def hyperelasticity(domain, q, p, nf=0):
# Based on https://github.com/firedrakeproject/firedrake-bench/blob/experiments/forms/firedrake_forms.py
V = ufl.FunctionSpace(domain, ufl.VectorElement('P', domain.ufl_cell(), q))
P = ufl.FunctionSpace(domain, ufl.VectorElement('P', domain.ufl_cell(), p))
v = ufl.TestFunction(V)
du = ufl.TrialFunction(V) # Incremental displacement
u = ufl.Coefficient(V) # Displacement from previous iteration
B = ufl.Coefficient(V) # Body force per unit mass
# Kinematics
I = ufl.Identity(domain.ufl_cell().topological_dimension())
F = I + ufl.grad(u) # Deformation gradient
C = F.T*F # Right Cauchy-Green tensor
E = (C - I)/2 # Euler-Lagrange strain tensor
E = ufl.variable(E)
# Material constants
mu = ufl.Constant(domain) # Lame's constants
lmbda = ufl.Constant(domain)
# Strain energy function (material model)
psi = lmbda/2*(ufl.tr(E)**2) + mu*ufl.tr(E*E)
S = ufl.diff(psi, E) # Second Piola-Kirchhoff stress tensor
PK = F*S # First Piola-Kirchoff stress tensor
# Variational problem
it = ufl.inner(PK, ufl.grad(v)) - ufl.inner(B, v)
f = [ufl.Coefficient(P) for _ in range(nf)]
return ufl.derivative(reduce(ufl.inner,
list(map(ufl.div, f)) + [it])*ufl.dx, u, du)
def to_reference_coordinates(ufl_coordinate_element, parameters):
# Set up UFL form
cell = ufl_coordinate_element.cell()
domain = ufl.Mesh(ufl_coordinate_element)
K = ufl.JacobianInverse(domain)
x = ufl.SpatialCoordinate(domain)
x0_element = ufl.VectorElement("Real", cell, 0)
x0 = ufl.Coefficient(ufl.FunctionSpace(domain, x0_element))
expr = ufl.dot(K, x - x0)
# Translation to GEM
C = ufl.Coefficient(ufl.FunctionSpace(domain, ufl_coordinate_element))
expr = ufl_utils.preprocess_expression(expr)
expr = ufl_utils.simplify_abs(expr)
builder = firedrake_interface.KernelBuilderBase()
builder.domain_coordinate[domain] = C
builder._coefficient(C, "C")
builder._coefficient(x0, "x0")
dim = cell.topological_dimension()
point = gem.Variable('X', (dim, ))
context = tsfc.fem.GemPointContext(
interface=builder,
ufl_cell=cell,
precision=parameters["precision"],
point_indices=(),
point_expr=point,
)
translator = tsfc.fem.Translator(context)
ir = map_expr_dag(translator, expr)
# Unroll result
ir = [gem.Indexed(ir, alpha) for alpha in numpy.ndindex(ir.shape)]
# Unroll IndexSums
max_extent = parameters["unroll_indexsum"]
if max_extent:
def predicate(index):
return index.extent <= max_extent
ir = gem.optimise.unroll_indexsum(ir, predicate=predicate)
# Translate to COFFEE
ir = impero_utils.preprocess_gem(ir)
return_variable = gem.Variable('dX', (dim, ))
assignments = [(gem.Indexed(return_variable, (i, )), e)
for i, e in enumerate(ir)]
impero_c = impero_utils.compile_gem(assignments, ())
body = tsfc.coffee.generate(impero_c, {}, parameters["precision"])
body.open_scope = False
return body
def test_form_coefficient():
cell = ufl.triangle
element = ufl.FiniteElement("Lagrange", cell, 1)
u, v = ufl.TestFunction(element), ufl.TrialFunction(element)
g = ufl.Coefficient(element)
a = g * ufl.inner(u, v) * ufl.dx
forms = [a]
compiled_forms, module = ffc.codegeneration.jit.compile_forms(forms)
for f, compiled_f in zip(forms, compiled_forms):
assert compiled_f.rank == len(f.arguments())
form0 = compiled_forms[0][0].create_cell_integral(-1)
A = np.zeros((3, 3), dtype=np.float64)
w = np.array([1.0, 1.0, 1.0], dtype=np.float64)
c = np.array([], dtype=np.float64)
ffi = cffi.FFI()
coords = np.array([0.0, 0.0, 1.0, 0.0, 0.0, 1.0], dtype=np.float64)
form0.tabulate_tensor(ffi.cast('double *', A.ctypes.data),
ffi.cast('double *', w.ctypes.data),
ffi.cast('double *', c.ctypes.data),
ffi.cast('double *', coords.ctypes.data), ffi.NULL,
ffi.NULL)
A_analytic = np.array([[2, 1, 1], [1, 2, 1], [1, 1, 2]],
dtype=np.float64) / 24.0
A_diff = (A - A_analytic)
assert np.isclose(A_diff.max(), 0.0)
assert np.isclose(A_diff.min(), 0.0)
def form(V, itype, request):
if request.param == "functional":
u = ufl.Coefficient(V)
v = ufl.Coefficient(V)
elif request.param == "1-form":
u = ufl.Coefficient(V)
v = ufl.TestFunction(V)
elif request.param == "2-form":
u = ufl.TrialFunction(V)
v = ufl.TestFunction(V)
if itype == "cell":
return ufl.inner(u, v)*ufl.dx
elif itype == "ext_facet":
return ufl.inner(u, v)*ufl.ds
elif itype == "int_facet":
return ufl.inner(u('+'), v('-'))*ufl.dS
def inject_kernel(Vf, Vc):
hierarchy, level = utils.get_level(Vc.ufl_domain())
cache = hierarchy._shared_data_cache["transfer_kernels"]
coordinates = Vf.ufl_domain().coordinates
key = (("inject", ) +
Vf.ufl_element().value_shape() +
entity_dofs_key(Vc.finat_element.entity_dofs()) +
entity_dofs_key(Vf.finat_element.entity_dofs()) +
entity_dofs_key(Vc.mesh().coordinates.function_space().finat_element.entity_dofs()) +
entity_dofs_key(coordinates.function_space().finat_element.entity_dofs()))
try:
return cache[key]
except KeyError:
ncandidate = hierarchy.coarse_to_fine_cells[level].shape[1]
if Vc.finat_element.entity_dofs() == Vc.finat_element.entity_closure_dofs():
return cache.setdefault(key, (dg_injection_kernel(Vf, Vc, ncandidate), True))
coordinates = Vf.ufl_domain().coordinates
evaluate_kernel = compile_element(ufl.Coefficient(Vf))
to_reference_kernel = to_reference_coordinates(coordinates.ufl_element())
coords_element = create_element(coordinates.ufl_element())
Vf_element = create_element(Vf.ufl_element())
kernel = """
%(to_reference)s
%(evaluate)s
void inject_kernel(double *R, const double *X, const double *f, const double *Xf)
{
double Xref[%(tdim)d];
int cell = -1;
for (int i = 0; i < %(ncandidate)d; i++) {
const double *Xfi = Xf + i*%(Xf_cell_inc)d;
to_reference_coords_kernel(Xref, X, Xfi);
if (%(inside_cell)s) {
cell = i;
break;
}
}
if (cell == -1) {
abort();
}
const double *fi = f + cell*%(f_cell_inc)d;
for ( int i = 0; i < %(Rdim)d; i++ ) {
R[i] = 0;
}
evaluate_kernel(R, fi, Xref);
}
""" % {
"to_reference": str(to_reference_kernel),
"evaluate": str(evaluate_kernel),
"inside_cell": inside_check(Vc.finat_element.cell, eps=1e-8, X="Xref"),
"tdim": Vc.ufl_domain().topological_dimension(),
"ncandidate": ncandidate,
"Rdim": numpy.prod(Vf_element.value_shape),
"Xf_cell_inc": coords_element.space_dimension(),
"f_cell_inc": Vf_element.space_dimension()
}
return cache.setdefault(key, (op2.Kernel(kernel, name="inject_kernel"), False))
def set_coordinates(self, domain):
"""Prepare the coordinate field.
:arg domain: :class:`ufl.Domain`
"""
# Create a fake coordinate coefficient for a domain.
f = ufl.Coefficient(ufl.FunctionSpace(domain, domain.ufl_coordinate_element()))
self.domain_coordinate[domain] = f
self.coordinates_arg = self._coefficient(f, "macro_coords")
def helmholtz(domain, q, p, nf=0):
# Based on https://github.com/firedrakeproject/firedrake-bench/blob/experiments/forms/firedrake_forms.py
V = ufl.FunctionSpace(domain, ufl.FiniteElement('P', domain.ufl_cell(), q))
P = ufl.FunctionSpace(domain, ufl.FiniteElement('P', domain.ufl_cell(), p))
u = ufl.TrialFunction(V)
v = ufl.TestFunction(V)
f = [ufl.Coefficient(P) for _ in range(nf)]
it = ufl.dot(ufl.grad(v), ufl.grad(u)) + 1.0*v*u
return reduce(ufl.inner, f + [it])*ufl.dx
def test_matvec(compile_args):
"""Test evaluation of linear rank-0 form.
Evaluates expression c * A_ij * f_j where c is a Constant,
A_ij is a user specified constant matrix and f_j is j-th component
of user specified vector-valued finite element function (in P1 space).
"""
e = ufl.VectorElement("P", "triangle", 1)
mesh = ufl.Mesh(e)
V = ufl.FunctionSpace(mesh, e)
f = ufl.Coefficient(V)
a_mat = np.array([[1.0, 2.0], [1.0, 1.0]])
a = ufl.as_matrix(a_mat)
expr = ufl.Constant(mesh) * ufl.dot(a, f)
points = np.array([[0.0, 0.0], [1.0, 0.0], [0.0, 1.0]])
obj, module = ffcx.codegeneration.jit.compile_expressions(
[(expr, points)], cffi_extra_compile_args=compile_args)
ffi = cffi.FFI()
kernel = obj[0][0]
c_type, np_type = float_to_type("double")
A = np.zeros((3, 2), dtype=np_type)
f_mat = np.array([[1.0, 2.0, 3.0], [4.0, 5.0, 6.0]])
# Coefficient storage XYXYXY
w = np.array(f_mat.T.flatten(), dtype=np_type)
c = np.array([0.5], dtype=np_type)
# Coords storage XYXYXY
coords = np.array([0.0, 0.0, 1.0, 0.0, 0.0, 1.0], dtype=np.float64)
kernel.tabulate_expression(
ffi.cast('{type} *'.format(type=c_type), A.ctypes.data),
ffi.cast('{type} *'.format(type=c_type), w.ctypes.data),
ffi.cast('{type} *'.format(type=c_type), c.ctypes.data),
ffi.cast('double *', coords.ctypes.data))
# Check the computation against correct NumPy value
assert np.allclose(A, 0.5 * np.dot(a_mat, f_mat).T)
# Prepare NumPy array of points attached to the expression
length = kernel.num_points * kernel.topological_dimension
points_kernel = np.frombuffer(
ffi.buffer(kernel.points, length * ffi.sizeof("double")), np.double)
points_kernel = points_kernel.reshape(points.shape)
assert np.allclose(points, points_kernel)
# Check the value shape attached to the expression
value_shape = np.frombuffer(
ffi.buffer(kernel.value_shape,
kernel.num_components * ffi.sizeof("int")), np.intc)
assert np.allclose(expr.ufl_shape, value_shape)
def test_ufl_only_simple():
mesh = ufl.Mesh(ufl.VectorElement("P", ufl.triangle, 1))
V = ufl.FunctionSpace(mesh, ufl.FiniteElement("P", ufl.triangle, 2))
v = ufl.Coefficient(V)
expr = ufl.inner(v, v)
W = V
to_element = create_element(W.ufl_element())
ast, oriented, needs_cell_sizes, coefficients, first_coeff_fake_coords, *_ = compile_expression_dual_evaluation(
expr, to_element, coffee=False)
assert first_coeff_fake_coords is False
def test_ufl_only_to_contravariant_piola():
mesh = ufl.Mesh(ufl.VectorElement("P", ufl.triangle, 1))
V = ufl.FunctionSpace(mesh, ufl.FiniteElement("P", ufl.triangle, 2))
v = ufl.Coefficient(V)
expr = ufl.as_vector([v, v])
W = ufl.FunctionSpace(mesh, ufl.FiniteElement("RT", ufl.triangle, 1))
to_element = create_element(W.ufl_element())
ast, oriented, needs_cell_sizes, coefficients, first_coeff_fake_coords, *_ = compile_expression_dual_evaluation(
expr, to_element, coffee=False)
assert first_coeff_fake_coords is True
def set_coordinates(self, domain):
"""Prepare the coordinate field.
:arg domain: :class:`ufl.Domain`
"""
# Create a fake coordinate coefficient for a domain.
f = ufl.Coefficient(ufl.FunctionSpace(domain, domain.ufl_coordinate_element()))
self.domain_coordinate[domain] = f
self.coordinates_args, expression = prepare_coordinates(
f, "coordinate_dofs", interior_facet=self.interior_facet)
self.coefficient_map[f] = expression
def test_ufl_only_shape_mismatch():
mesh = ufl.Mesh(ufl.VectorElement("P", ufl.triangle, 1))
V = ufl.FunctionSpace(mesh, ufl.FiniteElement("RT", ufl.triangle, 1))
v = ufl.Coefficient(V)
expr = ufl.inner(v, v)
assert expr.ufl_shape == ()
W = V
to_element = create_element(W.ufl_element())
assert to_element.value_shape == (2, )
with pytest.raises(ValueError):
ast, oriented, needs_cell_sizes, coefficients, first_coeff_fake_coords, *_ = compile_expression_dual_evaluation(
expr, to_element, coffee=False)
def elasticity(domain, q, p, nf=0):
# Based on https://github.com/firedrakeproject/firedrake-bench/blob/experiments/forms/firedrake_forms.py
V = ufl.FunctionSpace(domain, ufl.VectorElement('P', domain.ufl_cell(), q))
P = ufl.FunctionSpace(domain, ufl.FiniteElement('P', domain.ufl_cell(), p))
u = ufl.TrialFunction(V)
v = ufl.TestFunction(V)
def eps(v):
return ufl.grad(v) + ufl.transpose(ufl.grad(v))
it = 0.25*ufl.inner(eps(v), eps(u))
f = [ufl.Coefficient(P) for _ in range(nf)]
return reduce(ufl.inner, f + [it])*ufl.dx
def test_estimated_degree():
cell = ufl.tetrahedron
mesh = ufl.Mesh(ufl.VectorElement('P', cell, 1))
V = ufl.FunctionSpace(mesh, ufl.FiniteElement('P', cell, 1))
f = ufl.Coefficient(V)
u = ufl.TrialFunction(V)
v = ufl.TestFunction(V)
a = u * v * ufl.tanh(ufl.sqrt(ufl.sinh(f) / ufl.sin(f**f))) * ufl.dx
handler = MockHandler()
logger.addHandler(handler)
with pytest.raises(RuntimeError):
compile_form(a)
logger.removeHandler(handler)
def __init__(self, spline, ufl_element):
self._ufl_coef = ufl.Coefficient(ufl_element)
t = self._ufl_coef
knots = spline.knots
coef_array = spline.coef_array
# assigning left polynomial
form = ufl.conditional(lt(t, knots[0]), 1., 0.)\
* Polynomial(coef_array[0])(t)
# assigning internal polynomials
for knot, knot_, coef in\
zip(knots[:-1], knots[1:], coef_array[1:-1]):
form += ufl.conditional(And(ge(t, knot), lt(t, knot_)), 1., 0.)\
* Polynomial(coef)(t)
# assigning right polynomial
form += ufl.conditional(ge(t, knots[-1]), 1., 0.)\
* Polynomial(coef_array[-1])(t)
self._ufl_form = form
def assemble_mixed_mass_matrix(V_A, V_B):
"""
Construct the mixed mass matrix of two function spaces,
using the TrialFunction from V_A and the TestFunction
from V_B.
"""
if len(V_A) > 1 or len(V_B) > 1:
raise NotImplementedError(
"Sorry, only implemented for non-mixed spaces")
if V_A.ufl_element().mapping() != "identity" or V_B.ufl_element().mapping(
) != "identity":
msg = """
Sorry, only implemented for affine maps for now. To do non-affine, we'd need to
import much more of the assembly engine of UFL/TSFC/etc to do the assembly on
each supermesh cell.
"""
raise NotImplementedError(msg)
mesh_A = V_A.mesh()
mesh_B = V_B.mesh()
dim = mesh_A.geometric_dimension()
assert dim == mesh_B.geometric_dimension()
assert dim == mesh_A.topological_dimension()
assert dim == mesh_B.topological_dimension()
(mh_A, level_A) = get_level(mesh_A)
(mh_B, level_B) = get_level(mesh_B)
if mesh_A is mesh_B:
def likely(cell_A):
return [cell_A]
else:
if (mh_A is None or mh_B is None) or (mh_A is not mh_B):
# No mesh hierarchy structure, call libsupermesh for
# intersection finding
intersections = intersection_finder(mesh_A, mesh_B)
likely = intersections.__getitem__
else:
# We do have a mesh hierarchy, use it
if abs(level_A - level_B) > 1:
raise NotImplementedError(
"Only works for transferring between adjacent levels for now."
)
# What are the cells of B that (probably) intersect with a given cell in A?
if level_A > level_B:
cell_map = mh_A.fine_to_coarse_cells[level_A]
def likely(cell_A):
return cell_map[cell_A]
elif level_A < level_B:
cell_map = mh_A.coarse_to_fine_cells[level_A]
def likely(cell_A):
return cell_map[cell_A]
assert V_A.value_size == V_B.value_size
orig_value_size = V_A.value_size
if V_A.value_size > 1:
V_A = firedrake.FunctionSpace(mesh_A,
V_A.ufl_element().sub_elements()[0])
if V_B.value_size > 1:
V_B = firedrake.FunctionSpace(mesh_B,
V_B.ufl_element().sub_elements()[0])
assert V_A.value_size == 1
assert V_B.value_size == 1
preallocator = PETSc.Mat().create(comm=mesh_A.comm)
preallocator.setType(PETSc.Mat.Type.PREALLOCATOR)
rset = V_B.dof_dset
cset = V_A.dof_dset
nrows = rset.layout_vec.getSizes()
ncols = cset.layout_vec.getSizes()
preallocator.setLGMap(rmap=rset.scalar_lgmap, cmap=cset.scalar_lgmap)
preallocator.setSizes(size=(nrows, ncols), bsize=1)
preallocator.setUp()
zeros = numpy.zeros((V_B.cell_node_map().arity, V_A.cell_node_map().arity),
dtype=ScalarType)
for cell_A, dofs_A in enumerate(V_A.cell_node_map().values):
for cell_B in likely(cell_A):
dofs_B = V_B.cell_node_map().values_with_halo[cell_B, :]
preallocator.setValuesLocal(dofs_B, dofs_A, zeros)
preallocator.assemble()
dnnz, onnz = get_preallocation(preallocator, nrows[0])
# Unroll from block to AIJ
dnnz = dnnz * cset.cdim
dnnz = numpy.repeat(dnnz, rset.cdim)
onnz = onnz * cset.cdim
onnz = numpy.repeat(onnz, cset.cdim)
preallocator.destroy()
assert V_A.value_size == V_B.value_size
rdim = V_B.dof_dset.cdim
cdim = V_A.dof_dset.cdim
#
# Preallocate M_AB.
#
mat = PETSc.Mat().create(comm=mesh_A.comm)
mat.setType(PETSc.Mat.Type.AIJ)
rsizes = tuple(n * rdim for n in nrows)
csizes = tuple(c * cdim for c in ncols)
mat.setSizes(size=(rsizes, csizes), bsize=(rdim, cdim))
mat.setPreallocationNNZ((dnnz, onnz))
mat.setLGMap(rmap=rset.lgmap, cmap=cset.lgmap)
# TODO: Boundary conditions not handled.
mat.setOption(mat.Option.IGNORE_OFF_PROC_ENTRIES, False)
mat.setOption(mat.Option.NEW_NONZERO_ALLOCATION_ERR, True)
mat.setOption(mat.Option.KEEP_NONZERO_PATTERN, True)
mat.setOption(mat.Option.UNUSED_NONZERO_LOCATION_ERR, False)
mat.setOption(mat.Option.IGNORE_ZERO_ENTRIES, True)
mat.setUp()
evaluate_kernel_A = compile_element(ufl.Coefficient(V_A),
name="evaluate_kernel_A")
evaluate_kernel_B = compile_element(ufl.Coefficient(V_B),
name="evaluate_kernel_B")
# We only need one of these since we assume that the two meshes both have CG1 coordinates
to_reference_kernel = to_reference_coordinates(
mesh_A.coordinates.ufl_element())
if dim == 2:
reference_mesh = UnitTriangleMesh(comm=COMM_SELF)
else:
reference_mesh = UnitTetrahedronMesh(comm=COMM_SELF)
evaluate_kernel_S = compile_element(ufl.Coefficient(
reference_mesh.coordinates.function_space()),
name="evaluate_kernel_S")
V_S_A = FunctionSpace(reference_mesh, V_A.ufl_element())
V_S_B = FunctionSpace(reference_mesh, V_B.ufl_element())
M_SS = assemble(inner(TrialFunction(V_S_A), TestFunction(V_S_B)) * dx)
M_SS = M_SS.M.handle[:, :]
node_locations_A = utils.physical_node_locations(
V_S_A).dat.data_ro_with_halos
node_locations_B = utils.physical_node_locations(
V_S_B).dat.data_ro_with_halos
num_nodes_A = node_locations_A.shape[0]
num_nodes_B = node_locations_B.shape[0]
to_reference_kernel = to_reference_coordinates(
mesh_A.coordinates.ufl_element())
supermesh_kernel_str = """
#include "libsupermesh-c.h"
#include <petsc.h>
%(to_reference)s
%(evaluate_S)s
%(evaluate_A)s
%(evaluate_B)s
#define complex_mode %(complex_mode)s
#define PrintInfo(...) do { if (PetscLogPrintInfo) printf(__VA_ARGS__); } while (0)
static void print_array(PetscScalar *arr, int d)
{
for(int j=0; j<d; j++)
PrintInfo(stderr, "%%+.2f ", arr[j]);
}
static void print_coordinates(PetscScalar *simplex, int d)
{
for(int i=0; i<d+1; i++)
{
PrintInfo("\t");
print_array(&simplex[d*i], d);
PrintInfo("\\n");
}
}
#if complex_mode
static void seperate_real_and_imag(PetscScalar *simplex, double *real_simplex, double *imag_simplex, int d)
{
for(int i=0; i<d+1; i++)
{
for(int j=0; j<d; j++)
{
real_simplex[d*i+j] = creal(simplex[d*i+j]);
imag_simplex[d*i+j] = cimag(simplex[d*i+j]);
}
}
}
static void merge_back_to_simplex(PetscScalar* simplex, double* real_simplex, double* imag_simplex, int d)
{
print_coordinates(simplex,d);
for(int i=0; i<d+1; i++)
{
for(int j=0; j<d; j++)
{
simplex[d*i+j] = real_simplex[d*i+j]+imag_simplex[d*i+j]*_Complex_I;
}
}
}
#endif
int supermesh_kernel(PetscScalar* simplex_A, PetscScalar* simplex_B, PetscScalar* simplices_C, PetscScalar* nodes_A, PetscScalar* nodes_B, PetscScalar* M_SS, PetscScalar* outptr, int num_ele)
{
#define d %(dim)s
#define num_nodes_A %(num_nodes_A)s
#define num_nodes_B %(num_nodes_B)s
double simplex_ref_measure;
PrintInfo("simplex_A coordinates\\n");
print_coordinates(simplex_A, d);
PrintInfo("simplex_B coordinates\\n");
print_coordinates(simplex_B, d);
int num_elements = num_ele;
if (d == 2) simplex_ref_measure = 0.5;
else if (d == 3) simplex_ref_measure = 1.0/6;
PetscScalar R_AS[num_nodes_A][num_nodes_A];
PetscScalar R_BS[num_nodes_B][num_nodes_B];
PetscScalar coeffs_A[%(num_nodes_A)s] = {0.};
PetscScalar coeffs_B[%(num_nodes_B)s] = {0.};
PetscScalar reference_nodes_A[num_nodes_A][d];
PetscScalar reference_nodes_B[num_nodes_B][d];
#if complex_mode
double real_simplex_A[d*(d+1)];
double imag_simplex_A[d*(d+1)];
seperate_real_and_imag(simplex_A, real_simplex_A, imag_simplex_A, d);
double real_simplex_B[d*(d+1)];
double imag_simplex_B[d*(d+1)];
seperate_real_and_imag(simplex_B, real_simplex_B, imag_simplex_B, d);
double real_simplices_C[num_elements*d*(d+1)];
double imag_simplices_C[num_elements*d*(d+1)];
for (int ii=0; ii<num_elements*d*(d+1); ++ii) imag_simplices_C[ii] = 0.;
%(libsupermesh_intersect_simplices)s(real_simplex_A, real_simplex_B, real_simplices_C, &num_elements);
merge_back_to_simplex(simplex_A, real_simplex_A, imag_simplex_A, d);
merge_back_to_simplex(simplex_B, real_simplex_B, imag_simplex_B, d);
for(int s=0; s<num_elements; s++)
{
PetscScalar* simplex_C = &simplices_C[s * d * (d+1)];
double* real_simplex_C = &real_simplices_C[s * d * (d+1)];
double* imag_simplex_C = &imag_simplices_C[s * d * (d+1)];
merge_back_to_simplex(simplex_C, real_simplex_C, imag_simplex_C, d);
}
#else
%(libsupermesh_intersect_simplices)s(simplex_A, simplex_B, simplices_C, &num_elements);
#endif
PrintInfo("Supermesh consists of %%i elements\\n", num_elements);
// would like to do this
//PetscScalar MAB[%(num_nodes_A)s][%(num_nodes_B)s] = (PetscScalar (*)[%(num_nodes_B)s])outptr;
// but have to do this instead because we don't grok C
PetscScalar (*MAB)[num_nodes_A] = (PetscScalar (*)[num_nodes_A])outptr;
PetscScalar (*MSS)[num_nodes_A] = (PetscScalar (*)[num_nodes_A])M_SS; // note the underscore
for ( int i = 0; i < num_nodes_B; i++ ) {
for (int j = 0; j < num_nodes_A; j++) {
MAB[i][j] = 0.0;
}
}
for(int s=0; s<num_elements; s++)
{
PetscScalar* simplex_S = &simplices_C[s * d * (d+1)];
double simplex_S_measure;
#if complex_mode
double real_simplex_S[d*(d+1)];
double imag_simplex_S[d*(d+1)];
seperate_real_and_imag(simplex_S, real_simplex_S, imag_simplex_S, d);
%(libsupermesh_simplex_measure)s(real_simplex_S, &simplex_S_measure);
merge_back_to_simplex(simplex_S, real_simplex_S, imag_simplex_S, d);
#else
%(libsupermesh_simplex_measure)s(simplex_S, &simplex_S_measure);
#endif
PrintInfo("simplex_S coordinates with measure %%f\\n", simplex_S_measure);
print_coordinates(simplex_S, d);
PrintInfo("Start mapping nodes for V_A\\n");
PetscScalar physical_nodes_A[num_nodes_A][d];
for(int n=0; n < num_nodes_A; n++) {
PetscScalar* reference_node_location = &nodes_A[n*d];
PetscScalar* physical_node_location = physical_nodes_A[n];
for (int j=0; j < d; j++) physical_node_location[j] = 0.0;
pyop2_kernel_evaluate_kernel_S(physical_node_location, simplex_S, reference_node_location);
PrintInfo("\\tNode ");
print_array(reference_node_location, d);
PrintInfo(" mapped to ");
print_array(physical_node_location, d);
PrintInfo("\\n");
}
PrintInfo("Start mapping nodes for V_B\\n");
PetscScalar physical_nodes_B[num_nodes_B][d];
for(int n=0; n < num_nodes_B; n++) {
PetscScalar* reference_node_location = &nodes_B[n*d];
PetscScalar* physical_node_location = physical_nodes_B[n];
for (int j=0; j < d; j++) physical_node_location[j] = 0.0;
pyop2_kernel_evaluate_kernel_S(physical_node_location, simplex_S, reference_node_location);
PrintInfo("\\tNode ");
print_array(reference_node_location, d);
PrintInfo(" mapped to ");
print_array(physical_node_location, d);
PrintInfo("\\n");
}
PrintInfo("==========================================================\\n");
PrintInfo("Start pulling back dof from S into reference space for A.\\n");
for(int n=0; n < num_nodes_A; n++) {
for(int i=0; i<d; i++) reference_nodes_A[n][i] = 0.;
to_reference_coords_kernel(reference_nodes_A[n], physical_nodes_A[n], simplex_A);
PrintInfo("Pulling back ");
print_array(physical_nodes_A[n], d);
PrintInfo(" to ");
print_array(reference_nodes_A[n], d);
PrintInfo("\\n");
}
PrintInfo("Start pulling back dof from S into reference space for B.\\n");
for(int n=0; n < num_nodes_B; n++) {
for(int i=0; i<d; i++) reference_nodes_B[n][i] = 0.;
to_reference_coords_kernel(reference_nodes_B[n], physical_nodes_B[n], simplex_B);
PrintInfo("Pulling back ");
print_array(physical_nodes_B[n], d);
PrintInfo(" to ");
print_array(reference_nodes_B[n], d);
PrintInfo("\\n");
}
PrintInfo("Start evaluating basis functions of V_A at dofs for V_A on S\\n");
for(int i=0; i<num_nodes_A; i++) {
coeffs_A[i] = 1.;
for(int j=0; j<num_nodes_A; j++) {
R_AS[i][j] = 0.;
pyop2_kernel_evaluate_kernel_A(&R_AS[i][j], coeffs_A, reference_nodes_A[j]);
}
print_array(R_AS[i], num_nodes_A);
PrintInfo("\\n");
coeffs_A[i] = 0.;
}
PrintInfo("Start evaluating basis functions of V_B at dofs for V_B on S\\n");
for(int i=0; i<num_nodes_B; i++) {
coeffs_B[i] = 1.;
for(int j=0; j<num_nodes_B; j++) {
R_BS[i][j] = 0.;
pyop2_kernel_evaluate_kernel_B(&R_BS[i][j], coeffs_B, reference_nodes_B[j]);
}
print_array(R_BS[i], num_nodes_B);
PrintInfo("\\n");
coeffs_B[i] = 0.;
}
PrintInfo("Start doing the matmatmat mult\\n");
for ( int i = 0; i < num_nodes_B; i++ ) {
for (int j = 0; j < num_nodes_A; j++) {
for ( int k = 0; k < num_nodes_B; k++) {
for ( int l = 0; l < num_nodes_A; l++) {
MAB[i][j] += (simplex_S_measure/simplex_ref_measure) * R_BS[i][k] * MSS[k][l] * R_AS[j][l];
}
}
}
}
}
return num_elements;
}
""" % {
"evaluate_S":
str(evaluate_kernel_S),
"evaluate_A":
str(evaluate_kernel_A),
"evaluate_B":
str(evaluate_kernel_B),
"to_reference":
str(to_reference_kernel),
"num_nodes_A":
num_nodes_A,
"num_nodes_B":
num_nodes_B,
"libsupermesh_simplex_measure":
"libsupermesh_triangle_area"
if dim == 2 else "libsupermesh_tetrahedron_volume",
"libsupermesh_intersect_simplices":
"libsupermesh_intersect_tris_real"
if dim == 2 else "libsupermesh_intersect_tets_real",
"dim":
dim,
"complex_mode":
1 if complex_mode else 0
}
dirs = get_petsc_dir() + (sys.prefix, )
includes = ["-I%s/include" % d for d in dirs]
libs = ["-L%s/lib" % d for d in dirs]
libs = libs + ["-Wl,-rpath,%s/lib" % d
for d in dirs] + ["-lpetsc", "-lsupermesh"]
lib = load(supermesh_kernel_str,
"c",
"supermesh_kernel",
cppargs=includes,
ldargs=libs,
argtypes=[
ctypes.c_voidp, ctypes.c_voidp, ctypes.c_voidp,
ctypes.c_voidp, ctypes.c_voidp, ctypes.c_voidp,
ctypes.c_voidp
],
restype=ctypes.c_int)
ammm(V_A, V_B, likely, node_locations_A, node_locations_B, M_SS,
ctypes.addressof(lib), mat)
if orig_value_size == 1:
return mat
else:
(lrows, grows), (lcols, gcols) = mat.getSizes()
lrows *= orig_value_size
grows *= orig_value_size
lcols *= orig_value_size
gcols *= orig_value_size
size = ((lrows, grows), (lcols, gcols))
context = BlockMatrix(mat, orig_value_size)
blockmat = PETSc.Mat().createPython(size,
context=context,
comm=mat.comm)
blockmat.setUp()
return blockmat
from minidolfin.meshing import read_meshio, write_meshio
from minidolfin.dofmap import build_dofmap
from minidolfin.assembling import assemble
from minidolfin.bcs import bc_apply
# Call gmsh
subprocess.call(['gmsh', '-3', 'cylinder.geo'])
# Read gmsh format
mesh = read_meshio('cylinder.msh')
element = ufl.VectorElement("P", ufl.tetrahedron, 1)
DG0 = ufl.FiniteElement("DG", ufl.tetrahedron, 0)
u, v = ufl.TrialFunction(element), ufl.TestFunction(element)
E = ufl.Coefficient(DG0)
nu = 0.25
mu = E / (2.0 * (1.0 + nu))
lmbda = E * nu / ((1.0 + nu) * (1.0 - 2.0 * nu))
def epsilon(v):
return 0.5 * (ufl.grad(v) + ufl.grad(v).T)
def sigma(v):
return 2.0*mu*epsilon(v) + lmbda*ufl.tr(epsilon(v)) \
* ufl.Identity(v.geometric_dimension())
a = ufl.inner(sigma(u), epsilon(v)) * ufl.dx
def holzapfel_ogden(mesh, q, p, nf=0):
# Based on https://gist.github.com/meg-simula/3ab3fd63264c8cf1912b
#
# Original credit note:
# "Original implementation by Gabriel Balaban,
# modified by Marie E. Rognes"
from ufl import (Constant, VectorConstant, Identity, Coefficient,
TestFunction, conditional, det, diff, dot, exp,
grad, inner, tr, variable)
# Define some random parameters
a = Constant(mesh)
b = Constant(mesh)
a_s = Constant(mesh)
b_s = Constant(mesh)
a_f = Constant(mesh)
b_f = Constant(mesh)
a_fs = Constant(mesh)
b_fs = Constant(mesh)
# For more fun, make these general vector fields rather than
# constants:
e_s = VectorConstant(mesh)
e_f = VectorConstant(mesh)
# Define the isochoric energy contribution
def isochoric(C):
I_1 = tr(C)
I4_f = dot(e_f, C*e_f)
I4_s = dot(e_s, C*e_s)
I8_fs = dot(e_s, C*e_f)
def heaviside(x):
return conditional(x < 1, 0, 1)
def scaled_exp(a, b, x):
return a/(2*b)*(exp(b*x) - 1)
E_1 = scaled_exp(a, b, I_1 - 3)
E_f = heaviside(I4_f)*scaled_exp(a_f, b_f, (I4_f - 1)**2)
E_s = heaviside(I4_s)*scaled_exp(a_s, b_s, (I4_s - 1)**2)
E_3 = scaled_exp(a_fs, b_fs, I8_fs**2)
E = E_1 + E_f + E_s + E_3
return E
# Define mesh and function space
V = ufl.FunctionSpace(mesh, ufl.VectorElement("CG", mesh.ufl_cell(), q))
u = Coefficient(V)
v = TestFunction(V)
# Misc elasticity related tensors and other quantities
I = Identity(mesh.ufl_cell().topological_dimension())
F = grad(u) + I
F = variable(F)
J = det(F)
Cbar = J**(-2/3)*F.T*F
# Define energy
Psi = isochoric(Cbar)
# Find first Piola-Kirchhoff tensor
P = diff(Psi, F)
# Define the variational formulation
it = inner(P, grad(v))
P = ufl.FunctionSpace(mesh, ufl.VectorElement('P', mesh.ufl_cell(), p))
f = [ufl.Coefficient(P) for _ in range(nf)]
return ufl.derivative(reduce(ufl.inner,
list(map(ufl.div, f)) + [it])*ufl.dx, u)
import time
import ufl
import numpy
from minidolfin.meshing import read_mesh
from minidolfin.dofmap import build_dofmap
from minidolfin.assembling import symass
from minidolfin.bcs import build_dirichlet_dofs
mesh = read_mesh(
'https://raw.githubusercontent.com/chrisrichardson/meshdata/master/data/rectangle_mesh.xdmf'
) # noqa
element = ufl.FiniteElement("P", ufl.triangle, 1)
u, v = ufl.TrialFunction(element), ufl.TestFunction(element)
f = ufl.Coefficient(element)
a = ufl.inner(ufl.grad(u), ufl.grad(v)) * ufl.dx
L = ufl.cos(1.0) * v * ufl.dx
dofmap = build_dofmap(element, mesh)
def u_bound(x):
return x[0]
t = time.time()
bc_dofs, bc_vals = build_dirichlet_dofs(dofmap, u_bound)
bc_map = {i: v for i, v in zip(bc_dofs, bc_vals)}
elapsed = time.time() - t
print('BC time = ', elapsed)
def compile_expression_dual_evaluation(expression,
to_element,
*,
domain=None,
interface=None,
parameters=None,
coffee=False):
"""Compile a UFL expression to be evaluated against a compile-time known reference element's dual basis.
Useful for interpolating UFL expressions into e.g. N1curl spaces.
:arg expression: UFL expression
:arg to_element: A FInAT element for the target space
:arg domain: optional UFL domain the expression is defined on (required when expression contains no domain).
:arg interface: backend module for the kernel interface
:arg parameters: parameters object
:arg coffee: compile coffee kernel instead of loopy kernel
"""
import coffee.base as ast
import loopy as lp
# Just convert FInAT element to FIAT for now.
# Dual evaluation in FInAT will bring a thorough revision.
to_element = to_element.fiat_equivalent
if any(len(dual.deriv_dict) != 0 for dual in to_element.dual_basis()):
raise NotImplementedError(
"Can only interpolate onto dual basis functionals without derivative evaluation, sorry!"
)
if parameters is None:
parameters = default_parameters()
else:
_ = default_parameters()
_.update(parameters)
parameters = _
# Determine whether in complex mode
complex_mode = is_complex(parameters["scalar_type"])
# Find out which mapping to apply
try:
mapping, = set(to_element.mapping())
except ValueError:
raise NotImplementedError(
"Don't know how to interpolate onto zany spaces, sorry")
expression = apply_mapping(expression, mapping, domain)
# Apply UFL preprocessing
expression = ufl_utils.preprocess_expression(expression,
complex_mode=complex_mode)
# Initialise kernel builder
if interface is None:
if coffee:
import tsfc.kernel_interface.firedrake as firedrake_interface_coffee
interface = firedrake_interface_coffee.ExpressionKernelBuilder
else:
# Delayed import, loopy is a runtime dependency
import tsfc.kernel_interface.firedrake_loopy as firedrake_interface_loopy
interface = firedrake_interface_loopy.ExpressionKernelBuilder
builder = interface(parameters["scalar_type"])
arguments = extract_arguments(expression)
argument_multiindices = tuple(
builder.create_element(arg.ufl_element()).get_indices()
for arg in arguments)
# Replace coordinates (if any) unless otherwise specified by kwarg
if domain is None:
domain = expression.ufl_domain()
assert domain is not None
# Collect required coefficients
first_coefficient_fake_coords = False
coefficients = extract_coefficients(expression)
if has_type(expression, GeometricQuantity) or any(
fem.needs_coordinate_mapping(c.ufl_element())
for c in coefficients):
# Create a fake coordinate coefficient for a domain.
coords_coefficient = ufl.Coefficient(
ufl.FunctionSpace(domain, domain.ufl_coordinate_element()))
builder.domain_coordinate[domain] = coords_coefficient
builder.set_cell_sizes(domain)
coefficients = [coords_coefficient] + coefficients
first_coefficient_fake_coords = True
builder.set_coefficients(coefficients)
# Split mixed coefficients
expression = ufl_utils.split_coefficients(expression,
builder.coefficient_split)
# Translate to GEM
kernel_cfg = dict(
interface=builder,
ufl_cell=domain.ufl_cell(),
# FIXME: change if we ever implement
# interpolation on facets.
integral_type="cell",
argument_multiindices=argument_multiindices,
index_cache={},
scalar_type=parameters["scalar_type"])
if all(
isinstance(dual, PointEvaluation)
for dual in to_element.dual_basis()):
# This is an optimisation for point-evaluation nodes which
# should go away once FInAT offers the interface properly
qpoints = []
# Everything is just a point evaluation.
for dual in to_element.dual_basis():
ptdict = dual.get_point_dict()
qpoint, = ptdict.keys()
(qweight, component), = ptdict[qpoint]
assert allclose(qweight, 1.0)
assert component == ()
qpoints.append(qpoint)
point_set = PointSet(qpoints)
config = kernel_cfg.copy()
config.update(point_set=point_set)
# Allow interpolation onto QuadratureElements to refer to the quadrature
# rule they represent
if isinstance(to_element, FIAT.QuadratureElement):
assert allclose(asarray(qpoints), asarray(to_element._points))
quad_rule = QuadratureRule(point_set, to_element._weights)
config["quadrature_rule"] = quad_rule
expr, = fem.compile_ufl(expression, **config, point_sum=False)
# In some cases point_set.indices may be dropped from expr, but nothing
# new should now appear
assert set(expr.free_indices) <= set(
chain(point_set.indices, *argument_multiindices))
shape_indices = tuple(gem.Index() for _ in expr.shape)
basis_indices = point_set.indices
ir = gem.Indexed(expr, shape_indices)
else:
# This is general code but is more unrolled than necssary.
dual_expressions = [] # one for each functional
broadcast_shape = len(expression.ufl_shape) - len(
to_element.value_shape())
shape_indices = tuple(gem.Index()
for _ in expression.ufl_shape[:broadcast_shape])
expr_cache = {} # Sharing of evaluation of the expression at points
for dual in to_element.dual_basis():
pts = tuple(sorted(dual.get_point_dict().keys()))
try:
expr, point_set = expr_cache[pts]
except KeyError:
point_set = PointSet(pts)
config = kernel_cfg.copy()
config.update(point_set=point_set)
expr, = fem.compile_ufl(expression, **config, point_sum=False)
# In some cases point_set.indices may be dropped from expr, but
# nothing new should now appear
assert set(expr.free_indices) <= set(
chain(point_set.indices, *argument_multiindices))
expr = gem.partial_indexed(expr, shape_indices)
expr_cache[pts] = expr, point_set
weights = collections.defaultdict(list)
for p in pts:
for (w, cmp) in dual.get_point_dict()[p]:
weights[cmp].append(w)
qexprs = gem.Zero()
for cmp in sorted(weights):
qweights = gem.Literal(weights[cmp])
qexpr = gem.Indexed(expr, cmp)
qexpr = gem.index_sum(
gem.Indexed(qweights, point_set.indices) * qexpr,
point_set.indices)
qexprs = gem.Sum(qexprs, qexpr)
assert qexprs.shape == ()
assert set(qexprs.free_indices) == set(
chain(shape_indices, *argument_multiindices))
dual_expressions.append(qexprs)
basis_indices = (gem.Index(), )
ir = gem.Indexed(gem.ListTensor(dual_expressions), basis_indices)
# Build kernel body
return_indices = basis_indices + shape_indices + tuple(
chain(*argument_multiindices))
return_shape = tuple(i.extent for i in return_indices)
return_var = gem.Variable('A', return_shape)
if coffee:
return_arg = ast.Decl(parameters["scalar_type"],
ast.Symbol('A', rank=return_shape))
else:
return_arg = lp.GlobalArg("A",
dtype=parameters["scalar_type"],
shape=return_shape)
return_expr = gem.Indexed(return_var, return_indices)
# TODO: one should apply some GEM optimisations as in assembly,
# but we don't for now.
ir, = impero_utils.preprocess_gem([ir])
impero_c = impero_utils.compile_gem([(return_expr, ir)], return_indices)
index_names = dict(
(idx, "p%d" % i) for (i, idx) in enumerate(basis_indices))
# Handle kernel interface requirements
builder.register_requirements([ir])
# Build kernel tuple
return builder.construct_kernel(return_arg, impero_c, index_names,
first_coefficient_fake_coords)
def inject_kernel(Vf, Vc):
hierarchy, level = utils.get_level(Vc.ufl_domain())
cache = hierarchy._shared_data_cache["transfer_kernels"]
coordinates = Vf.ufl_domain().coordinates
key = (
("inject", ) + Vf.ufl_element().value_shape() +
entity_dofs_key(Vc.finat_element.entity_dofs()) +
entity_dofs_key(Vf.finat_element.entity_dofs()) + entity_dofs_key(
Vc.mesh().coordinates.function_space().finat_element.entity_dofs())
+ entity_dofs_key(
coordinates.function_space().finat_element.entity_dofs()))
try:
return cache[key]
except KeyError:
ncandidate = hierarchy.coarse_to_fine_cells[level].shape[1]
if Vc.finat_element.entity_dofs(
) == Vc.finat_element.entity_closure_dofs():
return cache.setdefault(
key, (dg_injection_kernel(Vf, Vc, ncandidate), True))
coordinates = Vf.ufl_domain().coordinates
evaluate_kernel = compile_element(ufl.Coefficient(Vf))
to_reference_kernel = to_reference_coordinates(
coordinates.ufl_element())
coords_element = create_element(coordinates.ufl_element())
Vf_element = create_element(Vf.ufl_element())
kernel = """
%(to_reference)s
%(evaluate)s
__attribute__((noinline)) /* Clang bug */
static void pyop2_kernel_inject(double *R, const double *X, const double *f, const double *Xf)
{
double Xref[%(tdim)d];
int cell = -1;
int bestcell = -1;
double bestdist = 1e10;
for (int i = 0; i < %(ncandidate)d; i++) {
const double *Xfi = Xf + i*%(Xf_cell_inc)d;
double celldist = 2*bestdist;
to_reference_coords_kernel(Xref, X, Xfi);
if (%(inside_cell)s) {
cell = i;
break;
}
%(compute_celldist)s
if (celldist < bestdist) {
bestdist = celldist;
bestcell = i;
}
}
if (cell == -1) {
/* We didn't find a cell that contained this point exactly.
Did we find one that was close enough? */
if (bestdist < 10) {
cell = bestcell;
} else {
fprintf(stderr, "Could not identify cell in transfer operator. Point: ");
for (int coord = 0; coord < %(spacedim)s; coord++) {
fprintf(stderr, "%%.14e ", X[coord]);
}
fprintf(stderr, "\\n");
fprintf(stderr, "Number of candidates: %%d. Best distance located: %%14e", %(ncandidate)d, bestdist);
abort();
}
}
const double *fi = f + cell*%(f_cell_inc)d;
for ( int i = 0; i < %(Rdim)d; i++ ) {
R[i] = 0;
}
pyop2_kernel_evaluate(R, fi, Xref);
}
""" % {
"to_reference":
str(to_reference_kernel),
"evaluate":
str(evaluate_kernel),
"inside_cell":
inside_check(Vc.finat_element.cell, eps=1e-8, X="Xref"),
"spacedim":
Vc.finat_element.cell.get_spatial_dimension(),
"compute_celldist":
compute_celldist(
Vc.finat_element.cell, X="Xref", celldist="celldist"),
"tdim":
Vc.ufl_domain().topological_dimension(),
"ncandidate":
ncandidate,
"Rdim":
numpy.prod(Vf_element.value_shape),
"Xf_cell_inc":
coords_element.space_dimension(),
"f_cell_inc":
Vf_element.space_dimension()
}
return cache.setdefault(
key, (op2.Kernel(kernel, name="pyop2_kernel_inject"), False))
def coordinate_coefficient(domain):
"""Create a fake coordinate coefficient for a domain."""
return ufl.Coefficient(ufl.FunctionSpace(domain, domain.ufl_coordinate_element()))
def dg_injection_kernel(Vf, Vc, ncell):
from firedrake import Tensor, AssembledVector, TestFunction, TrialFunction
from firedrake.slate.slac import compile_expression
macro_builder = MacroKernelBuilder(ScalarType_c, ncell)
f = ufl.Coefficient(Vf)
macro_builder.set_coefficients([f])
macro_builder.set_coordinates(Vf.mesh())
Vfe = create_element(Vf.ufl_element())
macro_quadrature_rule = make_quadrature(
Vfe.cell, estimate_total_polynomial_degree(ufl.inner(f, f)))
index_cache = {}
parameters = default_parameters()
integration_dim, entity_ids = lower_integral_type(Vfe.cell, "cell")
macro_cfg = dict(interface=macro_builder,
ufl_cell=Vf.ufl_cell(),
precision=parameters["precision"],
integration_dim=integration_dim,
entity_ids=entity_ids,
index_cache=index_cache,
quadrature_rule=macro_quadrature_rule)
fexpr, = fem.compile_ufl(f, **macro_cfg)
X = ufl.SpatialCoordinate(Vf.mesh())
C_a, = fem.compile_ufl(X, **macro_cfg)
detJ = ufl_utils.preprocess_expression(
abs(ufl.JacobianDeterminant(f.ufl_domain())))
macro_detJ, = fem.compile_ufl(detJ, **macro_cfg)
Vce = create_element(Vc.ufl_element())
coarse_builder = firedrake_interface.KernelBuilder("cell", "otherwise", 0,
ScalarType_c)
coarse_builder.set_coordinates(Vc.mesh())
argument_multiindices = (Vce.get_indices(), )
argument_multiindex, = argument_multiindices
return_variable, = coarse_builder.set_arguments((ufl.TestFunction(Vc), ),
argument_multiindices)
integration_dim, entity_ids = lower_integral_type(Vce.cell, "cell")
# Midpoint quadrature for jacobian on coarse cell.
quadrature_rule = make_quadrature(Vce.cell, 0)
coarse_cfg = dict(interface=coarse_builder,
ufl_cell=Vc.ufl_cell(),
precision=parameters["precision"],
integration_dim=integration_dim,
entity_ids=entity_ids,
index_cache=index_cache,
quadrature_rule=quadrature_rule)
X = ufl.SpatialCoordinate(Vc.mesh())
K = ufl_utils.preprocess_expression(ufl.JacobianInverse(Vc.mesh()))
C_0, = fem.compile_ufl(X, **coarse_cfg)
K, = fem.compile_ufl(K, **coarse_cfg)
i = gem.Index()
j = gem.Index()
C_0 = gem.Indexed(C_0, (j, ))
C_0 = gem.index_sum(C_0, quadrature_rule.point_set.indices)
C_a = gem.Indexed(C_a, (j, ))
X_a = gem.Sum(C_0, gem.Product(gem.Literal(-1), C_a))
K_ij = gem.Indexed(K, (i, j))
K_ij = gem.index_sum(K_ij, quadrature_rule.point_set.indices)
X_a = gem.index_sum(gem.Product(K_ij, X_a), (j, ))
C_0, = quadrature_rule.point_set.points
C_0 = gem.Indexed(gem.Literal(C_0), (i, ))
# fine quad points in coarse reference space.
X_a = gem.Sum(C_0, gem.Product(gem.Literal(-1), X_a))
X_a = gem.ComponentTensor(X_a, (i, ))
# Coarse basis function evaluated at fine quadrature points
phi_c = fem.fiat_to_ufl(
Vce.point_evaluation(0, X_a, (Vce.cell.get_dimension(), 0)), 0)
tensor_indices = tuple(gem.Index(extent=d) for d in f.ufl_shape)
phi_c = gem.Indexed(phi_c, argument_multiindex + tensor_indices)
fexpr = gem.Indexed(fexpr, tensor_indices)
quadrature_weight = macro_quadrature_rule.weight_expression
expr = gem.Product(gem.IndexSum(gem.Product(phi_c, fexpr), tensor_indices),
gem.Product(macro_detJ, quadrature_weight))
quadrature_indices = macro_builder.indices + macro_quadrature_rule.point_set.indices
reps = spectral.Integrals([expr], quadrature_indices,
argument_multiindices, parameters)
assignments = spectral.flatten([(return_variable, reps)], index_cache)
return_variables, expressions = zip(*assignments)
expressions = impero_utils.preprocess_gem(expressions,
**spectral.finalise_options)
assignments = list(zip(return_variables, expressions))
impero_c = impero_utils.compile_gem(assignments,
quadrature_indices +
argument_multiindex,
remove_zeros=True)
index_names = []
def name_index(index, name):
index_names.append((index, name))
if index in index_cache:
for multiindex, suffix in zip(index_cache[index],
string.ascii_lowercase):
name_multiindex(multiindex, name + suffix)
def name_multiindex(multiindex, name):
if len(multiindex) == 1:
name_index(multiindex[0], name)
else:
for i, index in enumerate(multiindex):
name_index(index, name + str(i))
name_multiindex(quadrature_indices, 'ip')
for multiindex, name in zip(argument_multiindices, ['j', 'k']):
name_multiindex(multiindex, name)
index_names.extend(zip(macro_builder.indices, ["entity"]))
body = generate_coffee(impero_c, index_names, parameters["precision"],
ScalarType_c)
retarg = ast.Decl(ScalarType_c,
ast.Symbol("R", rank=(Vce.space_dimension(), )))
local_tensor = coarse_builder.local_tensor
local_tensor.init = ast.ArrayInit(
numpy.zeros(Vce.space_dimension(), dtype=ScalarType_c))
body.children.insert(0, local_tensor)
args = [retarg] + macro_builder.kernel_args + [
macro_builder.coordinates_arg, coarse_builder.coordinates_arg
]
# Now we have the kernel that computes <f, phi_c>dx_c
# So now we need to hit it with the inverse mass matrix on dx_c
u = TrialFunction(Vc)
v = TestFunction(Vc)
expr = Tensor(ufl.inner(u, v) * ufl.dx).inv * AssembledVector(
ufl.Coefficient(Vc))
Ainv, = compile_expression(expr)
Ainv = Ainv.kinfo.kernel
A = ast.Symbol(local_tensor.sym.symbol)
R = ast.Symbol("R")
body.children.append(
ast.FunCall(Ainv.name, R, coarse_builder.coordinates_arg.sym, A))
from coffee.base import Node
assert isinstance(Ainv._code, Node)
return op2.Kernel(ast.Node([
Ainv._code,
ast.FunDecl("void",
"pyop2_kernel_injection_dg",
args,
body,
pred=["static", "inline"])
]),
name="pyop2_kernel_injection_dg",
cpp=True,
include_dirs=Ainv._include_dirs,
headers=Ainv._headers)
def mesh(element):
return ufl.Domain(ufl.Coefficient(element))
