def test_norm_obj_array(actx_factory, p):
"""Test :func:`grudge.symbolic.operators.norm` for object arrays."""
actx = actx_factory()
dim = 2
mesh = mgen.generate_regular_rect_mesh(a=(-0.5, ) * dim,
b=(0.5, ) * dim,
nelements_per_axis=(8, ) * dim,
order=1)
discr = DiscretizationCollection(actx, mesh, order=4)
w = make_obj_array([1.0, 2.0, 3.0])[:dim]
# {{ scalar
sym_w = sym.var("w")
norm = bind(discr, sym.norm(p, sym_w))(actx, w=w[0])
norm_exact = w[0]
logger.info("norm: %.5e %.5e", norm, norm_exact)
assert abs(norm - norm_exact) < 1.0e-14
# }}}
# {{{ vector
sym_w = sym.make_sym_array("w", dim)
norm = bind(discr, sym.norm(p, sym_w))(actx, w=w)
norm_exact = np.sqrt(np.sum(w**2)) if p == 2 else np.max(w)
logger.info("norm: %.5e %.5e", norm, norm_exact)
assert abs(norm - norm_exact) < 1.0e-14
def test_surface_mass_operator_inverse(actx_factory, name):
actx = actx_factory()
# {{{ cases
if name == "2-1-ellipse":
from mesh_data import EllipseMeshBuilder
builder = EllipseMeshBuilder(radius=3.1, aspect_ratio=2.0)
elif name == "spheroid":
from mesh_data import SpheroidMeshBuilder
builder = SpheroidMeshBuilder()
else:
raise ValueError("unknown geometry name: %s" % name)
# }}}
# {{{ convergence
from pytools.convergence import EOCRecorder
eoc = EOCRecorder()
for resolution in builder.resolutions:
mesh = builder.get_mesh(resolution, builder.mesh_order)
discr = DiscretizationCollection(actx, mesh, order=builder.order)
volume_discr = discr.discr_from_dd(dof_desc.DD_VOLUME)
logger.info("ndofs: %d", volume_discr.ndofs)
logger.info("nelements: %d", volume_discr.mesh.nelements)
# {{{ compute inverse mass
dd = dof_desc.DD_VOLUME
sym_f = sym.cos(4.0 * sym.nodes(mesh.ambient_dim, dd)[0])
sym_op = sym.InverseMassOperator(dd, dd)(sym.MassOperator(dd, dd)(
sym.var("f")))
f = bind(discr, sym_f)(actx)
f_inv = bind(discr, sym_op)(actx, f=f)
inv_error = bind(
discr,
sym.norm(2,
sym.var("x") - sym.var("y")) / sym.norm(2, sym.var("y")))(
actx, x=f_inv, y=f)
# }}}
h_max = bind(
discr,
sym.h_max_from_volume(discr.ambient_dim, dim=discr.dim,
dd=dd))(actx)
eoc.add_data_point(h_max, inv_error)
# }}}
logger.info("inverse mass error\n%s", str(eoc))
# NOTE: both cases give 1.0e-16-ish at the moment, but just to be on the
# safe side, choose a slightly larger tolerance
assert eoc.max_error() < 1.0e-14
def test_operator_compiler_overwrite(actx_factory):
"""Tests that the same expression in ``eval_code`` and ``discr_code``
does not confuse the OperatorCompiler in grudge/symbolic/compiler.py.
"""
actx = actx_factory()
ambient_dim = 2
target_order = 4
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(a=(-0.5, ) * ambient_dim,
b=(0.5, ) * ambient_dim,
n=(8, ) * ambient_dim,
order=1)
discr = DiscretizationCollection(actx, mesh, order=target_order)
# {{{ test
sym_u = sym.nodes(ambient_dim)
sym_div_u = sum(d(u) for d, u in zip(sym.nabla(ambient_dim), sym_u))
div_u = bind(discr, sym_div_u)(actx)
error = bind(discr, sym.norm(2, sym.var("x")))(actx, x=div_u - discr.dim)
logger.info("error: %.5e", error)
def test_bessel(ctx_factory):
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
dims = 2
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(a=(0.1, ) * dims,
b=(1.0, ) * dims,
n=(8, ) * dims)
discr = DGDiscretizationWithBoundaries(actx, mesh, order=3)
nodes = sym.nodes(dims)
r = sym.cse(sym.sqrt(nodes[0]**2 + nodes[1]**2))
# https://dlmf.nist.gov/10.6.1
n = 3
bessel_zero = (sym.bessel_j(n + 1, r) + sym.bessel_j(n - 1, r) -
2 * n / r * sym.bessel_j(n, r))
z = bind(discr, sym.norm(2, bessel_zero))(actx)
assert z < 1e-15
def test_function_symbol_array(ctx_factory, array_type):
ctx = ctx_factory()
queue = cl.CommandQueue(ctx)
actx = PyOpenCLArrayContext(queue)
from meshmode.mesh.generation import generate_regular_rect_mesh
dim = 2
mesh = generate_regular_rect_mesh(a=(-0.5, ) * dim,
b=(0.5, ) * dim,
n=(8, ) * dim,
order=4)
discr = DGDiscretizationWithBoundaries(actx, mesh, order=4)
volume_discr = discr.discr_from_dd(sym.DD_VOLUME)
ndofs = sum(grp.ndofs for grp in volume_discr.groups)
import pyopencl.clrandom # noqa: F401
if array_type == "scalar":
sym_x = sym.var("x")
x = unflatten(actx, volume_discr,
cl.clrandom.rand(queue, ndofs, dtype=np.float))
elif array_type == "vector":
sym_x = sym.make_sym_array("x", dim)
x = make_obj_array([
unflatten(actx, volume_discr,
cl.clrandom.rand(queue, ndofs, dtype=np.float))
for _ in range(dim)
])
else:
raise ValueError("unknown array type")
norm = bind(discr, sym.norm(2, sym_x))(x=x)
assert isinstance(norm, float)
def test_incorrect_assignment_aggregation(actx_factory, ambient_dim):
"""Tests that the greedy assignemnt aggregation code works on a non-trivial
expression (on which it didn't work at the time of writing).
"""
actx = actx_factory()
target_order = 4
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(a=(-0.5, ) * ambient_dim,
b=(0.5, ) * ambient_dim,
n=(8, ) * ambient_dim,
order=1)
discr = DiscretizationCollection(actx, mesh, order=target_order)
# {{{ test with a relative norm
from grudge.dof_desc import DD_VOLUME
dd = DD_VOLUME
sym_x = sym.make_sym_array("y", ambient_dim, dd=dd)
sym_y = sym.make_sym_array("y", ambient_dim, dd=dd)
sym_norm_y = sym.norm(2, sym_y, dd=dd)
sym_norm_d = sym.norm(2, sym_x - sym_y, dd=dd)
sym_op = sym_norm_d / sym_norm_y
logger.info("%s", sym.pretty(sym_op))
# FIXME: this shouldn't raise a RuntimeError
with pytest.raises(RuntimeError):
bind(discr, sym_op)(actx, x=1.0, y=discr.discr_from_dd(dd).nodes())
# }}}
# {{{ test with repeated mass inverses
sym_minv_y = sym.cse(sym.InverseMassOperator()(sym_y), "minv_y")
sym_u = make_obj_array([0.5 * sym.Ones(dd), 0.0, 0.0])[:ambient_dim]
sym_div_u = sum(d(u) for d, u in zip(sym.nabla(ambient_dim), sym_u))
sym_op = sym.MassOperator(dd)(sym_u) \
+ sym.MassOperator(dd)(sym_minv_y * sym_div_u)
logger.info("%s", sym.pretty(sym_op))
# FIXME: this shouldn't raise a RuntimeError either
bind(discr, sym_op)(actx, y=discr.discr_from_dd(dd).nodes())
def test_stepper_equivalence(ctx_factory, order=4):
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(
queue,
allocator=cl_tools.MemoryPool(cl_tools.ImmediateAllocator(queue))
)
dims = 2
sym_operator, discr = get_wave_op_with_discr(
actx, dims=dims, order=order)
#sym_operator_direct, discr = get_wave_op_with_discr_direct(
# actx, dims=dims, order=order)
if dims == 2:
dt = 0.04
elif dims == 3:
dt = 0.02
ic = flat_obj_array(discr.zeros(actx),
[discr.zeros(actx) for i in range(discr.dim)])
bound_op = bind(discr, sym_operator)
stepper = RK4TimeStepper(
discr, "w", bound_op, 1 + discr.dim, get_wave_component)
fused_stepper = FusedRK4TimeStepper(
discr, "w", sym_operator, 1 + discr.dim,
get_wave_component)
t_start = 0
t_end = 0.5
nsteps = int(np.ceil((t_end + 1e-9) / dt))
print("dt=%g nsteps=%d" % (dt, nsteps))
step = 0
norm = bind(discr, sym.norm(2, sym.var("u_ref") - sym.var("u")))
fused_steps = fused_stepper.run(ic, t_start, dt, t_end)
for t_ref, (u_ref, _v_ref) in stepper.run(ic, t_start, dt, t_end):
step += 1
logger.debug("step %d/%d", step, nsteps)
t, (u, v) = next(fused_steps)
assert t == t_ref, step
assert norm(u=u, u_ref=u_ref) <= 1e-13, step
def test_stepper_equivalence(ctx_factory, order=4):
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
dims = 2
sym_operator, _ = get_strong_wave_op_with_discr(cl_ctx,
dims=dims,
order=order)
sym_operator_direct, discr = get_strong_wave_op_with_discr_direct(
cl_ctx, dims=dims, order=order)
if dims == 2:
dt = 0.04
elif dims == 3:
dt = 0.02
from pytools.obj_array import join_fields
ic = join_fields(discr.zeros(queue),
[discr.zeros(queue) for i in range(discr.dim)])
bound_op = bind(discr, sym_operator)
stepper = RK4TimeStepper(queue, discr, "w", bound_op, 1 + discr.dim,
get_strong_wave_component)
fused_stepper = FusedRK4TimeStepper(queue, discr, "w", sym_operator_direct,
1 + discr.dim,
get_strong_wave_component)
t_start = 0
t_end = 0.5
nsteps = int(np.ceil((t_end + 1e-9) / dt))
print("dt=%g nsteps=%d" % (dt, nsteps))
step = 0
norm = bind(discr, sym.norm(2, sym.var("u_ref") - sym.var("u")))
fused_steps = fused_stepper.run(ic, t_start, dt, t_end)
for t_ref, (u_ref, v_ref) in stepper.run(ic, t_start, dt, t_end):
step += 1
logger.debug("step %d/%d", step, nsteps)
t, (u, v) = next(fused_steps)
assert t == t_ref, step
assert norm(queue, u=u, u_ref=u_ref) <= 1e-13, step
def conv_test(descr, use_quad):
logger.info("-" * 75)
logger.info(descr)
logger.info("-" * 75)
eoc_rec = EOCRecorder()
ns = [20, 25]
for n in ns:
mesh = mgen.generate_regular_rect_mesh(a=(-0.5, ) * dims,
b=(0.5, ) * dims,
nelements_per_axis=(n, ) *
dims,
order=order)
if use_quad:
discr_tag_to_group_factory = {
"product": QuadratureSimplexGroupFactory(order=4 * order)
}
else:
discr_tag_to_group_factory = {"product": None}
discr = DiscretizationCollection(
actx,
mesh,
order=order,
discr_tag_to_group_factory=discr_tag_to_group_factory)
bound_op = bind(discr, op.sym_operator())
fields = bind(discr, gaussian_mode())(actx, t=0)
norm = bind(discr, sym.norm(2, sym.var("u")))
esc = bound_op(u=fields)
total_error = norm(u=esc)
eoc_rec.add_data_point(1.0 / n, total_error)
logger.info(
"\n%s",
eoc_rec.pretty_print(abscissa_label="h", error_label="L2 Error"))
return eoc_rec.order_estimate(), np.array(
[x[1] for x in eoc_rec.history])
def conv_test(descr, use_quad):
print("-" * 75)
print(descr)
print("-" * 75)
eoc_rec = EOCRecorder()
ns = [20, 25]
for n in ns:
mesh = generate_regular_rect_mesh(a=(-0.5, ) * dims,
b=(0.5, ) * dims,
n=(n, ) * dims,
order=order)
if use_quad:
quad_tag_to_group_factory = {
"product": QuadratureSimplexGroupFactory(order=4 * order)
}
else:
quad_tag_to_group_factory = {"product": None}
discr = DGDiscretizationWithBoundaries(
cl_ctx,
mesh,
order=order,
quad_tag_to_group_factory=quad_tag_to_group_factory)
bound_op = bind(discr, op.sym_operator())
fields = bind(discr, gaussian_mode())(queue, t=0)
norm = bind(discr, sym.norm(2, sym.var("u")))
esc = bound_op(queue, u=fields)
total_error = norm(queue, u=esc)
eoc_rec.add_data_point(1.0 / n, total_error)
print(
eoc_rec.pretty_print(abscissa_label="h", error_label="LInf Error"))
return eoc_rec.order_estimate(), np.array(
[x[1] for x in eoc_rec.history])
def test_bessel(actx_factory):
actx = actx_factory()
dims = 2
mesh = mgen.generate_regular_rect_mesh(a=(0.1, ) * dims,
b=(1.0, ) * dims,
nelements_per_axis=(8, ) * dims)
discr = DiscretizationCollection(actx, mesh, order=3)
nodes = sym.nodes(dims)
r = sym.cse(sym.sqrt(nodes[0]**2 + nodes[1]**2))
# https://dlmf.nist.gov/10.6.1
n = 3
bessel_zero = (sym.bessel_j(n + 1, r) + sym.bessel_j(n - 1, r) -
2 * n / r * sym.bessel_j(n, r))
z = bind(discr, sym.norm(2, bessel_zero))(actx)
assert z < 1e-15
def test_function_symbol_array(actx_factory, array_type):
"""Test if `FunctionSymbol` distributed properly over object arrays."""
actx = actx_factory()
dim = 2
mesh = mgen.generate_regular_rect_mesh(a=(-0.5, ) * dim,
b=(0.5, ) * dim,
nelements_per_axis=(8, ) * dim,
order=4)
discr = DiscretizationCollection(actx, mesh, order=4)
volume_discr = discr.discr_from_dd(dof_desc.DD_VOLUME)
if array_type == "scalar":
sym_x = sym.var("x")
x = thaw(actx, actx.np.cos(volume_discr.nodes()[0]))
elif array_type == "vector":
sym_x = sym.make_sym_array("x", dim)
x = thaw(actx, volume_discr.nodes())
else:
raise ValueError("unknown array type")
norm = bind(discr, sym.norm(2, sym_x))(x=x)
assert isinstance(norm, float)
def _norm(self, p):
return bind(self, sym.norm(p, sym.var("arg")), local_only=True)
def main(ctx_factory, dim=2, order=4, visualize=False):
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
# {{{ parameters
# domain [-d/2, d/2]^dim
d = 1.0
# number of points in each dimension
npoints = 20
# grid spacing
h = d / npoints
# cfl
dt_factor = 2.0
# final time
final_time = 1.0
# compute number of steps
dt = dt_factor * h / order**2
nsteps = int(final_time // dt) + 1
dt = final_time / nsteps + 1.0e-15
# velocity field
c = np.array([0.5] * dim)
norm_c = la.norm(c)
# flux
flux_type = "central"
# }}}
# {{{ discretization
from meshmode.mesh.generation import generate_box_mesh
mesh = generate_box_mesh(
[np.linspace(-d / 2, d / 2, npoints) for _ in range(dim)], order=order)
from grudge import DiscretizationCollection
discr = DiscretizationCollection(actx, mesh, order=order)
# }}}
# {{{ symbolic operators
def f(x):
return sym.sin(3 * x)
def u_analytic(x):
t = sym.var("t", dof_desc.DD_SCALAR)
return f(-np.dot(c, x) / norm_c + t * norm_c)
from grudge.models.advection import WeakAdvectionOperator
op = WeakAdvectionOperator(c,
inflow_u=u_analytic(sym.nodes(dim, BTAG_ALL)),
flux_type=flux_type)
bound_op = bind(discr, op.sym_operator())
u = bind(discr, u_analytic(sym.nodes(dim)))(actx, t=0)
def rhs(t, u):
return bound_op(t=t, u=u)
# }}}
# {{{ time stepping
from grudge.shortcuts import set_up_rk4
dt_stepper = set_up_rk4("u", dt, u, rhs)
plot = Plotter(actx, discr, order, visualize=visualize, ylim=[-1.1, 1.1])
norm = bind(discr, sym.norm(2, sym.var("u")))
step = 0
norm_u = 0.0
for event in dt_stepper.run(t_end=final_time):
if not isinstance(event, dt_stepper.StateComputed):
continue
if step % 10 == 0:
norm_u = norm(u=event.state_component)
plot(event, "fld-weak-%04d" % step)
step += 1
logger.info("[%04d] t = %.5f |u| = %.5e", step, event.t, norm_u)
def _norm(dcoll, p, dd):
return bind(dcoll,
sym.norm(p, sym.var("arg", dd=dd), dd=dd),
local_only=True)
def main(write_output=True, order=4):
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
dims = 2
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(a=(-0.5, ) * dims,
b=(0.5, ) * dims,
n=(16, ) * dims)
if mesh.dim == 2:
dt = 0.04
elif mesh.dim == 3:
dt = 0.02
print("%d elements" % mesh.nelements)
discr = DGDiscretizationWithBoundaries(cl_ctx, mesh, order=order)
source_center = np.array([0.1, 0.22, 0.33])[:mesh.dim]
source_width = 0.05
source_omega = 3
sym_x = sym.nodes(mesh.dim)
sym_source_center_dist = sym_x - source_center
sym_t = sym.ScalarVariable("t")
from grudge.models.wave import StrongWaveOperator
from meshmode.mesh import BTAG_ALL, BTAG_NONE
op = StrongWaveOperator(
-0.1,
discr.dim,
source_f=(
sym.sin(source_omega * sym_t) *
sym.exp(-np.dot(sym_source_center_dist, sym_source_center_dist) /
source_width**2)),
dirichlet_tag=BTAG_NONE,
neumann_tag=BTAG_NONE,
radiation_tag=BTAG_ALL,
flux_type="upwind")
queue = cl.CommandQueue(discr.cl_context)
from pytools.obj_array import join_fields
fields = join_fields(discr.zeros(queue),
[discr.zeros(queue) for i in range(discr.dim)])
# FIXME
#dt = op.estimate_rk4_timestep(discr, fields=fields)
op.check_bc_coverage(mesh)
# print(sym.pretty(op.sym_operator()))
bound_op = bind(discr, op.sym_operator())
def rhs(t, w):
return bound_op(queue, t=t, w=w)
dt_stepper = set_up_rk4("w", dt, fields, rhs)
final_t = 10
nsteps = int(final_t / dt)
print("dt=%g nsteps=%d" % (dt, nsteps))
from grudge.shortcuts import make_visualizer
vis = make_visualizer(discr, vis_order=order)
step = 0
norm = bind(discr, sym.norm(2, sym.var("u")))
from time import time
t_last_step = time()
for event in dt_stepper.run(t_end=final_t):
if isinstance(event, dt_stepper.StateComputed):
assert event.component_id == "w"
step += 1
print(step, event.t, norm(queue, u=event.state_component[0]),
time() - t_last_step)
if step % 10 == 0:
vis.write_vtk_file("fld-wave-min-%04d.vtu" % step, [
("u", event.state_component[0]),
("v", event.state_component[1:]),
])
t_last_step = time()
def test_convergence_maxwell(ctx_factory, order):
"""Test whether 3D Maxwell's actually converges"""
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
from pytools.convergence import EOCRecorder
eoc_rec = EOCRecorder()
dims = 3
ns = [4, 6, 8]
for n in ns:
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(a=(0.0, ) * dims,
b=(1.0, ) * dims,
n=(n, ) * dims)
discr = DGDiscretizationWithBoundaries(actx, mesh, order=order)
epsilon = 1
mu = 1
from grudge.models.em import get_rectangular_cavity_mode
sym_mode = get_rectangular_cavity_mode(1, (1, 2, 2))
analytic_sol = bind(discr, sym_mode)
fields = analytic_sol(actx, t=0, epsilon=epsilon, mu=mu)
from grudge.models.em import MaxwellOperator
op = MaxwellOperator(epsilon, mu, flux_type=0.5, dimensions=dims)
op.check_bc_coverage(mesh)
bound_op = bind(discr, op.sym_operator())
def rhs(t, w):
return bound_op(t=t, w=w)
dt = 0.002
final_t = dt * 5
nsteps = int(final_t / dt)
from grudge.shortcuts import set_up_rk4
dt_stepper = set_up_rk4("w", dt, fields, rhs)
logger.info("dt %.5e nsteps %5d", dt, nsteps)
norm = bind(discr, sym.norm(2, sym.var("u")))
step = 0
for event in dt_stepper.run(t_end=final_t):
if isinstance(event, dt_stepper.StateComputed):
assert event.component_id == "w"
esc = event.state_component
step += 1
logger.debug("[%04d] t = %.5e", step, event.t)
sol = analytic_sol(actx, mu=mu, epsilon=epsilon, t=step * dt)
vals = [norm(u=(esc[i] - sol[i])) / norm(u=sol[i])
for i in range(5)] # noqa E501
total_error = sum(vals)
eoc_rec.add_data_point(1.0 / n, total_error)
logger.info(
"\n%s", eoc_rec.pretty_print(abscissa_label="h",
error_label="L2 Error"))
assert eoc_rec.order_estimate() > order
def test_convergence_advec(ctx_factory,
mesh_name,
mesh_pars,
op_type,
flux_type,
order,
visualize=False):
"""Test whether 2D advection actually converges"""
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
from pytools.convergence import EOCRecorder
eoc_rec = EOCRecorder()
for mesh_par in mesh_pars:
if mesh_name == "segment":
from meshmode.mesh.generation import generate_box_mesh
mesh = generate_box_mesh([np.linspace(-1.0, 1.0, mesh_par)],
order=order)
dim = 1
dt_factor = 1.0
elif mesh_name == "disk":
pytest.importorskip("meshpy")
from meshpy.geometry import make_circle, GeometryBuilder
from meshpy.triangle import MeshInfo, build
geob = GeometryBuilder()
geob.add_geometry(*make_circle(1))
mesh_info = MeshInfo()
geob.set(mesh_info)
mesh_info = build(mesh_info, max_volume=mesh_par)
from meshmode.mesh.io import from_meshpy
mesh = from_meshpy(mesh_info, order=1)
dim = 2
dt_factor = 4
elif mesh_name.startswith("rect"):
dim = int(mesh_name[4:])
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(a=(-0.5, ) * dim,
b=(0.5, ) * dim,
n=(mesh_par, ) * dim,
order=4)
if dim == 2:
dt_factor = 4
elif dim == 3:
dt_factor = 2
else:
raise ValueError("dt_factor not known for %dd" % dim)
else:
raise ValueError("invalid mesh name: " + mesh_name)
v = np.array([0.27, 0.31, 0.1])[:dim]
norm_v = la.norm(v)
def f(x):
return sym.sin(10 * x)
def u_analytic(x):
return f(-v.dot(x) / norm_v + sym.var("t", sym.DD_SCALAR) * norm_v)
from grudge.models.advection import (StrongAdvectionOperator,
WeakAdvectionOperator)
discr = DGDiscretizationWithBoundaries(actx, mesh, order=order)
op_class = {
"strong": StrongAdvectionOperator,
"weak": WeakAdvectionOperator,
}[op_type]
op = op_class(v,
inflow_u=u_analytic(sym.nodes(dim, sym.BTAG_ALL)),
flux_type=flux_type)
bound_op = bind(discr, op.sym_operator())
u = bind(discr, u_analytic(sym.nodes(dim)))(actx, t=0)
def rhs(t, u):
return bound_op(t=t, u=u)
if dim == 3:
final_time = 0.1
else:
final_time = 0.2
h_max = bind(discr, sym.h_max_from_volume(discr.ambient_dim))(actx)
dt = dt_factor * h_max / order**2
nsteps = (final_time // dt) + 1
dt = final_time / nsteps + 1e-15
from grudge.shortcuts import set_up_rk4
dt_stepper = set_up_rk4("u", dt, u, rhs)
last_u = None
from grudge.shortcuts import make_visualizer
vis = make_visualizer(discr, vis_order=order)
step = 0
for event in dt_stepper.run(t_end=final_time):
if isinstance(event, dt_stepper.StateComputed):
step += 1
logger.debug("[%04d] t = %.5f", step, event.t)
last_t = event.t
last_u = event.state_component
if visualize:
vis.write_vtk_file("fld-%s-%04d.vtu" % (mesh_par, step),
[("u", event.state_component)])
error_l2 = bind(discr,
sym.norm(2,
sym.var("u") - u_analytic(sym.nodes(dim))))(
t=last_t, u=last_u)
logger.info("h_max %.5e error %.5e", h_max, error_l2)
eoc_rec.add_data_point(h_max, error_l2)
logger.info(
"\n%s", eoc_rec.pretty_print(abscissa_label="h",
error_label="L2 Error"))
assert eoc_rec.order_estimate() > order
def mpi_communication_entrypoint():
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
from mpi4py import MPI
comm = MPI.COMM_WORLD
i_local_rank = comm.Get_rank()
num_parts = comm.Get_size()
from meshmode.distributed import MPIMeshDistributor, get_partition_by_pymetis
mesh_dist = MPIMeshDistributor(comm)
dim = 2
dt = 0.04
order = 4
if mesh_dist.is_mananger_rank():
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(a=(-0.5, ) * dim,
b=(0.5, ) * dim,
n=(16, ) * dim)
part_per_element = get_partition_by_pymetis(mesh, num_parts)
local_mesh = mesh_dist.send_mesh_parts(mesh, part_per_element,
num_parts)
else:
local_mesh = mesh_dist.receive_mesh_part()
vol_discr = DGDiscretizationWithBoundaries(cl_ctx,
local_mesh,
order=order,
mpi_communicator=comm)
source_center = np.array([0.1, 0.22, 0.33])[:local_mesh.dim]
source_width = 0.05
source_omega = 3
sym_x = sym.nodes(local_mesh.dim)
sym_source_center_dist = sym_x - source_center
sym_t = sym.ScalarVariable("t")
from grudge.models.wave import StrongWaveOperator
from meshmode.mesh import BTAG_ALL, BTAG_NONE
op = StrongWaveOperator(
-0.1,
vol_discr.dim,
source_f=(
sym.sin(source_omega * sym_t) *
sym.exp(-np.dot(sym_source_center_dist, sym_source_center_dist) /
source_width**2)),
dirichlet_tag=BTAG_NONE,
neumann_tag=BTAG_NONE,
radiation_tag=BTAG_ALL,
flux_type="upwind")
from pytools.obj_array import join_fields
fields = join_fields(
vol_discr.zeros(queue),
[vol_discr.zeros(queue) for i in range(vol_discr.dim)])
# FIXME
# dt = op.estimate_rk4_timestep(vol_discr, fields=fields)
# FIXME: Should meshmode consider BTAG_PARTITION to be a boundary?
# Fails because: "found faces without boundary conditions"
# op.check_bc_coverage(local_mesh)
from pytools.log import LogManager, \
add_general_quantities, \
add_run_info, \
IntervalTimer, EventCounter
log_filename = None
# NOTE: LogManager hangs when using a file on a shared directory.
# log_filename = 'grudge_log.dat'
logmgr = LogManager(log_filename, "w", comm)
add_run_info(logmgr)
add_general_quantities(logmgr)
log_quantities =\
{"rank_data_swap_timer": IntervalTimer("rank_data_swap_timer",
"Time spent evaluating RankDataSwapAssign"),
"rank_data_swap_counter": EventCounter("rank_data_swap_counter",
"Number of RankDataSwapAssign instructions evaluated"),
"exec_timer": IntervalTimer("exec_timer",
"Total time spent executing instructions"),
"insn_eval_timer": IntervalTimer("insn_eval_timer",
"Time spend evaluating instructions"),
"future_eval_timer": IntervalTimer("future_eval_timer",
"Time spent evaluating futures"),
"busy_wait_timer": IntervalTimer("busy_wait_timer",
"Time wasted doing busy wait")}
for quantity in log_quantities.values():
logmgr.add_quantity(quantity)
# print(sym.pretty(op.sym_operator()))
bound_op = bind(vol_discr, op.sym_operator())
# print(bound_op)
# 1/0
def rhs(t, w):
val, rhs.profile_data = bound_op(queue,
profile_data=rhs.profile_data,
log_quantities=log_quantities,
t=t,
w=w)
return val
rhs.profile_data = {}
dt_stepper = set_up_rk4("w", dt, fields, rhs)
final_t = 4
nsteps = int(final_t / dt)
print("rank=%d dt=%g nsteps=%d" % (i_local_rank, dt, nsteps))
# from grudge.shortcuts import make_visualizer
# vis = make_visualizer(vol_discr, vis_order=order)
step = 0
norm = bind(vol_discr, sym.norm(2, sym.var("u")))
from time import time
t_last_step = time()
logmgr.tick_before()
for event in dt_stepper.run(t_end=final_t):
if isinstance(event, dt_stepper.StateComputed):
assert event.component_id == "w"
step += 1
print(step, event.t, norm(queue, u=event.state_component[0]),
time() - t_last_step)
# if step % 10 == 0:
# vis.write_vtk_file("rank%d-fld-%04d.vtu" % (i_local_rank, step),
# [("u", event.state_component[0]),
# ("v", event.state_component[1:])])
t_last_step = time()
logmgr.tick_after()
logmgr.tick_before()
logmgr.tick_after()
def print_profile_data(data):
print("""execute() for rank %d:
\tInstruction Evaluation: %f%%
\tFuture Evaluation: %f%%
\tBusy Wait: %f%%
\tTotal: %f seconds""" %
(i_local_rank, data['insn_eval_time'] / data['total_time'] * 100,
data['future_eval_time'] / data['total_time'] * 100,
data['busy_wait_time'] / data['total_time'] * 100,
data['total_time']))
print_profile_data(rhs.profile_data)
logmgr.close()
logger.debug("Rank %d exiting", i_local_rank)
def main(write_output=True, order=4):
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
dims = 2
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(
a=(-0.5,)*dims,
b=(0.5,)*dims,
nelements_per_axis=(20,)*dims)
discr = DiscretizationCollection(actx, mesh, order=order)
source_center = np.array([0.1, 0.22, 0.33])[:mesh.dim]
source_width = 0.05
source_omega = 3
sym_x = sym.nodes(mesh.dim)
sym_source_center_dist = sym_x - source_center
sym_t = sym.ScalarVariable("t")
c = sym.If(sym.Comparison(
np.dot(sym_x, sym_x), "<", 0.15),
np.float32(0.1), np.float32(0.2))
from grudge.models.wave import VariableCoefficientWeakWaveOperator
from meshmode.mesh import BTAG_ALL, BTAG_NONE
op = VariableCoefficientWeakWaveOperator(c,
discr.dim,
source_f=(
sym.sin(source_omega*sym_t)
* sym.exp(
-np.dot(sym_source_center_dist, sym_source_center_dist)
/ source_width**2)),
dirichlet_tag=BTAG_NONE,
neumann_tag=BTAG_NONE,
radiation_tag=BTAG_ALL,
flux_type="upwind")
from pytools.obj_array import flat_obj_array
fields = flat_obj_array(discr.zeros(actx),
[discr.zeros(actx) for i in range(discr.dim)])
op.check_bc_coverage(mesh)
c_eval = bind(discr, c)(actx)
bound_op = bind(discr, op.sym_operator())
def rhs(t, w):
return bound_op(t=t, w=w)
if mesh.dim == 2:
dt = 0.04 * 0.3
elif mesh.dim == 3:
dt = 0.02 * 0.1
dt_stepper = set_up_rk4("w", dt, fields, rhs)
final_t = 1
nsteps = int(final_t/dt)
print("dt=%g nsteps=%d" % (dt, nsteps))
from grudge.shortcuts import make_visualizer
vis = make_visualizer(discr)
step = 0
norm = bind(discr, sym.norm(2, sym.var("u")))
from time import time
t_last_step = time()
for event in dt_stepper.run(t_end=final_t):
if isinstance(event, dt_stepper.StateComputed):
assert event.component_id == "w"
step += 1
print(step, event.t, norm(u=event.state_component[0]),
time()-t_last_step)
if step % 10 == 0:
vis.write_vtk_file("fld-var-propogation-speed-%04d.vtu" % step,
[
("u", event.state_component[0]),
("v", event.state_component[1:]),
("c", c_eval),
])
t_last_step = time()
def main(write_output=True, order=4):
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
comm = MPI.COMM_WORLD
num_parts = comm.Get_size()
from meshmode.distributed import MPIMeshDistributor, get_partition_by_pymetis
mesh_dist = MPIMeshDistributor(comm)
if mesh_dist.is_mananger_rank():
dims = 2
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(a=(-0.5, ) * dims,
b=(0.5, ) * dims,
n=(16, ) * dims)
print("%d elements" % mesh.nelements)
part_per_element = get_partition_by_pymetis(mesh, num_parts)
local_mesh = mesh_dist.send_mesh_parts(mesh, part_per_element,
num_parts)
del mesh
else:
local_mesh = mesh_dist.receive_mesh_part()
discr = DGDiscretizationWithBoundaries(actx,
local_mesh,
order=order,
mpi_communicator=comm)
if local_mesh.dim == 2:
dt = 0.04
elif local_mesh.dim == 3:
dt = 0.02
source_center = np.array([0.1, 0.22, 0.33])[:local_mesh.dim]
source_width = 0.05
source_omega = 3
sym_x = sym.nodes(local_mesh.dim)
sym_source_center_dist = sym_x - source_center
sym_t = sym.ScalarVariable("t")
from grudge.models.wave import StrongWaveOperator
from meshmode.mesh import BTAG_ALL, BTAG_NONE
op = StrongWaveOperator(
-0.1,
discr.dim,
source_f=(
sym.sin(source_omega * sym_t) *
sym.exp(-np.dot(sym_source_center_dist, sym_source_center_dist) /
source_width**2)),
dirichlet_tag=BTAG_NONE,
neumann_tag=BTAG_NONE,
radiation_tag=BTAG_ALL,
flux_type="upwind")
from pytools.obj_array import flat_obj_array
fields = flat_obj_array(discr.zeros(actx),
[discr.zeros(actx) for i in range(discr.dim)])
# FIXME
#dt = op.estimate_rk4_timestep(discr, fields=fields)
op.check_bc_coverage(local_mesh)
# print(sym.pretty(op.sym_operator()))
bound_op = bind(discr, op.sym_operator())
def rhs(t, w):
return bound_op(t=t, w=w)
dt_stepper = set_up_rk4("w", dt, fields, rhs)
final_t = 10
nsteps = int(final_t / dt)
print("dt=%g nsteps=%d" % (dt, nsteps))
from grudge.shortcuts import make_visualizer
vis = make_visualizer(discr, vis_order=order)
step = 0
norm = bind(discr, sym.norm(2, sym.var("u")))
from time import time
t_last_step = time()
rank = comm.Get_rank()
for event in dt_stepper.run(t_end=final_t):
if isinstance(event, dt_stepper.StateComputed):
assert event.component_id == "w"
step += 1
print(step, event.t, norm(u=event.state_component[0]),
time() - t_last_step)
if step % 10 == 0:
vis.write_vtk_file(
"fld-wave-min-mpi-%03d-%04d.vtu" % (
rank,
step,
), [
("u", event.state_component[0]),
("v", event.state_component[1:]),
])
t_last_step = time()
def _norm(self, p, dd):
return bind(self,
sym.norm(p, sym.var("arg", dd=dd), dd=dd),
local_only=True)
def _eval_error(x):
return bind(discr, sym.norm(np.inf, sym.var("x", dd=df), dd=df))(actx,
x=x)
def test_surface_divergence_theorem(actx_factory, mesh_name, visualize=False):
r"""Check the surface divergence theorem.
.. math::
\int_Sigma \phi \nabla_i f_i =
\int_\Sigma \nabla_i \phi f_i +
\int_\Sigma \kappa \phi f_i n_i +
\int_{\partial \Sigma} \phi f_i m_i
where :math:`n_i` is the surface normal and :class:`m_i` is the
face normal (which should be orthogonal to both the surface normal
and the face tangent).
"""
actx = actx_factory()
# {{{ cases
if mesh_name == "2-1-ellipse":
from mesh_data import EllipseMeshBuilder
builder = EllipseMeshBuilder(radius=3.1, aspect_ratio=2.0)
elif mesh_name == "spheroid":
from mesh_data import SpheroidMeshBuilder
builder = SpheroidMeshBuilder()
elif mesh_name == "circle":
from mesh_data import EllipseMeshBuilder
builder = EllipseMeshBuilder(radius=1.0, aspect_ratio=1.0)
elif mesh_name == "starfish":
from mesh_data import StarfishMeshBuilder
builder = StarfishMeshBuilder()
elif mesh_name == "sphere":
from mesh_data import SphereMeshBuilder
builder = SphereMeshBuilder(radius=1.0, mesh_order=16)
else:
raise ValueError("unknown mesh name: %s" % mesh_name)
# }}}
# {{{ convergene
def f(x):
return flat_obj_array(
sym.sin(3 * x[1]) + sym.cos(3 * x[0]) + 1.0,
sym.sin(2 * x[0]) + sym.cos(x[1]),
3.0 * sym.cos(x[0] / 2) + sym.cos(x[1]),
)[:ambient_dim]
from pytools.convergence import EOCRecorder
eoc_global = EOCRecorder()
eoc_local = EOCRecorder()
theta = np.pi / 3.33
ambient_dim = builder.ambient_dim
if ambient_dim == 2:
mesh_rotation = np.array([
[np.cos(theta), -np.sin(theta)],
[np.sin(theta), np.cos(theta)],
])
else:
mesh_rotation = np.array([
[1.0, 0.0, 0.0],
[0.0, np.cos(theta), -np.sin(theta)],
[0.0, np.sin(theta), np.cos(theta)],
])
mesh_offset = np.array([0.33, -0.21, 0.0])[:ambient_dim]
for i, resolution in enumerate(builder.resolutions):
from meshmode.mesh.processing import affine_map
from meshmode.discretization.connection import FACE_RESTR_ALL
mesh = builder.get_mesh(resolution, builder.mesh_order)
mesh = affine_map(mesh, A=mesh_rotation, b=mesh_offset)
from meshmode.discretization.poly_element import \
QuadratureSimplexGroupFactory
discr = DiscretizationCollection(actx,
mesh,
order=builder.order,
discr_tag_to_group_factory={
"product":
QuadratureSimplexGroupFactory(
2 * builder.order)
})
volume = discr.discr_from_dd(dof_desc.DD_VOLUME)
logger.info("ndofs: %d", volume.ndofs)
logger.info("nelements: %d", volume.mesh.nelements)
dd = dof_desc.DD_VOLUME
dq = dd.with_discr_tag("product")
df = dof_desc.as_dofdesc(FACE_RESTR_ALL)
ambient_dim = discr.ambient_dim
dim = discr.dim
# variables
sym_f = f(sym.nodes(ambient_dim, dd=dd))
sym_f_quad = f(sym.nodes(ambient_dim, dd=dq))
sym_kappa = sym.summed_curvature(ambient_dim, dim=dim, dd=dq)
sym_normal = sym.surface_normal(ambient_dim, dim=dim,
dd=dq).as_vector()
sym_face_normal = sym.normal(df, ambient_dim, dim=dim - 1)
sym_face_f = sym.project(dd, df)(sym_f)
# operators
sym_stiff = sum(
sym.StiffnessOperator(d)(f) for d, f in enumerate(sym_f))
sym_stiff_t = sum(
sym.StiffnessTOperator(d)(f) for d, f in enumerate(sym_f))
sym_k = sym.MassOperator(dq,
dd)(sym_kappa * sym_f_quad.dot(sym_normal))
sym_flux = sym.FaceMassOperator()(sym_face_f.dot(sym_face_normal))
# sum everything up
sym_op_global = sym.NodalSum(dd)(sym_stiff - (sym_stiff_t + sym_k))
sym_op_local = sym.ElementwiseSumOperator(dd)(sym_stiff -
(sym_stiff_t + sym_k +
sym_flux))
# evaluate
op_global = bind(discr, sym_op_global)(actx)
op_local = bind(discr, sym_op_local)(actx)
err_global = abs(op_global)
err_local = bind(discr, sym.norm(np.inf, sym.var("x")))(actx,
x=op_local)
logger.info("errors: global %.5e local %.5e", err_global, err_local)
# compute max element size
h_max = bind(
discr,
sym.h_max_from_volume(discr.ambient_dim, dim=discr.dim,
dd=dd))(actx)
eoc_global.add_data_point(h_max, err_global)
eoc_local.add_data_point(h_max, err_local)
if visualize:
from grudge.shortcuts import make_visualizer
vis = make_visualizer(discr, vis_order=builder.order)
filename = f"surface_divergence_theorem_{mesh_name}_{i:04d}.vtu"
vis.write_vtk_file(filename, [("r", actx.np.log10(op_local))],
overwrite=True)
# }}}
order = min(builder.order, builder.mesh_order) - 0.5
logger.info("\n%s", str(eoc_global))
logger.info("\n%s", str(eoc_local))
assert eoc_global.max_error() < 1.0e-12 \
or eoc_global.order_estimate() > order - 0.5
assert eoc_local.max_error() < 1.0e-12 \
or eoc_local.order_estimate() > order - 0.5
def main(dims, write_output=True, order=4):
cl_ctx = cl.create_some_context()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(a=(0.0, ) * dims,
b=(1.0, ) * dims,
nelements_per_axis=(4, ) * dims)
discr = DiscretizationCollection(actx, mesh, order=order)
if 0:
epsilon0 = 8.8541878176e-12 # C**2 / (N m**2)
mu0 = 4 * np.pi * 1e-7 # N/A**2.
epsilon = 1 * epsilon0
mu = 1 * mu0
else:
epsilon = 1
mu = 1
from grudge.models.em import MaxwellOperator
op = MaxwellOperator(epsilon, mu, flux_type=0.5, dimensions=dims)
if dims == 3:
sym_mode = get_rectangular_cavity_mode(1, (1, 2, 2))
fields = bind(discr, sym_mode)(actx, t=0, epsilon=epsilon, mu=mu)
else:
sym_mode = get_rectangular_cavity_mode(1, (2, 3))
fields = bind(discr, sym_mode)(actx, t=0)
# FIXME
#dt = op.estimate_rk4_timestep(discr, fields=fields)
op.check_bc_coverage(mesh)
# print(sym.pretty(op.sym_operator()))
bound_op = bind(discr, op.sym_operator())
def rhs(t, w):
return bound_op(t=t, w=w)
if mesh.dim == 2:
dt = 0.004
elif mesh.dim == 3:
dt = 0.002
dt_stepper = set_up_rk4("w", dt, fields, rhs)
final_t = dt * STEPS
nsteps = int(final_t / dt)
print("dt=%g nsteps=%d" % (dt, nsteps))
from grudge.shortcuts import make_visualizer
vis = make_visualizer(discr)
step = 0
norm = bind(discr, sym.norm(2, sym.var("u")))
from time import time
t_last_step = time()
e, h = op.split_eh(fields)
if 1:
vis.write_vtk_file("fld-cavities-%04d.vtu" % step, [
("e", e),
("h", h),
])
for event in dt_stepper.run(t_end=final_t):
if isinstance(event, dt_stepper.StateComputed):
assert event.component_id == "w"
step += 1
print(step, event.t, norm(u=e[0]), norm(u=e[1]), norm(u=h[0]),
norm(u=h[1]),
time() - t_last_step)
if step % 10 == 0:
e, h = op.split_eh(event.state_component)
vis.write_vtk_file("fld-cavities-%04d.vtu" % step, [
("e", e),
("h", h),
])
t_last_step = time()
def main(ctx_factory, dim=2, order=4, product_tag=None, visualize=False):
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
# {{{ parameters
# sphere radius
radius = 1.0
# sphere resolution
resolution = 64 if dim == 2 else 1
# cfl
dt_factor = 2.0
# final time
final_time = np.pi
# velocity field
sym_x = sym.nodes(dim)
c = make_obj_array([-sym_x[1], sym_x[0], 0.0])[:dim]
# flux
flux_type = "lf"
# }}}
# {{{ discretization
if dim == 2:
from meshmode.mesh.generation import make_curve_mesh, ellipse
mesh = make_curve_mesh(lambda t: radius * ellipse(1.0, t),
np.linspace(0.0, 1.0, resolution + 1), order)
elif dim == 3:
from meshmode.mesh.generation import generate_icosphere
mesh = generate_icosphere(radius,
order=4 * order,
uniform_refinement_rounds=resolution)
else:
raise ValueError("unsupported dimension")
discr_tag_to_group_factory = {}
if product_tag == "none":
product_tag = None
else:
product_tag = dof_desc.DISCR_TAG_QUAD
from meshmode.discretization.poly_element import \
PolynomialWarpAndBlendGroupFactory, \
QuadratureSimplexGroupFactory
discr_tag_to_group_factory[dof_desc.DISCR_TAG_BASE] = \
PolynomialWarpAndBlendGroupFactory(order)
if product_tag:
discr_tag_to_group_factory[product_tag] = \
QuadratureSimplexGroupFactory(order=4*order)
from grudge import DiscretizationCollection
discr = DiscretizationCollection(
actx, mesh, discr_tag_to_group_factory=discr_tag_to_group_factory)
volume_discr = discr.discr_from_dd(dof_desc.DD_VOLUME)
logger.info("ndofs: %d", volume_discr.ndofs)
logger.info("nelements: %d", volume_discr.mesh.nelements)
# }}}
# {{{ symbolic operators
def f_initial_condition(x):
return x[0]
from grudge.models.advection import SurfaceAdvectionOperator
op = SurfaceAdvectionOperator(c, flux_type=flux_type, quad_tag=product_tag)
bound_op = bind(discr, op.sym_operator())
u0 = bind(discr, f_initial_condition(sym_x))(actx, t=0)
def rhs(t, u):
return bound_op(actx, t=t, u=u)
# check velocity is tangential
sym_normal = sym.surface_normal(dim, dim=dim - 1,
dd=dof_desc.DD_VOLUME).as_vector()
error = bind(discr, sym.norm(2, c.dot(sym_normal)))(actx)
logger.info("u_dot_n: %.5e", error)
# }}}
# {{{ time stepping
# compute time step
h_min = bind(discr, sym.h_max_from_volume(discr.ambient_dim,
dim=discr.dim))(actx)
dt = dt_factor * h_min / order**2
nsteps = int(final_time // dt) + 1
dt = final_time / nsteps + 1.0e-15
logger.info("dt: %.5e", dt)
logger.info("nsteps: %d", nsteps)
from grudge.shortcuts import set_up_rk4
dt_stepper = set_up_rk4("u", dt, u0, rhs)
plot = Plotter(actx, discr, order, visualize=visualize)
norm = bind(discr, sym.norm(2, sym.var("u")))
norm_u = norm(actx, u=u0)
step = 0
event = dt_stepper.StateComputed(0.0, 0, 0, u0)
plot(event, "fld-surface-%04d" % 0)
if visualize and dim == 3:
from grudge.shortcuts import make_visualizer
vis = make_visualizer(discr)
vis.write_vtk_file("fld-surface-velocity.vtu",
[("u", bind(discr, c)(actx)),
("n", bind(discr, sym_normal)(actx))],
overwrite=True)
df = dof_desc.DOFDesc(FACE_RESTR_INTERIOR)
face_discr = discr.connection_from_dds(dof_desc.DD_VOLUME, df).to_discr
face_normal = bind(
discr, sym.normal(df, face_discr.ambient_dim,
dim=face_discr.dim))(actx)
from meshmode.discretization.visualization import make_visualizer
vis = make_visualizer(actx, face_discr)
vis.write_vtk_file("fld-surface-face-normals.vtu",
[("n", face_normal)],
overwrite=True)
for event in dt_stepper.run(t_end=final_time, max_steps=nsteps + 1):
if not isinstance(event, dt_stepper.StateComputed):
continue
step += 1
if step % 10 == 0:
norm_u = norm(actx, u=event.state_component)
plot(event, "fld-surface-%04d" % step)
logger.info("[%04d] t = %.5f |u| = %.5e", step, event.t, norm_u)
plot(event, "fld-surface-%04d" % step)
def main(ctx_factory, dim=2, order=4, product_tag=None, visualize=False):
cl_ctx = ctx_factory()
queue = cl.CommandQueue(cl_ctx)
actx = PyOpenCLArrayContext(queue)
# {{{ parameters
# domain [0, d]^dim
d = 1.0
# number of points in each dimension
npoints = 25
# grid spacing
h = d / npoints
# cfl
dt_factor = 1.0
# finale time
final_time = 0.5
# time steps
dt = dt_factor * h / order**2
nsteps = int(final_time // dt) + 1
dt = final_time / nsteps + 1.0e-15
# flux
flux_type = "upwind"
# velocity field
sym_x = sym.nodes(dim)
if dim == 1:
c = sym_x
else:
# solid body rotation
c = flat_obj_array(np.pi * (d / 2 - sym_x[1]),
np.pi * (sym_x[0] - d / 2), 0)[:dim]
# }}}
# {{{ discretization
from meshmode.mesh.generation import generate_regular_rect_mesh
mesh = generate_regular_rect_mesh(a=(0, ) * dim,
b=(d, ) * dim,
npoints_per_axis=(npoints, ) * dim,
order=order)
from meshmode.discretization.poly_element import \
QuadratureSimplexGroupFactory
if product_tag:
discr_tag_to_group_factory = {
product_tag: QuadratureSimplexGroupFactory(order=4 * order)
}
else:
discr_tag_to_group_factory = {}
from grudge import DiscretizationCollection
discr = DiscretizationCollection(
actx,
mesh,
order=order,
discr_tag_to_group_factory=discr_tag_to_group_factory)
# }}}
# {{{ symbolic operators
# gaussian parameters
source_center = np.array([0.5, 0.75, 0.0])[:dim]
source_width = 0.05
dist_squared = np.dot(sym_x - source_center, sym_x - source_center)
def f_gaussian(x):
return sym.exp(-dist_squared / source_width**2)
def f_step(x):
return sym.If(sym.Comparison(dist_squared, "<", (4 * source_width)**2),
1, 0)
def u_bc(x):
return 0.0
from grudge.models.advection import VariableCoefficientAdvectionOperator
op = VariableCoefficientAdvectionOperator(c,
u_bc(sym.nodes(dim, BTAG_ALL)),
quad_tag=product_tag,
flux_type=flux_type)
bound_op = bind(discr, op.sym_operator())
u = bind(discr, f_gaussian(sym.nodes(dim)))(actx, t=0)
def rhs(t, u):
return bound_op(t=t, u=u)
# }}}
# {{{ time stepping
from grudge.shortcuts import set_up_rk4
dt_stepper = set_up_rk4("u", dt, u, rhs)
plot = Plotter(actx, discr, order, visualize=visualize, ylim=[-0.1, 1.1])
step = 0
norm = bind(discr, sym.norm(2, sym.var("u")))
for event in dt_stepper.run(t_end=final_time):
if not isinstance(event, dt_stepper.StateComputed):
continue
if step % 10 == 0:
norm_u = norm(u=event.state_component)
plot(event, "fld-var-velocity-%04d" % step)
step += 1
logger.info("[%04d] t = %.5f |u| = %.5e", step, event.t, norm_u)
