def test_to_fd_consistency(ctx_factory, mm_mesh, fspace_degree):
fspace_degree += mm_mesh.groups[0].order
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
factory = InterpolatoryQuadratureSimplexGroupFactory(fspace_degree)
discr = Discretization(actx, mm_mesh, factory)
fdrake_connection = build_connection_to_firedrake(discr)
fdrake_fspace = fdrake_connection.firedrake_fspace()
# Check consistency
check_consistency(fdrake_fspace, discr)
def test_to_fd_idempotency(ctx_factory, mm_mesh, fspace_degree):
"""
Make sure mm->fd->mm and (mm->)->fd->mm->fd are identity
"""
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
# make sure degree is higher order than mesh
fspace_degree += mm_mesh.groups[0].order
# Make a function space and a function with unique values at each node
factory = InterpolatoryQuadratureSimplexGroupFactory(fspace_degree)
discr = Discretization(actx, mm_mesh, factory)
fdrake_connection = build_connection_to_firedrake(discr)
fdrake_mesh = fdrake_connection.firedrake_fspace().mesh()
dtype = fdrake_mesh.coordinates.dat.data.dtype
mm_unique = discr.zeros(actx, dtype=dtype)
unique_vals = np.arange(np.size(mm_unique[0]), dtype=dtype)
mm_unique[0].set(unique_vals.reshape(mm_unique[0].shape))
mm_unique_copy = DOFArray(actx, (mm_unique[0].copy(), ))
# Test for idempotency mm->fd->mm
fdrake_unique = fdrake_connection.from_meshmode(mm_unique)
fdrake_connection.from_firedrake(fdrake_unique, out=mm_unique_copy)
np.testing.assert_allclose(actx.to_numpy(mm_unique_copy[0]),
actx.to_numpy(mm_unique[0]),
atol=CLOSE_ATOL)
# Test for idempotency (mm->)fd->mm->fd
fdrake_unique_copy = fdrake_connection.from_meshmode(mm_unique_copy)
np.testing.assert_allclose(fdrake_unique_copy.dat.data,
fdrake_unique.dat.data,
atol=CLOSE_ATOL)
def test_to_fd_transfer(ctx_factory, fspace_degree, mesh_name, mesh_pars, dim):
"""
Make sure creating a function which projects onto
one dimension then transports it is the same
(up to resampling error) as projecting to one
dimension on the transported mesh
"""
# build estimate-of-convergence recorder
from pytools.convergence import EOCRecorder
# dimension projecting onto -> EOCRecorder
eoc_recorders = {d: EOCRecorder() for d in range(dim)}
# make a computing context
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
# Get each of the refinements of the meshmeshes and record
# conversions errors
for mesh_par in mesh_pars:
if mesh_name in ("blob2d-order1", "blob2d-order4"):
assert dim == 2
from meshmode.mesh.io import read_gmsh
mm_mesh = read_gmsh(f"{mesh_name}-h{mesh_par}.msh",
force_ambient_dim=dim)
h = float(mesh_par)
elif mesh_name == "warp":
from meshmode.mesh.generation import generate_warped_rect_mesh
mm_mesh = generate_warped_rect_mesh(dim, order=4, n=mesh_par)
h = 1 / mesh_par
else:
raise ValueError("mesh_name not recognized")
# Make discr and connect it to firedrake
factory = InterpolatoryQuadratureSimplexGroupFactory(fspace_degree)
discr = Discretization(actx, mm_mesh, factory)
fdrake_connection = build_connection_to_firedrake(discr)
fdrake_fspace = fdrake_connection.firedrake_fspace()
spatial_coord = SpatialCoordinate(fdrake_fspace.mesh())
# get the group's nodes in a numpy array
nodes = discr.nodes()
group_nodes = np.array(
[actx.to_numpy(dof_arr[0]) for dof_arr in nodes])
for d in range(dim):
meshmode_f = discr.zeros(actx)
meshmode_f[0][:] = group_nodes[d, :, :]
# connect to firedrake and evaluate expr in firedrake
fdrake_f = Function(fdrake_fspace).interpolate(spatial_coord[d])
# transport to firedrake and record error
mm2fd_f = fdrake_connection.from_meshmode(meshmode_f)
err = np.max(np.abs(fdrake_f.dat.data - mm2fd_f.dat.data))
eoc_recorders[d].add_data_point(h, err)
# assert that order is correct or error is "low enough"
for d, eoc_rec in eoc_recorders.items():
print("\nvector *x* -> *x[%s]*\n" % d, eoc_rec)
assert (eoc_rec.order_estimate() >= fspace_degree
or eoc_rec.max_error() < 2e-14)
def main():
# If can't import firedrake, do nothing
#
# filename MUST include "firedrake" (i.e. match *firedrake*.py) in order
# to be run during CI
try:
import firedrake # noqa : F401
except ImportError:
return 0
# For this example, imagine we wish to solve the Laplace equation
# on a meshmode mesh with some given Dirichlet boundary conditions,
# and decide to use firedrake.
#
# To verify this is working, we use a solution to the wave equation
# to get our boundary conditions
# {{{ First we make a discretization in meshmode and get our bcs
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
from meshmode.array_context import PyOpenCLArrayContext
actx = PyOpenCLArrayContext(queue)
nel_1d = 16
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(a=(-0.5, -0.5),
b=(0.5, 0.5),
n=(nel_1d, nel_1d))
order = 3
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import \
InterpolatoryQuadratureSimplexGroupFactory
group_factory = InterpolatoryQuadratureSimplexGroupFactory(order=order)
discr = Discretization(actx, mesh, group_factory)
# Get our solution: we will use
# Real(e^z) = Real(e^{x+iy})
# = e^x Real(e^{iy})
# = e^x cos(y)
nodes = discr.nodes()
from meshmode.dof_array import thaw
for i in range(len(nodes)):
nodes[i] = thaw(actx, nodes[i])
# First index is dimension
candidate_sol = actx.np.exp(nodes[0]) * actx.np.cos(nodes[1])
# }}}
# {{{ Now send candidate_sol into firedrake and use it for boundary conditions
from meshmode.interop.firedrake import build_connection_to_firedrake
fd_connection = build_connection_to_firedrake(discr, group_nr=0)
# convert candidate_sol to firedrake
fd_candidate_sol = fd_connection.from_meshmode(candidate_sol)
# get the firedrake function space
fd_fspace = fd_connection.firedrake_fspace()
# set up dirichlet laplace problem in fd and solve
from firedrake import (FunctionSpace, TrialFunction, TestFunction,
Function, inner, grad, dx, Constant, project,
DirichletBC, solve)
# because it's easier to write down the variational problem,
# we're going to project from our "DG" space
# into a continuous one.
cfd_fspace = FunctionSpace(fd_fspace.mesh(), "CG", order)
u = TrialFunction(cfd_fspace)
v = TestFunction(cfd_fspace)
sol = Function(cfd_fspace)
a = inner(grad(u), grad(v)) * dx
rhs = Constant(0.0) * v * dx
bc_value = project(fd_candidate_sol, cfd_fspace)
bc = DirichletBC(cfd_fspace, bc_value, "on_boundary")
params = {"ksp_monitor": None}
solve(a == rhs, sol, bcs=[bc], solver_parameters=params)
# project back into our "DG" space
sol = project(sol, fd_fspace)
# }}}
# {{{ Take the solution from firedrake and compare it to candidate_sol
true_sol = fd_connection.from_firedrake(sol, actx=actx)
# pull back into numpy
true_sol = actx.to_numpy(true_sol[0])
candidate_sol = actx.to_numpy(candidate_sol[0])
print("l^2 difference between candidate solution and firedrake solution=",
np.linalg.norm(true_sol - candidate_sol))