def fdrake_mesh(request):
mesh_name = request.param
if mesh_name == "FiredrakeUnitIntervalMesh":
return UnitIntervalMesh(100)
elif mesh_name == "FiredrakeUnitSquareMesh":
return UnitSquareMesh(10, 10)
elif mesh_name == "FiredrakeUnitSquareMesh-order2":
m = UnitSquareMesh(10, 10)
fspace = VectorFunctionSpace(m, "CG", 2)
coords = Function(fspace).interpolate(SpatialCoordinate(m))
from firedrake.mesh import Mesh
return Mesh(coords)
elif mesh_name == "FiredrakeUnitCubeMesh":
return UnitCubeMesh(5, 5, 5)
elif mesh_name not in ("annulus.msh", "blob2d-order1-h4e-2.msh",
"blob2d-order1-h6e-2.msh",
"blob2d-order1-h8e-2.msh"):
raise ValueError("Unexpected value for request.param")
# Firedrake can't read in higher order meshes from gmsh,
# so we can only use the order1 blobs
from firedrake import Mesh
fd_mesh = Mesh(mesh_name)
fd_mesh.init()
return fd_mesh
def run(problem, tensor, size_factor, degree):
formname = problem.__name__
cellname = 'cube' if tensor else 'simplex'
PETSc.Sys.Print("%s: %s, degree=%d" % (formname, cellname, degree))
num_cells = COMM_WORLD.size * max(1, 1e7 * size_factor / (degree + 1)**{'spectral': 4, 'coffee': 6}[args.mode])
h = int(floor(cbrt(num_cells / COMM_WORLD.size)))
w = int(floor(sqrt(num_cells / h)))
d = int(round(num_cells / (w * h)))
num_cells = w * d * h
if tensor:
mesh = ExtrudedMesh(UnitSquareMesh(w, d, quadrilateral=True), h)
else:
mesh = UnitCubeMesh(w, d, h)
comm = mesh.comm
J = problem(mesh, int(degree))
# Warmup and allocate
A = assemble(J, mat_type="matfree", form_compiler_parameters={'mode': args.mode})
A.force_evaluation()
Ap = A.petscmat
x, y = Ap.createVecs()
assert x.size == y.size
num_dofs = x.size
Ap.mult(x, y)
stage = PETSc.Log.Stage("%s(%d) %s" % (formname, degree, cellname))
with stage:
assemble(J, mat_type="matfree", form_compiler_parameters={'mode': args.mode}, tensor=A)
A.force_evaluation()
Ap = A.petscmat
for _ in range(num_matvecs):
Ap.mult(x, y)
parloop = parloop_event.getPerfInfo()
matmult = matmult_event.getPerfInfo()
assert parloop["count"] == 2 * num_matvecs
assert matmult["count"] == num_matvecs
parloop_time = comm.allreduce(parloop["time"], op=MPI.SUM) / (comm.size * num_matvecs)
matmult_time = comm.allreduce(matmult["time"], op=MPI.SUM) / (comm.size * num_matvecs)
matfree_overhead = (1 - parloop_time / matmult_time)
PETSc.Sys.Print("Matrix-free action overhead: %.1f%%" % (matfree_overhead * 100,))
if COMM_WORLD.rank == 0:
header = not os.path.exists(filepath)
data = {"num_cells": num_cells,
"num_dofs": num_dofs,
"num_procs": comm.size,
"tsfc_mode": args.mode,
"problem": formname,
"cell_type": cellname,
"degree": degree,
"matmult_time": matmult_time,
"parloop_time": parloop_time}
df = pandas.DataFrame(data, index=[0])
df.to_csv(filepath, index=False, mode='a', header=header)
def setUp(self):
"""
Create a function builder and input file.
"""
self.mesh = UnitSquareMesh(10, 10)
self.V = FunctionSpace(self.mesh, 'CG', 1)
self.fb = FileBuilder(self.mesh, self.V)
self.input = NamedTemporaryFile(mode='w+')
self.fb.assign('path', self.input.name)
def __init__(self):
N = 5
self.mesh = UnitSquareMesh(N, N)
self.T0 = self.mesh.coordinates.copy(deepcopy=True)
# random perturmabion
h = 1 / N
self.X = SpatialCoordinate(self.mesh)
W = VectorFunctionSpace(self.mesh, "CG", 1)
self.w = Function(W)
vec = self.w.vector()
np.random.seed(1)
vec.set_local(
np.random.uniform(-h / 3., h / 3., size=vec.get_local().shape))
self.name = "missing name"
self.bc = None
def get_fdrake_mesh_and_h_from_par(mesh_par):
if fdrake_mesh_name == "UnitInterval":
assert dim == 1
n = mesh_par
fdrake_mesh = UnitIntervalMesh(n)
h = 1 / n
elif fdrake_mesh_name == "UnitSquare":
assert dim == 2
n = mesh_par
fdrake_mesh = UnitSquareMesh(n, n)
h = 1 / n
elif fdrake_mesh_name == "UnitCube":
assert dim == 3
n = mesh_par
fdrake_mesh = UnitCubeMesh(n, n, n)
h = 1 / n
elif fdrake_mesh_name in ("blob2d-order1", "blob2d-order4"):
assert dim == 2
if fdrake_mesh_name == "blob2d-order1":
from firedrake import Mesh
fdrake_mesh = Mesh(f"{fdrake_mesh_name}-h{mesh_par}.msh",
dim=dim)
else:
from meshmode.mesh.io import read_gmsh
from meshmode.interop.firedrake import export_mesh_to_firedrake
mm_mesh = read_gmsh(f"{fdrake_mesh_name}-h{mesh_par}.msh",
force_ambient_dim=dim)
fdrake_mesh, _, _ = export_mesh_to_firedrake(mm_mesh)
h = float(mesh_par)
elif fdrake_mesh_name == "warp":
from meshmode.mesh.generation import generate_warped_rect_mesh
from meshmode.interop.firedrake import export_mesh_to_firedrake
mm_mesh = generate_warped_rect_mesh(dim,
order=4,
nelements_side=mesh_par)
fdrake_mesh, _, _ = export_mesh_to_firedrake(mm_mesh)
h = 1 / mesh_par
else:
raise ValueError("fdrake_mesh_name not recognized")
return (fdrake_mesh, h)
def regularization_form(r):
mesh = UnitSquareMesh(2 ** r, 2 ** r)
x = SpatialCoordinate(mesh)
S = VectorFunctionSpace(mesh, "CG", 1)
beta = 4.0
reg_solver = RegularizationSolver(S, mesh, beta=beta, gamma=0.0, dx=dx)
# Exact solution with free Neumann boundary conditions for this domain
u_exact = Function(S)
u_exact_component = cos(x[0] * pi * 2) * cos(x[1] * pi * 2)
u_exact.interpolate(as_vector((u_exact_component, u_exact_component)))
f = Function(S)
theta = TestFunction(S)
f_component = (1 + beta * 8 * pi * pi) * u_exact_component
f.interpolate(as_vector((f_component, f_component)))
rhs_form = inner(f, theta) * dx
velocity = Function(S)
rhs = assemble(rhs_form)
reg_solver.solve(velocity, rhs)
File("solution_vel_unitsquare.pvd").write(velocity)
return norm(project(u_exact - velocity, S))
from firedrake import UnitSquareMesh, FunctionSpace, TrialFunction, TestFunction
from firedrake import SpatialCoordinate, dx, pi, sin, dot, grad, DirichletBC
from firedrake import assemble, Function, solve
import stat_fem
from stat_fem.covariance_functions import sqexp
try:
import matplotlib.pyplot as plt
makeplots = True
except ImportError:
makeplots = False
# Set up base FEM, which solves Poisson's equation on a square mesh
nx = 101
mesh = UnitSquareMesh(nx - 1, nx - 1)
V = FunctionSpace(mesh, "CG", 1)
u = TrialFunction(V)
v = TestFunction(V)
f = Function(V)
x = SpatialCoordinate(mesh)
f.interpolate((8 * pi * pi) * sin(x[0] * pi * 2) * sin(x[1] * pi * 2))
a = (dot(grad(v), grad(u))) * dx
L = f * v * dx
bc = DirichletBC(V, 0., "on_boundary")
A = assemble(a, bcs=bc)
def heat(butcher_tableau):
N = 4
dt = Constant(1.0 / N)
t = Constant(0.0)
msh = UnitSquareMesh(N, N)
deg = 2
V = FunctionSpace(msh, "CG", deg)
x, y = SpatialCoordinate(msh)
uexact = t * (x + y)
rhs = expand_derivatives(diff(uexact, t)) - div(grad(uexact))
sols = []
luparams = {
"mat_type": "aij",
"snes_type": "ksponly",
"ksp_type": "preonly",
"pc_type": "lu"
}
ranaLD = {
"mat_type": "aij",
"snes_type": "ksponly",
"ksp_type": "gmres",
"ksp_monitor": None,
"pc_type": "python",
"pc_python_type": "irksome.RanaLD",
"aux": {
"pc_type": "fieldsplit",
"pc_fieldsplit_type": "multiplicative"
}
}
per_field = {"ksp_type": "preonly", "pc_type": "gamg"}
for s in range(butcher_tableau.num_stages):
ranaLD["fieldsplit_%s" % (s, )] = per_field
ranaDU = {
"mat_type": "aij",
"snes_type": "ksponly",
"ksp_type": "gmres",
"ksp_monitor": None,
"pc_type": "python",
"pc_python_type": "irksome.RanaDU",
"aux": {
"pc_type": "fieldsplit",
"pc_fieldsplit_type": "multiplicative"
}
}
for s in range(butcher_tableau.num_stages):
ranaLD["fieldsplit_%s" % (s, )] = per_field
params = [luparams, ranaLD, ranaDU]
for solver_parameters in params:
F, u, bc = Fubc(V, uexact, rhs)
stepper = TimeStepper(F,
butcher_tableau,
t,
dt,
u,
bcs=bc,
solver_parameters=solver_parameters)
stepper.advance()
sols.append(u)
errs = [errornorm(sols[0], uu) for uu in sols[1:]]
return numpy.max(errs)
atol=CLOSE_ATOL)
# Ensure the discretization and the firedrake function space reference element
# agree on some basic properties
finat_elt = fdrake_fspace.finat_element
assert len(discr.groups) == 1
assert discr.groups[0].order == finat_elt.degree
assert discr.groups[0].nunit_dofs == finat_elt.space_dimension()
# }}}
# {{{ Boundary tags checking
bdy_tests = [
(UnitSquareMesh(10, 10), [1, 2, 3, 4], [0, 0, 1, 1], [0.0, 1.0, 0.0, 1.0]),
(UnitCubeMesh(5, 5, 5), [1, 2, 3, 4, 5,
6], [0, 0, 1, 1, 2,
2], [0.0, 1.0, 0.0, 1.0, 0.0, 1.0]),
]
@pytest.mark.parametrize(
"square_or_cube_mesh,bdy_ids,coord_indices,coord_values", bdy_tests)
@pytest.mark.parametrize("only_convert_bdy", (True, False))
def test_bdy_tags(square_or_cube_mesh, bdy_ids, coord_indices, coord_values,
only_convert_bdy):
"""
Make sure the given boundary ids cover the converted mesh.
Make sure that the given coordinate have the given value for the
corresponding boundary tag (see :mod:`firedrake.utility_meshes`'s
def make_mesh(nx, ny, nz, quadrilateral=False):
return ExtrudedMesh(UnitSquareMesh(nx, ny,
quadrilateral=quadrilateral),
nz,
layer_height=1.0 / nz)
plt.savefig("plots/RectangleMesh.png")
# -> SquareMesh
# -------------
# using SquareMesh (possible use of quadrilateral elements)
mesh = SquareMesh(nx, ny, L, quadrilateral=quad)
triplot(mesh)
plt.legend()
plt.savefig("plots/SquareMesh.png")
# -> UnitSquareMesh
# -----------------
# possible use of quadrilateral elements
mesh = UnitSquareMesh(nx, ny, quadrilateral=not quad)
triplot(mesh)
plt.legend()
plt.savefig("plots/UnitSquareMesh.png")
# -> PeriodicRectangleMesh
# ------------------------
# possible use of quadrilateral elements
mesh = PeriodicRectangleMesh(nx+1, ny, Lx, Ly)
triplot(mesh)
plt.legend()
plt.savefig("plots/PeriodicRectangleMesh.png")
# -> PeriodicSquareMesh
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
from meshmode.interop.firedrake import build_connection_from_firedrake
from firedrake import (UnitSquareMesh, FunctionSpace, SpatialCoordinate,
Function, cos)
# Create a firedrake mesh and interpolate cos(x+y) onto it
fd_mesh = UnitSquareMesh(10, 10)
fd_fspace = FunctionSpace(fd_mesh, "DG", 2)
spatial_coord = SpatialCoordinate(fd_mesh)
fd_fntn = Function(fd_fspace).interpolate(cos(sum(spatial_coord)))
# Make connections
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
fd_connection = build_connection_from_firedrake(actx, fd_fspace)
fd_bdy_connection = \
build_connection_from_firedrake(actx,
fd_fspace,
restrict_to_boundary="on_boundary")
# Plot the meshmode meshes that the connections connect to
import matplotlib.pyplot as plt
from meshmode.mesh.visualization import draw_2d_mesh
fig, (ax1, ax2) = plt.subplots(1, 2)
ax1.set_title("FiredrakeConnection")
plt.sca(ax1)
draw_2d_mesh(fd_connection.discr.mesh,
draw_vertex_numbers=False,
draw_element_numbers=False,
set_bounding_box=True)
ax2.set_title("FiredrakeConnection 'on_boundary'")
plt.sca(ax2)
draw_2d_mesh(fd_bdy_connection.discr.mesh,
draw_vertex_numbers=False,
draw_element_numbers=False,
set_bounding_box=True)
plt.show()
# Plot fd_fntn using unrestricted FiredrakeConnection
from meshmode.discretization.visualization import make_visualizer
discr = fd_connection.discr
vis = make_visualizer(actx, discr, discr.groups[0].order + 3)
field = fd_connection.from_firedrake(fd_fntn, actx=actx)
fig = plt.figure()
ax1 = fig.add_subplot(1, 2, 1, projection="3d")
ax1.set_title("cos(x+y) in\nFiredrakeConnection")
vis.show_scalar_in_matplotlib_3d(field, do_show=False)
# Now repeat using FiredrakeConnection restricted to "on_boundary"
bdy_discr = fd_bdy_connection.discr
bdy_vis = make_visualizer(actx, bdy_discr, bdy_discr.groups[0].order + 3)
bdy_field = fd_bdy_connection.from_firedrake(fd_fntn, actx=actx)
ax2 = fig.add_subplot(1, 2, 2, projection="3d")
plt.sca(ax2)
ax2.set_title("cos(x+y) in\nFiredrakeConnection 'on_boundary'")
bdy_vis.show_scalar_in_matplotlib_3d(bdy_field, do_show=False)
import matplotlib.cm as cm
fig.colorbar(cm.ScalarMappable())
plt.show()
np.testing.assert_allclose(lex_sorted_mm_verts, lex_sorted_fdrake_verts.T,
atol=CLOSE_ATOL)
# Ensure the discretization and the firedrake function space reference element
# agree on some basic properties
finat_elt = fdrake_fspace.finat_element
assert len(discr.groups) == 1
assert discr.groups[0].order == finat_elt.degree
assert discr.groups[0].nunit_dofs == finat_elt.space_dimension()
# }}}
# {{{ Boundary tags checking
bdy_tests = [(UnitSquareMesh(10, 10),
[1, 2, 3, 4],
[0, 0, 1, 1],
[0.0, 1.0, 0.0, 1.0]),
(UnitCubeMesh(5, 5, 5),
[1, 2, 3, 4, 5, 6],
[0, 0, 1, 1, 2, 2],
[0.0, 1.0, 0.0, 1.0, 0.0, 1.0]),
]
@pytest.mark.parametrize("square_or_cube_mesh,bdy_ids,coord_indices,coord_values",
bdy_tests)
@pytest.mark.parametrize("only_convert_bdy", (True, False))
def test_bdy_tags(square_or_cube_mesh, bdy_ids, coord_indices, coord_values,
only_convert_bdy):
error_threshold = 1e-3
if cell_type == "quad":
quadrilateral = True
elif cell_type == "tria":
quadrilateral = False
else:
raise ValueError("Cell type not supported")
# building reference solution
p = 1
initial_dt = 0.00005
# determining dt as f(p) in mesh
degrees = [5]
mesh = UnitSquareMesh(40, 40, quadrilateral=quadrilateral)
mh = MeshHierarchy(mesh, 3)
# determine maximum stable timestep with error < error_threshold
dts = np.zeros((len(mh) - 1, len(degrees)))
# construct reference solution
ref = solver_CG(mh[-1],
el=cell_type,
space=space,
deg=p,
T=0.50,
dt=initial_dt)
V_fine = _build_space(mh[-1], cell_type, space, p)
# step to increase timestep (step << dt)
def test_replace_subject(subject_type, replacement_type):
# ------------------------------------------------------------------------ #
# Only certain combinations of options are valid
# ------------------------------------------------------------------------ #
if subject_type == 'vector' and replacement_type != 'vector':
return True
elif replacement_type == 'vector' and subject_type != 'vector':
return True
# ------------------------------------------------------------------------ #
# Set up
# ------------------------------------------------------------------------ #
# Some basic labels
foo_label = Label("foo")
bar_label = Label("bar")
# Create mesh, function space and forms
n = 3
mesh = UnitSquareMesh(n, n)
V0 = FunctionSpace(mesh, "DG", 0)
V1 = FunctionSpace(mesh, "CG", 1)
V2 = VectorFunctionSpace(mesh, "DG", 0)
Vmixed = MixedFunctionSpace((V0, V1))
idx = None
# ------------------------------------------------------------------------ #
# Choose subject
# ------------------------------------------------------------------------ #
if subject_type == 'normal':
V = V0
elif subject_type == 'mixed':
V = Vmixed
if replacement_type == 'normal':
idx = 0
elif subject_type == 'vector':
V = V2
else:
raise ValueError
the_subject = Function(V)
not_subject = Function(V)
test = TestFunction(V)
form_1 = inner(the_subject, test)*dx
form_2 = inner(not_subject, test)*dx
term_1 = foo_label(subject(form_1, the_subject))
term_2 = bar_label(form_2)
labelled_form = term_1 + term_2
# ------------------------------------------------------------------------ #
# Choose replacement
# ------------------------------------------------------------------------ #
if replacement_type == 'normal':
V = V1
elif replacement_type == 'mixed':
V = Vmixed
if subject_type != 'mixed':
idx = 0
elif replacement_type == 'vector':
V = V2
elif replacement_type == 'tuple':
V = Vmixed
else:
raise ValueError
the_replacement = Function(V)
if replacement_type == 'tuple':
the_replacement = TrialFunctions(Vmixed)
if subject_type == 'normal':
idx = 0
# ------------------------------------------------------------------------ #
# Test replace_subject
# ------------------------------------------------------------------------ #
labelled_form = labelled_form.label_map(
lambda t: t.has_label(subject),
map_if_true=replace_subject(the_replacement, idx=idx)
)
rhs, div, assemble, File, solve
# Print log messages only from the root process in parallel
# parameters["std_out_all_processes"] = False;
# Set parameter values
T = 10.0
Re = 3000.0
Umax = 1.0
C = 0.3
N = int((Re**(0.75)) * 2.0)
dt = C * (1.0 / N) / Umax
mesh = UnitSquareMesh(N, N)
# Define function spaces (P2-P1)
V = VectorFunctionSpace(mesh, "Lagrange", 2)
Q = FunctionSpace(mesh, "Lagrange", 1)
# Define trial and test functions
u = TrialFunction(V)
p = TrialFunction(Q)
v = TestFunction(V)
q = TestFunction(Q)
# Define time-dependent pressure boundary condition
#p_in = Expression("sin(3.0*t)", t=0.0)
u_in = Expression(('1.0*(x[1]>0.5)+0.5*(x[1]<=0.5)', '0.0'))
form, parameters=parameters)[0]
indices = IndexDict(
{idx: sympy.symbols(name)
for idx, name in index_names})
expr = expression(impero_kernel.tree,
impero_kernel.temporaries,
indices,
top=True)
p1 = sympy.symbols("p") + 1
'''Currently assume p+1 quad points in each direction.'''
return expr.subs([(i, p1) for i in indices.values()]).expand()
m = ExtrudedMesh(UnitSquareMesh(2, 2, quadrilateral=True), 2)
mass = form.mass(m, 6)
poisson = form.poisson(m, 6)
hyperelasticity = form.hyperelasticity(m, 6)
curl_curl = form.curl_curl(m, 6)
parameters = firedrake.parameters['form_compiler'].copy()
parameters['return_impero'] = True
parameters['mode'] = 'spectral'
for mode, action in (("assembly", False), ("action", True)):
print(mode)
print(" mass: ", complexity(mass, parameters, action))
print(" laplacian: ", complexity(poisson, parameters, action))
print(" hyperelasticity:", complexity(hyperelasticity, parameters,
def setUp(self):
mesh = UnitSquareMesh(100, 100)
V = FunctionSpace(mesh, 'CG', 1)
self.factory = FunctionBuilderFactory(mesh=mesh, V=V)
def main():
# make function space and function
dim = 2 # 2 or 3
order = 1
logger.info(f"building {dim}D source and solution exprs")
if dim == 2:
m = UnitSquareMesh(32, 32)
elif dim == 3:
m = UnitCubeMesh(16, 16, 16)
else:
raise ValueError("dim must be 2 or 3, not %s" % dim)
# get spatial coordinate, shifted so that [0,1]^2 -> [-0.5,0.5]^2
xx = SpatialCoordinate(m)
shifted_xx = as_tensor([xx_i - 0.5 for xx_i in xx])
norm2 = sum([xx_i * xx_i for xx_i in shifted_xx])
alpha = 10
source_expr = -(4 * alpha**2 * norm2 - 2 * dim * alpha) * exp(
-alpha * norm2)
sol_expr = exp(-alpha * norm2)
logger.info("source_expr : %s" % source_expr)
logger.info("sol_expr : %s" % sol_expr)
logger.info(f"Building FunctionSpace of order {order}")
fspace = FunctionSpace(m, 'DG', order)
logger.info("interpolating source and solution")
source = Function(fspace).interpolate(source_expr)
sol = Function(fspace).interpolate(sol_expr)
from sumpy.kernel import LaplaceKernel
kernel = LaplaceKernel(m.geometric_dimension())
# We could set to a custom group factory if we wanted to,
# defaults to recursive nodes with 'lgl' nodes
#
# from meshmode.discretization.poly_element import (
# PolynomialWarpAndBlendGroupFactory)
# grp_factory = PolynomialWarpAndBlendGroupFactory(order)
grp_factory = None
# Build VolumePotential external operator
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
potential_data = {
'kernel': kernel,
'kernel_type': "Laplace",
'cl_ctx': cl_ctx,
'queue': queue,
'nlevels': 6,
'm_order': 20,
'dataset_filename': f"laplace-order{order}-{dim}D.hdf5",
'grp_factory': grp_factory,
'root_extent': 2,
'table_compute_method': "DrosteSum",
'table_kwargs': {
'force_recompute': False,
'n_brick_quad_points': 100,
'adaptive_level': False,
'use_symmetry': True,
'alpha': 0.1,
'nlevels': 15,
},
'fmm_kwargs': {},
}
logger.info("Creating volume potential")
# pot = VolumePotential(source, function_space=source.function_space(), operator_data=potential_data)
# logger.info("Evaluating potential and assembling L^2 Error")
# ell2_difference = sqrt(assemble(inner(pot - sol, pot - sol) * dx))
# print("L^2 difference: %e" % ell2_difference)
print("interpolation error: %e" % errornorm(sol_expr, sol))