def test_2d_gauss_theorem(actx_factory):
"""Verify Gauss's theorem explicitly on a mesh"""
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)
from meshmode.mesh.io import from_meshpy
mesh = from_meshpy(mesh_info, order=1)
actx = actx_factory()
discr = DGDiscretizationWithBoundaries(actx, mesh, order=2)
def f(x):
return flat_obj_array(
sym.sin(3*x[0])+sym.cos(3*x[1]),
sym.sin(2*x[0])+sym.cos(x[1]))
gauss_err = bind(discr,
sym.integral((
sym.nabla(2) * f(sym.nodes(2))
).sum())
- # noqa: W504
sym.integral(
sym.project("vol", sym.BTAG_ALL)(f(sym.nodes(2)))
.dot(sym.normal(sym.BTAG_ALL, 2)),
dd=sym.BTAG_ALL)
)(actx)
assert abs(gauss_err) < 1e-13
def test_2d_gauss_theorem(actx_factory):
"""Verify Gauss's theorem explicitly on a mesh"""
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)
from meshmode.mesh.io import from_meshpy
from meshmode.mesh import BTAG_ALL
mesh = from_meshpy(mesh_info, order=1)
actx = actx_factory()
dcoll = DiscretizationCollection(actx, mesh, order=2)
volm_disc = dcoll.discr_from_dd(dof_desc.DD_VOLUME)
x_volm = thaw(volm_disc.nodes(), actx)
def f(x):
return flat_obj_array(
actx.np.sin(3 * x[0]) + actx.np.cos(3 * x[1]),
actx.np.sin(2 * x[0]) + actx.np.cos(x[1]))
f_volm = f(x_volm)
int_1 = op.integral(dcoll, "vol", op.local_div(dcoll, f_volm))
prj_f = op.project(dcoll, "vol", BTAG_ALL, f_volm)
normal = thaw(dcoll.normal(BTAG_ALL), actx)
int_2 = op.integral(dcoll, BTAG_ALL, prj_f.dot(normal))
assert abs(int_1 - int_2) < 1e-13
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 test_convergence_advec(actx_factory,
mesh_name,
mesh_pars,
op_type,
flux_type,
order,
visualize=False):
"""Test whether 2D advection actually converges"""
actx = actx_factory()
from pytools.convergence import EOCRecorder
eoc_rec = EOCRecorder()
for mesh_par in mesh_pars:
if mesh_name == "segment":
mesh = mgen.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[-1:])
mesh = mgen.generate_regular_rect_mesh(
a=(-0.5, ) * dim,
b=(0.5, ) * dim,
nelements_per_axis=(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)
elif mesh_name.startswith("warped"):
dim = int(mesh_name[-1:])
mesh = mgen.generate_warped_rect_mesh(dim,
order=order,
nelements_side=mesh_par)
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 actx.np.sin(10 * x)
def u_analytic(x, t=0):
return f(-v.dot(x) / norm_v + t * norm_v)
from grudge.models.advection import (StrongAdvectionOperator,
WeakAdvectionOperator)
from meshmode.mesh import BTAG_ALL
dcoll = DiscretizationCollection(actx, mesh, order=order)
op_class = {
"strong": StrongAdvectionOperator,
"weak": WeakAdvectionOperator
}[op_type]
adv_operator = op_class(dcoll,
v,
inflow_u=lambda t: u_analytic(
thaw(dcoll.nodes(dd=BTAG_ALL), actx), t=t),
flux_type=flux_type)
nodes = thaw(dcoll.nodes(), actx)
u = u_analytic(nodes, t=0)
def rhs(t, u):
return adv_operator.operator(t, u)
if dim == 3:
final_time = 0.1
else:
final_time = 0.2
from grudge.dt_utils import h_max_from_volume
h_max = h_max_from_volume(dcoll, dim=dcoll.ambient_dim)
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(dcoll)
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 = op.norm(dcoll, last_u - u_analytic(nodes, t=last_t), 2)
logger.info("h_max %.5e error %.5e", h_max, error_l2)
eoc_rec.add_data_point(h_max, actx.to_numpy(error_l2))
logger.info(
"\n%s", eoc_rec.pretty_print(abscissa_label="h",
error_label="L2 Error"))
if mesh_name.startswith("warped"):
# NOTE: curvilinear meshes are hard
assert eoc_rec.order_estimate() > order - 0.5
else:
assert eoc_rec.order_estimate() > order