = mesh.topology.index_map(mesh.topology.dim)
num_cells = imap.size_local + imap.num_ghosts
indices = numpy.arange(0, num_cells)
values = numpy.full(indices.shape, 3, dtype=numpy.intc)
values[0] = 1
values[1] = 2
marker = dolfinx.mesh.MeshTags(mesh, mesh.topology.dim, indices, values)
dx = ufl.Measure('dx', subdomain_data=marker, domain=mesh)
w = dolfinx.Function(V)
with w.vector.localForm() as w_local:
w_local.set(0.5)
# Assemble matrix
a = w * ufl.inner(u, v) * (dx(1) + dx(2) + dx(3))
A = dolfinx.fem.assemble_matrix(a)
A.assemble()
norm1 = A.norm()
a2 = w * ufl.inner(u, v) * dx
A2 = dolfinx.fem.assemble_matrix(a2)
A2.assemble()
norm2 = A2.norm()
assert norm1 == pytest.approx(norm2, 1.0e-12)
# Assemble vector
L = ufl.inner(w, v) * (dx(1) + dx(2) + dx(3))
b = dolfinx.fem.assemble_vector(L)
b.ghostUpdate(addv=PETSc.InsertMode.ADD, mode=PETSc.ScatterMode.REVERSE)
L2 = ufl.inner(w, v) * dx
b2 = dolfinx.fem.assemble_vector(L2)
b2.ghostUpdate(addv=PETSc.InsertMode.ADD, mode=PETSc.ScatterMode.REVERSE)
assert b.norm() == pytest.approx(b2.norm(), 1.0e-12)
# Assemble scalar
L = w * (dx(1) + dx(2) + dx(3))
s = dolfinx.fem.assemble_scalar(L)
s = mesh.mpi_comm().allreduce(s, op=MPI.SUM)
L2 = w * dx
s2 = dolfinx.fem.assemble_scalar(L2)
s2 = mesh.mpi_comm().allreduce(s2, op=MPI.SUM)
assert (s == pytest.approx(s2, 1.0e-12)
and 0.5 == pytest.approx(s, 1.0e-12))
def test_assembly_ds_domains(mesh):
V = dolfinx.FunctionSpace(mesh, ("CG", 1))
u, v = ufl.TrialFunction(V), ufl.TestFunction(V)
marker = dolfinx.MeshFunction("size_t", mesh, mesh.topology.dim - 1, 0)
def bottom(x):
return numpy.isclose(x[1], 0.0)
def top(x):
return numpy.isclose(x[1], 1.0)
def left(x):
return numpy.isclose(x[0], 0.0)
def right(x):
return numpy.isclose(x[0], 1.0)
marker.mark(bottom, 111)
marker.mark(top, 222)
marker.mark(left, 333)
marker.mark(right, 444)
ds = ufl.Measure('ds', subdomain_data=marker, domain=mesh)
w = dolfinx.Function(V)
with w.vector.localForm() as w_local:
w_local.set(0.5)
# Assemble matrix
a = w * ufl.inner(u, v) * (ds(111) + ds(222) + ds(333) + ds(444))
A = dolfinx.fem.assemble_matrix(a)
A.assemble()
norm1 = A.norm()
a2 = w * ufl.inner(u, v) * ds
A2 = dolfinx.fem.assemble_matrix(a2)
A2.assemble()
norm2 = A2.norm()
assert norm1 == pytest.approx(norm2, 1.0e-12)
# Assemble vector
L = ufl.inner(w, v) * (ds(111) + ds(222) + ds(333) + ds(444))
b = dolfinx.fem.assemble_vector(L)
b.ghostUpdate(addv=PETSc.InsertMode.ADD, mode=PETSc.ScatterMode.REVERSE)
L2 = ufl.inner(w, v) * ds
b2 = dolfinx.fem.assemble_vector(L2)
b2.ghostUpdate(addv=PETSc.InsertMode.ADD, mode=PETSc.ScatterMode.REVERSE)
assert b.norm() == pytest.approx(b2.norm(), 1.0e-12)
# Assemble scalar
L = w * (ds(111) + ds(222) + ds(333) + ds(444))
s = dolfinx.fem.assemble_scalar(L)
s = dolfinx.MPI.sum(mesh.mpi_comm(), s)
L2 = w * ds
s2 = dolfinx.fem.assemble_scalar(L2)
s2 = dolfinx.MPI.sum(mesh.mpi_comm(), s2)
assert (s == pytest.approx(s2, 1.0e-12)
and 2.0 == pytest.approx(s, 1.0e-12))
def test_assembly_dx_domains(mode, meshtags_factory):
mesh = create_unit_square(MPI.COMM_WORLD, 10, 10, ghost_mode=mode)
V = FunctionSpace(mesh, ("Lagrange", 1))
u, v = ufl.TrialFunction(V), ufl.TestFunction(V)
# Prepare a marking structures
# indices cover all cells
# values are [1, 2, 3, 3, ...]
cell_map = mesh.topology.index_map(mesh.topology.dim)
num_cells = cell_map.size_local + cell_map.num_ghosts
indices = np.arange(0, num_cells)
values = np.full(indices.shape, 3, dtype=np.intc)
values[0] = 1
values[1] = 2
marker = meshtags_factory(mesh, mesh.topology.dim, indices, values)
dx = ufl.Measure('dx', subdomain_data=marker, domain=mesh)
w = Function(V)
w.x.array[:] = 0.5
# Assemble matrix
a = form(w * ufl.inner(u, v) * (dx(1) + dx(2) + dx(3)))
A = assemble_matrix(a)
A.assemble()
a2 = form(w * ufl.inner(u, v) * dx)
A2 = assemble_matrix(a2)
A2.assemble()
assert (A - A2).norm() < 1.0e-12
bc = dirichletbc(Function(V), range(30))
# Assemble vector
L = form(ufl.inner(w, v) * (dx(1) + dx(2) + dx(3)))
b = assemble_vector(L)
apply_lifting(b, [a], [[bc]])
b.ghostUpdate(addv=PETSc.InsertMode.ADD_VALUES,
mode=PETSc.ScatterMode.REVERSE)
set_bc(b, [bc])
L2 = form(ufl.inner(w, v) * dx)
b2 = assemble_vector(L2)
apply_lifting(b2, [a], [[bc]])
b2.ghostUpdate(addv=PETSc.InsertMode.ADD_VALUES,
mode=PETSc.ScatterMode.REVERSE)
set_bc(b2, [bc])
assert (b - b2).norm() < 1.0e-12
# Assemble scalar
L = form(w * (dx(1) + dx(2) + dx(3)))
s = assemble_scalar(L)
s = mesh.comm.allreduce(s, op=MPI.SUM)
assert s == pytest.approx(0.5, 1.0e-12)
L2 = form(w * dx)
s2 = assemble_scalar(L2)
s2 = mesh.comm.allreduce(s2, op=MPI.SUM)
assert s == pytest.approx(s2, 1.0e-12)
def norm_L2(u):
"""
Returns the L2 norm of the function u
"""
comm = u.function_space.mesh.comm
dx = ufl.Measure("dx", u.function_space.mesh)
norm_form = form(ufl.inner(u, u) * dx)
norm = np.sqrt(
comm.allreduce(assemble_scalar(norm_form), op=mpi4py.MPI.SUM))
return norm
def assemble(mesh, space, k):
V = fem.FunctionSpace(mesh, (space, k))
u, v = ufl.TrialFunction(V), ufl.TestFunction(V)
dx = ufl.Measure("dx", domain=mesh)
a = fem.form(ufl.inner(u, v) * dx)
A = fem.petsc.assemble_matrix(a)
A.assemble()
return A
def translate_facetarea(terminal, mt, ctx):
assert ctx.integral_type != 'cell'
domain = terminal.ufl_domain()
integrand, degree = one_times(ufl.Measure(ctx.integral_type, domain=domain))
config = {name: getattr(ctx, name)
for name in ["ufl_cell", "integration_dim",
"entity_ids", "precision", "index_cache"]}
config.update(interface=ctx, quadrature_degree=degree)
expr, = compile_ufl(integrand, point_sum=True, **config)
return expr
def test_facet_area1D():
mesh = create_unit_interval(MPI.COMM_WORLD, 10)
# NOTE: Area of a vertex is defined to 1 in ufl
c0 = ufl.FacetArea(mesh)
c = Constant(mesh, ScalarType(1))
ds = ufl.Measure("ds", domain=mesh)
a0 = mesh.comm.allreduce(assemble_scalar(form(c * ds)), op=MPI.SUM)
a = mesh.comm.allreduce(assemble_scalar(form(c0 * ds)), op=MPI.SUM)
assert numpy.isclose(a.real, 2)
assert numpy.isclose(a0.real, 2)
def initialize_geometry(self, mesh, facet_domains=None, cell_domains=None):
"""Stores mesh, domains and related quantities in a canonical member naming.
Creates attributes on self:
- mesh
- facet_domains
- cell_domains
- ds
- dS
- dx
"""
# Store geometry properties
self.mesh = mesh
self.facet_domains = facet_domains
self.cell_domains = cell_domains
# Fetch domains from mesh if necessary and avaiable
domains = mesh.domains()
if domains is not None:
dim = mesh.geometry().dim()
if self.facet_domains is None:
self.facet_domains = MeshFunction("size_t", mesh, dim - 1,
domains)
if self.cell_domains is None:
self.cell_domains = MeshFunction("size_t", mesh, dim, domains)
# Attach domains to measures for convenience
self.ds = ufl.Measure("ds",
domain=self.mesh,
subdomain_data=self.facet_domains)
self.dS = ufl.Measure("dS",
domain=self.mesh,
subdomain_data=self.facet_domains)
self.dx = ufl.Measure("dx",
domain=self.mesh,
subdomain_data=self.cell_domains)
def facet_avg(self, o):
if self.context.integral_type == "cell":
raise ValueError("Can't take FacetAvg in cell integral")
integrand, = o.ufl_operands
domain = o.ufl_domain()
measure = ufl.Measure(self.context.integral_type, domain=domain)
integrand, degree, argument_multiindices = entity_avg(integrand / CellVolume(domain), measure, self.context.argument_multiindices)
config = {name: getattr(self.context, name)
for name in ["ufl_cell", "precision", "index_cache"]},
config.update(quadrature_degree=degree, interface=self.context,
argument_multiindices=argument_multiindices)
expr, = compile_ufl(integrand, point_sum=True, **config)
return expr
def blocks(self):
dx = ufl.Measure("dx", self.mesh)
u, p = self.uu_[0:2]
v, q = self.vv_[0:2]
aa = [[
ufl.inner(self.sigma(u), symgrad(v)) * dx,
ufl.inner(p, v) * dx
], [ufl.inner(q, u) * dx, 0]]
# Notice that dot(sigma(Eps), symgrad(v)) = dot(Eps, sigma(symgrad(v)))
ff = [-ufl.inner(self.Eps, self.sigma(v)) * dx, 0]
return [aa, ff]
def blocks(self):
aa, ff = super(FormulationMinimallyConstrained, self).blocks()
n = ufl.FacetNormal(self.mesh)
ds = ufl.Measure("ds", self.mesh)
u, P = self.uu_[0], self.uu_[2]
v, Q = self.vv_[0], self.vv_[2]
aa[0].append(-ufl.inner(P, ufl.outer(v, n)) * ds)
aa[1].append(0)
aa.append([-ufl.inner(Q, ufl.outer(u, n)) * ds, 0, 0])
ff.append(0)
return [aa, ff]
def test_facet_area(mesh_factory):
"""
Compute facet area of cell. UFL currently only supports affine cells for this computation
"""
# NOTE: UFL only supports facet area calculations of affine cells
func, args, exact_area = mesh_factory
mesh = func(*args)
c0 = ufl.FacetArea(mesh)
c = Constant(mesh, ScalarType(1))
tdim = mesh.topology.dim
num_faces = 4 if tdim == 2 else 6
ds = ufl.Measure("ds", domain=mesh)
a = mesh.comm.allreduce(assemble_scalar(form(c * ds)), op=MPI.SUM)
a0 = mesh.comm.allreduce(assemble_scalar(form(c0 * ds)), op=MPI.SUM)
assert numpy.isclose(a.real, num_faces)
assert numpy.isclose(a0.real, num_faces * exact_area)
def cell_avg(self, o):
if self.context.integral_type != "cell":
# Need to create a cell-based quadrature rule and
# translate the expression using that (c.f. CellVolume
# below).
raise NotImplementedError("CellAvg on non-cell integrals not yet implemented")
integrand, = o.ufl_operands
domain = o.ufl_domain()
measure = ufl.Measure(self.context.integral_type, domain=domain)
integrand, degree, argument_multiindices = entity_avg(integrand / CellVolume(domain), measure, self.context.argument_multiindices)
config = {name: getattr(self.context, name)
for name in ["ufl_cell", "precision", "index_cache"]}
config.update(quadrature_degree=degree, interface=self.context,
argument_multiindices=argument_multiindices)
expr, = compile_ufl(integrand, point_sum=True, **config)
return expr
def blocks(self):
aa, ff = super(FormulationDirichletLagrange, self).blocks()
uD = self.others["uD"] if "uD" in self.others else df.Constant((0, 0))
ds = ufl.Measure("ds", self.mesh)
u, p = self.uu_[0], self.uu_[2]
v, q = self.vv_[0], self.vv_[2]
aa[0].append(ufl.inner(p, v) * ds)
aa[1].append(0)
aa.append([ufl.inner(q, u) * ds, 0, 0])
ff.append(ufl.inner(q, uD) * ds)
return [aa, ff]
def get_tangent(self):
if self.Chom_ is None:
self.Chom_ = np.zeros((self.nvoigt, self.nvoigt))
dy = ufl.Measure("dx", self.mesh)
vol = df.assemble(df.Constant(1.0) * dy)
y = ufl.SpatialCoordinate(self.mesh)
Eps = df.Constant(((0., 0.), (0., 0.))) # just placeholder
form = self.multiscale_model(self.mesh, self.sigma_law, Eps,
self.others)
a, f, bcs, W = form()
start = timer()
A = mp.block_assemble(a)
if len(bcs) > 0:
bcs.apply(A)
# decompose just once, since the matrix A is the same in every solve
solver = df.PETScLUSolver("superlu")
sol = mp.BlockFunction(W)
end = timer()
print("time assembling system", end - start)
for i in range(self.nvoigt):
start = timer()
Eps.assign(df.Constant(self.macro_strain(i)))
F = mp.block_assemble(f)
if len(bcs) > 0:
bcs.apply(F)
solver.solve(A, sol.block_vector(), F)
sol.block_vector().block_function().apply("to subfunctions")
sig_mu = self.sigma_law(df.dot(Eps, y) + sol[0])
sigma_hom = self.integrate(sig_mu, dy, (2, 2)) / vol
self.Chom_[:, i] = sigma_hom.flatten()[[0, 3, 1]]
end = timer()
print("time in solving system", end - start)
return self.Chom_
window_size=[2 * figsize, figsize])
else:
subplotter.show()
# Plotting a dolfinx.Function
# ===========================
# In the previous sections we have considered CG-1 spaces, which have a
# 1-1 correspondence with the vertices of the geometry. To be able to
# plot higher order function spaces, both CG and DG spaces, we have to
# adjust our plotting technique.
# We start by projecting a discontinuous function into a second order DG
# space Note that we use the `cell_tags` from the previous section to
# restrict the integration domain on the RHS.
dx = ufl.Measure("dx", subdomain_data=cell_tags)
V = dolfinx.FunctionSpace(mesh, ("DG", 2))
uh = dolfinx.Function(V)
u = ufl.TrialFunction(V)
v = ufl.TestFunction(V)
x = ufl.SpatialCoordinate(mesh)
a = ufl.inner(u, v) * dx
L = ufl.inner(x[0], v) * dx(1) + ufl.inner(0.01, v) * dx(0)
problem = dolfinx.fem.LinearProblem(a,
L,
u=uh,
petsc_options={
"ksp_type": "preonly",
"pc_type": "lu"
})
problem.solve()
def __init__(self, mesh, k, omega, c, wx, wy, amp):
P = FiniteElement("Lagrange", mesh.ufl_cell(), k)
self.V = FunctionSpace(mesh, P)
self.u, self.v = Function(self.V), Function(self.V)
self.g = Function(self.V)
self.g_deriv = Function(self.V)
self.omega = omega
self.c = c
self.a = amp
# GEOMETRY: rectangular domain with 5mm radius piston on left wall
# |------------------------------------------------------------|
# | |
# | |
# || |
# || |
# || <-- 5mm radius piston |
# || |
# || |
# | |
# | |
# |----------------------------------------------------------- |
# Locate boundary facets
tdim = mesh.topology.dim
# facets0 belong to 5mm radius piston at x=0
facets0 = locate_entities_boundary(mesh, tdim - 1,
lambda x: (x[0] < 1.0e-6) *
(np.abs(x[1]) < 5e-3))
# facets1 belong to right hand wall, at x=wx
facets1 = locate_entities_boundary(mesh, tdim - 1,
lambda x: x[0] > (wx - 1.0e-6))
# facets2 belong to top and bottom walls, at y=+wy/2 and y=-wy/2
facets2 = locate_entities_boundary(mesh, tdim - 1,
lambda x:
np.abs(x[1]) > (wy / 2 - 1.0e-6))
indices, pos = np.unique(np.hstack((facets0, facets1, facets2)),
return_index=True)
values = np.hstack((np.full(facets0.shape, 1, np.intc),
np.full(facets1.shape, 2, np.intc),
np.full(facets2.shape, 3, np.intc)))
marker = dolfinx.mesh.MeshTags(mesh, tdim - 1, indices, values[pos])
ds = ufl.Measure('ds', subdomain_data=marker, domain=mesh)
# dv, p = TrialFunction(self.V), TestFunction(self.V)
p = TestFunction(self.V)
beta = 3.5
delta0 = 3.0e-6
delta = delta0
# # EXPERIMENT: add absorbing layers to top and bottom ("PMLs")
# def delta_fun(x):
# lam = 2 * np.pi / k
# depth = 2 * lam
# dist = np.abs(x[1]) - (wy/2 - depth)
# inside = (dist >= 0)
# # outside = (dist < 0)
# return delta0 + inside * (dist**2) * 1e3
# delta = Function(self.V)
# delta.interpolate(delta_fun)
# delta.vector.ghostUpdate(addv=PETSc.InsertMode.INSERT,
# mode=PETSc.ScatterMode.FORWARD)
# with XDMFFile(mesh.mpi_comm(), "delta.xdmf", "w",
# encoding=XDMFFile.Encoding.HDF5) as file:
# file.write_mesh(mesh)
# file.write_function(delta)
# Westervelt equation
self.L1 = - inner(grad(self.u), grad(p)) * dx \
- (delta / c**2) * inner(grad(self.v), grad(p)) * dx \
+ (2 * beta / (rho * c**4)) * inner(self.v * self.v, p) * dx \
- (1 / c) * inner(self.v, p) * ds \
+ inner(self.g, p) * ds(1) \
+ (delta / c**2) * inner(self.g_deriv, p) * ds(1)
self.lumped = True
# Vector to be re-used for assembly
self.b = None
# TODO: precompile/pre-process Form L
if self.lumped:
# Westervelt equation
a = (1 / c**2) * \
(1 - 2 * beta * self.u / (rho * c**2)) * p * dx(degree=k) \
+ (delta / c**3) * p * ds
self.M = dolfinx.fem.assemble_vector(a)
self.M.ghostUpdate(addv=PETSc.InsertMode.ADD,
mode=PETSc.ScatterMode.REVERSE)
else:
# TODO: non-lumped version of Westervelt
# a = (1 / self.c**2) * inner(dv, p) * dx(degree=k * k)
M = dolfinx.fem.assemble_matrix(a)
M.assemble()
self.solver = PETSc.KSP().create(mesh.mpi_comm())
opts = PETSc.Options()
opts["ksp_type"] = "cg"
opts["ksp_rtol"] = 1.0e-8
self.solver.setFromOptions()
self.solver.setOperators(M)
# u_t = (b.value[1] * rho.value * dz * dy * dx**4) / (8 * 2 * mu.value * dz * dy**3 / 12)
# print(f"u_t = {u_t} [m]")
# ω_0 = numpy.sqrt((2 * mu.value * dz * dy**3 / 12) / (rho.value * dz * dy * dx**4)) * numpy.array([1.875**2, 4.694**2])
# T_0 = 2 * numpy.pi / ω_0
# print(f"ω_0 = {ω_0} [rad/s]")
# print(f"T_0 = {T_0} [s]")
# Global time
time = dolfinx.fem.Constant(mesh, 0.0) # [s]
# Time step size
dt = dolfinx.fem.Constant(mesh, 1e-2) # [s]
# Number of time steps
nT = 200
# Define integration measures
dx = ufl.Measure("dx", domain=mesh, subdomain_data=subdomains)
ds = ufl.Measure("ds", domain=mesh, subdomain_data=interfaces)
# Function spaces
Ue = ufl.VectorElement("CG", mesh.ufl_cell(), 2)
Uf = dolfinx.fem.FunctionSpace(mesh, Ue)
# Define functions
u = dolfinx.fem.Function(Uf, name="u")
ut = dolfinx.fem.Function(Uf, name="ut")
utt = dolfinx.fem.Function(Uf, name="utt")
u_ = dolfinx.fem.Function(Uf, name="u_") # boundary conditions
δu = ufl.TestFunction(Uf)
file.write_mesh(mesh)
# Function spaces
element_u = ufl.VectorElement("Lagrange", mesh.ufl_cell(), degree=1, dim=tdim)
V_u = dolfinx.fem.FunctionSpace(mesh, element_u)
# Define the state
u = dolfinx.fem.Function(V_u, name="Displacement")
u_ = dolfinx.fem.Function(V_u, name="Boundary Displacement")
ux_ = dolfinx.fem.Function(V_u.sub(0).collapse(), name="Boundary Displacement")
zero_u = dolfinx.fem.Function(V_u, name=" Boundary Displacement")
state = {"u": u}
# Measures
dx = ufl.Measure("dx", domain=mesh)
ds = ufl.Measure("ds", domain=mesh)
dofs_u_left = dolfinx.fem.locate_dofs_geometrical(
V_u, lambda x: np.isclose(x[0], 0.0))
dofs_u_right = dolfinx.fem.locate_dofs_geometrical(
V_u, lambda x: np.isclose(x[0], Lx))
dofs_ux_right = dolfinx.fem.locate_dofs_geometrical(
(V_u.sub(0), V_u.sub(0).collapse()), lambda x: np.isclose(x[0], Lx))
# Set Bcs Function
zero_u.interpolate(lambda x: (np.zeros_like(x[0]), np.zeros_like(x[1])))
u_.interpolate(lambda x: (np.ones_like(x[0]), 0 * np.ones_like(x[1])))
ux_.interpolate(lambda x: np.ones_like(x[0]))
for f in [zero_u, ux_]:
def test_assembly_dx_domains(mesh):
V = dolfin.FunctionSpace(mesh, ("CG", 1))
u, v = dolfin.TrialFunction(V), dolfin.TestFunction(V)
marker = dolfin.MeshFunction("size_t", mesh, mesh.topology.dim, 0)
values = marker.values
# Mark first, second and all other
# Their union is the whole domain
values[0] = 111
values[1] = 222
values[2:] = 333
dx = ufl.Measure('dx', subdomain_data=marker, domain=mesh)
w = dolfin.Function(V)
with w.vector.localForm() as w_local:
w_local.set(0.5)
#
# Assemble matrix
#
a = w * ufl.inner(u, v) * (dx(111) + dx(222) + dx(333))
A = dolfin.fem.assemble_matrix(a)
A.assemble()
norm1 = A.norm()
a2 = w * ufl.inner(u, v) * dx
A2 = dolfin.fem.assemble_matrix(a2)
A2.assemble()
norm2 = A2.norm()
assert norm1 == pytest.approx(norm2, 1.0e-12)
#
# Assemble vector
#
L = ufl.inner(w, v) * (dx(111) + dx(222) + dx(333))
b = dolfin.fem.assemble_vector(L)
b.ghostUpdate(addv=PETSc.InsertMode.ADD, mode=PETSc.ScatterMode.REVERSE)
L2 = ufl.inner(w, v) * dx
b2 = dolfin.fem.assemble_vector(L2)
b2.ghostUpdate(addv=PETSc.InsertMode.ADD, mode=PETSc.ScatterMode.REVERSE)
assert b.norm() == pytest.approx(b2.norm(), 1.0e-12)
#
# Assemble scalar
#
L = w * (dx(111) + dx(222) + dx(333))
s = dolfin.fem.assemble_scalar(L)
s = dolfin.MPI.sum(mesh.mpi_comm(), s)
L2 = w * dx
s2 = dolfin.fem.assemble_scalar(L2)
s2 = dolfin.MPI.sum(mesh.mpi_comm(), s2)
assert (s == pytest.approx(s2, 1.0e-12)
and 0.5 == pytest.approx(s, 1.0e-12))
def test_simple_triangle():
if MPI.COMM_WORLD.rank == 0:
import gmsh
gmsh.initialize()
gmsh.model.add("test")
p0 = gmsh.model.geo.addPoint(0.0, 0.0, 0.0)
p1 = gmsh.model.geo.addPoint(1.0, 0.0, 0.0)
p2 = gmsh.model.geo.addPoint(1.0, 1.0, 0.0)
p3 = gmsh.model.geo.addPoint(0.0, 1.0, 0.0)
p4 = gmsh.model.geo.addPoint(1.0, 0.5, 0.0)
l0 = gmsh.model.geo.addLine(p0, p1)
l1 = gmsh.model.geo.addCircleArc(p1, p4, p2)
l2 = gmsh.model.geo.addLine(p2, p3)
l3 = gmsh.model.geo.addLine(p3, p0)
cl0 = gmsh.model.geo.addCurveLoop([l0, l1, l2, l3])
s0 = gmsh.model.geo.addPlaneSurface([cl0])
gmsh.model.addPhysicalGroup(1, [l0, l2], 2)
gmsh.model.setPhysicalName(1, 2, "sides")
gmsh.model.addPhysicalGroup(1, [l1], 3)
gmsh.model.setPhysicalName(1, 3, "arc")
gmsh.model.addPhysicalGroup(2, [s0], 4)
gmsh.model.setPhysicalName(2, 4, "surface")
gmsh.model.geo.synchronize()
gmsh.model.mesh.generate()
gmsh.model.mesh.setOrder(2)
gmsh_model = gmsh.model
else:
gmsh_model = None
mesh, mts = dolfiny.mesh.gmsh_to_dolfin(gmsh_model, 2, prune_z=True)
mt1, keys1 = dolfiny.mesh.merge_meshtags(mts, 1)
mt2, keys2 = dolfiny.mesh.merge_meshtags(mts, 2)
assert mesh.geometry.dim == 2
assert mesh.topology.dim == 2
assert mts["arc"].dim == 1
with dolfinx.io.XDMFFile(MPI.COMM_WORLD, "mesh.xdmf", "w") as file:
file.write_mesh(mesh)
mesh.topology.create_connectivity(1, 2)
file.write_meshtags(mts["arc"])
ds = ufl.Measure("ds", subdomain_data=mt1, domain=mesh)
form = dolfinx.fem.form(1.0 * ds(keys1["sides"]) + 1.0 * ds(keys1["arc"]))
val = dolfinx.fem.assemble_scalar(form)
val = mesh.comm.allreduce(val, op=MPI.SUM)
assert numpy.isclose(val, 2.0 + 2.0 * numpy.pi * 0.5 / 2.0, rtol=1.0e-3)
dx = ufl.Measure("dx", subdomain_data=mt2, domain=mesh)
form = dolfinx.fem.form(1.0 * dx(keys2["surface"]))
val = dolfinx.fem.assemble_scalar(form)
val = mesh.comm.allreduce(val, op=MPI.SUM)
assert numpy.isclose(val, 1.0 + numpy.pi * 0.5**2 / 2.0, rtol=1.0e-3)
# Max inner ring velocity
v_inner_max = 0.1 # [m/s]
# Normal and tangential velocity at inner ring
v_n = dolfinx.fem.Constant(mesh, 0.0) # [m/s]
v_t = dolfinx.fem.Constant(mesh, 0.0) # [m/s] -- value set/updated in analysis
# Global time
time = dolfinx.fem.Constant(mesh, 0.0) # [s]
# Time step size
dt = dolfinx.fem.Constant(mesh, 0.05) # [s]
# Number of time steps
nT = 80
# Define integration measures
dx = ufl.Measure("dx",
domain=mesh,
subdomain_data=subdomains,
metadata={"quadrature_degree": 4})
ds = ufl.Measure("ds",
domain=mesh,
subdomain_data=interfaces,
metadata={"quadrature_degree": 4})
# Inner ring velocity
def v_inner_(t=0.0, vt=v_inner_max, g=5, a=1, b=3):
return vt * 0.25 * (np.tanh(g * (t - a)) + 1) * (np.tanh(-g * (t - b)) + 1)
# Function spaces
Ve = ufl.VectorElement("CG", mesh.ufl_cell(), 2)
Pe = ufl.FiniteElement("CG", mesh.ufl_cell(), 1)
def solve(self, f, filename):
# redifine constans for specific frequency
self.f = f
self.omega = 2 * np.pi * f
self.lmda = self.c / f
self.k0 = self.omega / self.c
# Load mesh
mesh, cell_tags, facet_tags = read_from_msh(filename,
cell_data=True,
facet_data=True,
gdim=2)
# Define function space
V = dolfinx.FunctionSpace(mesh, ("Lagrange", self.degree))
# Interpolate wavenumber k onto V
k = dolfinx.Constant(V, self.k0)
# Interpolate absorbing layer piece of wavenumber k_absorb onto V
k_absorb = dolfinx.Function(V)
adiabatic_layer = AdiabaticLayer(self.deg_absorber, self.k0, self.lmda)
k_absorb.interpolate(adiabatic_layer.eval)
# Interpolate incident wave field onto V
ui = dolfinx.Function(V)
ui_expr = IncidentWave(self.k0)
ui.interpolate(ui_expr.eval)
# Define variational problem
u = ufl.TrialFunction(V)
v = ufl.TestFunction(V)
ds_exited = ufl.Measure("ds",
domain=mesh,
subdomain_data=facet_tags,
subdomain_id=1)
a = ufl.inner(ufl.grad(u), ufl.grad(v)) * ufl.dx \
- k ** 2 * ufl.inner(u, v) * ufl.dx \
- k_absorb * ufl.inner(u, v) * ufl.dx
L = -1j * self.omega * self.rho_0 * ufl.inner(ui, v) * ufl.dx
# Assemble matrix and vector and set up direct solver
A = dolfinx.fem.assemble_matrix(a)
A.assemble()
b = dolfinx.fem.assemble_vector(L)
b.ghostUpdate(addv=PETSc.InsertMode.ADD,
mode=PETSc.ScatterMode.REVERSE)
solver = PETSc.KSP().create(mesh.mpi_comm())
opts = PETSc.Options()
opts["ksp_type"] = "preonly"
opts["pc_type"] = "lu"
opts["pc_factor_mat_solver_type"] = "mumps"
solver.setFromOptions()
solver.setOperators(A)
# Solve linear system
u = dolfinx.Function(V)
start = time.time()
solver.solve(b, u.vector)
end = time.time()
time_elapsed = end - start
print('Solve time: ', time_elapsed)
u.vector.ghostUpdate(addv=PETSc.InsertMode.INSERT,
mode=PETSc.ScatterMode.FORWARD)
save(mesh, u, f"../Solution/sol_{f}Hz.xdmf")
def test_assembly_ds_domains(mesh):
V = dolfinx.FunctionSpace(mesh, ("CG", 1))
u, v = ufl.TrialFunction(V), ufl.TestFunction(V)
def bottom(x):
return numpy.isclose(x[1], 0.0)
def top(x):
return numpy.isclose(x[1], 1.0)
def left(x):
return numpy.isclose(x[0], 0.0)
def right(x):
return numpy.isclose(x[0], 1.0)
bottom_facets = locate_entities_geometrical(mesh,
mesh.topology.dim - 1,
bottom,
boundary_only=True)
bottom_vals = numpy.full(bottom_facets.shape, 1, numpy.intc)
top_facets = locate_entities_geometrical(mesh,
mesh.topology.dim - 1,
top,
boundary_only=True)
top_vals = numpy.full(top_facets.shape, 2, numpy.intc)
left_facets = locate_entities_geometrical(mesh,
mesh.topology.dim - 1,
left,
boundary_only=True)
left_vals = numpy.full(left_facets.shape, 3, numpy.intc)
right_facets = locate_entities_geometrical(mesh,
mesh.topology.dim - 1,
right,
boundary_only=True)
right_vals = numpy.full(right_facets.shape, 6, numpy.intc)
indices = numpy.hstack(
(bottom_facets, top_facets, left_facets, right_facets))
values = numpy.hstack((bottom_vals, top_vals, left_vals, right_vals))
indices, pos = numpy.unique(indices, return_index=True)
marker = dolfinx.mesh.MeshTags(mesh, mesh.topology.dim - 1, indices,
values[pos])
ds = ufl.Measure('ds', subdomain_data=marker, domain=mesh)
w = dolfinx.Function(V)
with w.vector.localForm() as w_local:
w_local.set(0.5)
# Assemble matrix
a = w * ufl.inner(u, v) * (ds(1) + ds(2) + ds(3) + ds(6))
A = dolfinx.fem.assemble_matrix(a)
A.assemble()
norm1 = A.norm()
a2 = w * ufl.inner(u, v) * ds
A2 = dolfinx.fem.assemble_matrix(a2)
A2.assemble()
norm2 = A2.norm()
assert norm1 == pytest.approx(norm2, 1.0e-12)
# Assemble vector
L = ufl.inner(w, v) * (ds(1) + ds(2) + ds(3) + ds(6))
b = dolfinx.fem.assemble_vector(L)
b.ghostUpdate(addv=PETSc.InsertMode.ADD, mode=PETSc.ScatterMode.REVERSE)
L2 = ufl.inner(w, v) * ds
b2 = dolfinx.fem.assemble_vector(L2)
b2.ghostUpdate(addv=PETSc.InsertMode.ADD, mode=PETSc.ScatterMode.REVERSE)
assert b.norm() == pytest.approx(b2.norm(), 1.0e-12)
# Assemble scalar
L = w * (ds(1) + ds(2) + ds(3) + ds(6))
s = dolfinx.fem.assemble_scalar(L)
s = mesh.mpi_comm().allreduce(s, op=MPI.SUM)
L2 = w * ds
s2 = dolfinx.fem.assemble_scalar(L2)
s2 = mesh.mpi_comm().allreduce(s2, op=MPI.SUM)
assert (s == pytest.approx(s2, 1.0e-12)
and 2.0 == pytest.approx(s, 1.0e-12))
def test_assembly_ds_domains(mode):
mesh = dolfinx.generation.UnitSquareMesh(MPI.COMM_WORLD, 10, 10, ghost_mode=mode)
V = dolfinx.FunctionSpace(mesh, ("CG", 1))
u, v = ufl.TrialFunction(V), ufl.TestFunction(V)
def bottom(x):
return numpy.isclose(x[1], 0.0)
def top(x):
return numpy.isclose(x[1], 1.0)
def left(x):
return numpy.isclose(x[0], 0.0)
def right(x):
return numpy.isclose(x[0], 1.0)
bottom_facets = locate_entities_boundary(mesh, mesh.topology.dim - 1, bottom)
bottom_vals = numpy.full(bottom_facets.shape, 1, numpy.intc)
top_facets = locate_entities_boundary(mesh, mesh.topology.dim - 1, top)
top_vals = numpy.full(top_facets.shape, 2, numpy.intc)
left_facets = locate_entities_boundary(mesh, mesh.topology.dim - 1, left)
left_vals = numpy.full(left_facets.shape, 3, numpy.intc)
right_facets = locate_entities_boundary(mesh, mesh.topology.dim - 1, right)
right_vals = numpy.full(right_facets.shape, 6, numpy.intc)
indices = numpy.hstack((bottom_facets, top_facets, left_facets, right_facets))
values = numpy.hstack((bottom_vals, top_vals, left_vals, right_vals))
indices, pos = numpy.unique(indices, return_index=True)
marker = dolfinx.mesh.MeshTags(mesh, mesh.topology.dim - 1, indices, values[pos])
ds = ufl.Measure('ds', subdomain_data=marker, domain=mesh)
w = dolfinx.Function(V)
with w.vector.localForm() as w_local:
w_local.set(0.5)
bc = dolfinx.fem.DirichletBC(dolfinx.Function(V), range(30))
# Assemble matrix
a = w * ufl.inner(u, v) * (ds(1) + ds(2) + ds(3) + ds(6))
A = dolfinx.fem.assemble_matrix(a)
A.assemble()
norm1 = A.norm()
a2 = w * ufl.inner(u, v) * ds
A2 = dolfinx.fem.assemble_matrix(a2)
A2.assemble()
norm2 = A2.norm()
assert norm1 == pytest.approx(norm2, 1.0e-12)
# Assemble vector
L = ufl.inner(w, v) * (ds(1) + ds(2) + ds(3) + ds(6))
b = dolfinx.fem.assemble_vector(L)
dolfinx.fem.apply_lifting(b, [a], [[bc]])
b.ghostUpdate(addv=PETSc.InsertMode.ADD_VALUES,
mode=PETSc.ScatterMode.REVERSE)
dolfinx.fem.set_bc(b, [bc])
L2 = ufl.inner(w, v) * ds
b2 = dolfinx.fem.assemble_vector(L2)
dolfinx.fem.apply_lifting(b2, [a2], [[bc]])
b2.ghostUpdate(addv=PETSc.InsertMode.ADD_VALUES,
mode=PETSc.ScatterMode.REVERSE)
dolfinx.fem.set_bc(b2, [bc])
assert b.norm() == pytest.approx(b2.norm(), 1.0e-12)
# Assemble scalar
L = w * (ds(1) + ds(2) + ds(3) + ds(6))
s = dolfinx.fem.assemble_scalar(L)
s = mesh.mpi_comm().allreduce(s, op=MPI.SUM)
L2 = w * ds
s2 = dolfinx.fem.assemble_scalar(L2)
s2 = mesh.mpi_comm().allreduce(s2, op=MPI.SUM)
assert (s == pytest.approx(s2, 1.0e-12) and 2.0 == pytest.approx(s, 1.0e-12))
def free_end(x):
"""Marks the leftmost points of the cantilever"""
return numpy.isclose(x[0], 48.0)
def left(x):
"""Marks left part of boundary, where cantilever is attached to wall"""
return numpy.isclose(x[0], 0.0)
# Locate all facets at the free end and assign them value 1
free_end_facets = locate_entities_boundary(mesh, 1, free_end)
mt = dolfinx.mesh.MeshTags(mesh, 1, free_end_facets, 1)
ds = ufl.Measure("ds", subdomain_data=mt)
# Homogeneous boundary condition in displacement
u_bc = dolfinx.Function(U)
with u_bc.vector.localForm() as loc:
loc.set(0.0)
# Displacement BC is applied to the left side
left_facets = locate_entities_boundary(mesh, 1, left)
bdofs = locate_dofs_topological(U, 1, left_facets)
bc = dolfinx.fem.DirichletBC(u_bc, bdofs)
# Elastic stiffness tensor and Poisson ratio
E, nu = 1.0, 1.0 / 3.0
alpha_ub.interpolate(lambda x: np.ones_like(x[0]))
#In order to defined a function in a specific subspace of the model, it must be
#specified in the model 'V_u.sub(i)', where i = 0 -> x, 1 -> y, 2-> z.
#Don't forget to collapse, to choose only the DOF associated with the subspace.
#I don't think this part works to definy the body force applied in a geometry.
#It could be better to define it in the energy definition as constant. If not a
#constant, we might need to define as a space function.
# g = dolfinx.fem.Function(V_u, name="Body_pressure")
# with g.vector.localForm() as loc:
# loc.set(-78500.0)
# Integral measures -> in order to define the energy lately, it's necessary to
#define the integral measures, as such one is a integral.
dx = ufl.Measure("dx", domain=mesh) #-> volume measure
#We include here the subdomain data generated at the gmsh file.
ds = ufl.Measure("ds", subdomain_data=facet_tags,
domain=mesh) #-> surface measure
#ds(<number of the facet tags>)
#dS = ufl.Measure("dS", domain = mesh) - inner boundaries of the mesh -> not usefull
import models
from models import DamageElasticityModel as Brittle
model = Brittle(parameters.get('model'))
state = {'u': u, 'alpha': alpha}
#The total energy density is calculated this time using a already written
#function of the "model". This return the elasticity energy (with the a(alpha))
#and the damage energy term. To count for externals forces, it need to substract it
#from the total energy