def quadrature_rule(self):
dims = self.mesh_el_group.dim
if dims == 0:
return mp.ZeroDimensionalQuadrature()
elif dims == 1:
return mp.LegendreGaussQuadrature(self.order)
else:
return mp.VioreanuRokhlinSimplexQuadrature(self.order, dims)
def _quadrature_rule(self):
dims = self.mesh_el_group.dim
if dims == 0:
return mp.Quadrature(np.empty((0, 1)), np.empty((0, 1)))
elif dims == 1:
return mp.LegendreGaussQuadrature(self.order)
else:
return mp.VioreanuRokhlinSimplexQuadrature(self.order, dims)
def test_mesh_with_interior_unit_nodes(actx_factory, ambient_dim):
actx = actx_factory()
# NOTE: smaller orders or coarser meshes make the cases fail the
# node_vertex_consistency test; the default warp_and_blend_nodes have
# nodes at the vertices, so they pass for much smaller tolerances
order = 8
nelements = 32
n_minor = 2 * nelements
uniform_refinement_rounds = 4
import modepy as mp
if ambient_dim == 2:
unit_nodes = mp.LegendreGaussQuadrature(order,
force_dim_axis=True).nodes
mesh = mgen.make_curve_mesh(partial(mgen.ellipse, 2.0),
np.linspace(0.0, 1.0, nelements + 1),
order=order,
unit_nodes=unit_nodes)
elif ambient_dim == 3:
unit_nodes = mp.VioreanuRokhlinSimplexQuadrature(order, 2).nodes
mesh = mgen.generate_torus(4.0,
2.0,
n_major=2 * n_minor,
n_minor=n_minor,
order=order,
unit_nodes=unit_nodes)
mesh = mgen.generate_icosphere(
1.0,
uniform_refinement_rounds=uniform_refinement_rounds,
order=order,
unit_nodes=unit_nodes)
else:
raise ValueError(f"unsupported dimension: '{ambient_dim}'")
assert mesh.facial_adjacency_groups
assert mesh.nodal_adjacency
from meshmode.discretization import Discretization
from meshmode.discretization.poly_element import QuadratureSimplexGroupFactory
discr = Discretization(actx, mesh, QuadratureSimplexGroupFactory(order))
from meshmode.discretization.connection import make_face_restriction
conn = make_face_restriction(
actx,
discr,
group_factory=QuadratureSimplexGroupFactory(order),
boundary_tag=FACE_RESTR_ALL)
assert conn
def run(actx, *,
ambient_dim: int = 3,
resolution: int = None,
target_order: int = 4,
tmax: float = 1.0,
timestep: float = 1.0e-2,
group_factory_name: str = "warp_and_blend",
visualize: bool = True):
if ambient_dim not in (2, 3):
raise ValueError(f"unsupported dimension: {ambient_dim}")
mesh_order = target_order
radius = 1.0
# {{{ geometry
# {{{ element groups
import modepy as mp
import meshmode.discretization.poly_element as poly
# NOTE: picking the same unit nodes for the mesh and the discr saves
# a bit of work when reconstructing after a time step
if group_factory_name == "warp_and_blend":
group_factory_cls = poly.PolynomialWarpAndBlendGroupFactory
unit_nodes = mp.warp_and_blend_nodes(ambient_dim - 1, mesh_order)
elif group_factory_name == "quadrature":
group_factory_cls = poly.InterpolatoryQuadratureSimplexGroupFactory
if ambient_dim == 2:
unit_nodes = mp.LegendreGaussQuadrature(
mesh_order, force_dim_axis=True).nodes
else:
unit_nodes = mp.VioreanuRokhlinSimplexQuadrature(mesh_order, 2).nodes
else:
raise ValueError(f"unknown group factory: '{group_factory_name}'")
# }}}
# {{{ discretization
import meshmode.mesh.generation as gen
if ambient_dim == 2:
nelements = 8192 if resolution is None else resolution
mesh = gen.make_curve_mesh(
lambda t: radius * gen.ellipse(1.0, t),
np.linspace(0.0, 1.0, nelements + 1),
order=mesh_order,
unit_nodes=unit_nodes)
else:
nrounds = 4 if resolution is None else resolution
mesh = gen.generate_icosphere(radius,
uniform_refinement_rounds=nrounds,
order=mesh_order,
unit_nodes=unit_nodes)
from meshmode.discretization import Discretization
discr0 = Discretization(actx, mesh, group_factory_cls(target_order))
logger.info("ndofs: %d", discr0.ndofs)
logger.info("nelements: %d", discr0.mesh.nelements)
# }}}
if visualize:
from meshmode.discretization.visualization import make_visualizer
vis = make_visualizer(actx, discr0,
vis_order=target_order,
# NOTE: setting this to True will add some unnecessary
# resampling in Discretization.nodes for the vis_discr underneath
force_equidistant=False)
# }}}
# {{{ ode
def velocity_field(nodes, alpha=1.0):
return make_obj_array([
alpha * nodes[0], -alpha * nodes[1], 0.0 * nodes[0]
][:ambient_dim])
def source(t, x):
discr = reconstruct_discr_from_nodes(actx, discr0, x)
u = velocity_field(thaw(discr.nodes(), actx))
# {{{
# NOTE: these are just here because this was at some point used to
# profile some more operators (turned out well!)
from meshmode.discretization import num_reference_derivative
x = thaw(discr.nodes()[0], actx)
gradx = sum(
num_reference_derivative(discr, (i,), x)
for i in range(discr.dim))
intx = sum(actx.np.sum(xi * wi) for xi, wi in zip(x, discr.quad_weights()))
assert gradx is not None
assert intx is not None
# }}}
return u
# }}}
# {{{ evolve
maxiter = int(tmax // timestep) + 1
dt = tmax / maxiter + 1.0e-15
x = thaw(discr0.nodes(), actx)
t = 0.0
if visualize:
filename = f"moving-geometry-{0:09d}.vtu"
plot_solution(actx, vis, filename, discr0, t, x)
for n in range(1, maxiter + 1):
x = advance(actx, dt, t, x, source)
t += dt
if visualize:
discr = reconstruct_discr_from_nodes(actx, discr0, x)
vis = make_visualizer(actx, discr, vis_order=target_order)
# vis = vis.copy_with_same_connectivity(actx, discr)
filename = f"moving-geometry-{n:09d}.vtu"
plot_solution(actx, vis, filename, discr, t, x)
logger.info("[%05d/%05d] t = %.5e/%.5e dt = %.5e",
n, maxiter, t, tmax, dt)