def warp_and_refine_until_resolved(unwarped_mesh_or_refiner, warp_callable,
est_rel_interp_tolerance):
"""Given an original ("unwarped") :class:`meshmode.mesh.Mesh` and a
warping function *warp_callable* that takes and returns a mesh and a
tolerance to which the mesh should be resolved by the mapping polynomials,
this function will iteratively refine the *unwarped_mesh* until relative
interpolation error estimates on the warped version are smaller than
*est_rel_interp_tolerance* on each element.
:returns: The refined, unwarped mesh.
.. versionadded:: 2018.1
"""
from modepy.modes import simplex_onb
from modepy.matrices import vandermonde
from modepy.modal_decay import simplex_interp_error_coefficient_estimator_matrix
from meshmode.mesh.refinement import Refiner, RefinerWithoutAdjacency
if isinstance(unwarped_mesh_or_refiner,
(Refiner, RefinerWithoutAdjacency)):
refiner = unwarped_mesh_or_refiner
unwarped_mesh = refiner.get_current_mesh()
else:
unwarped_mesh = unwarped_mesh_or_refiner
refiner = Refiner(unwarped_mesh)
iteration = 0
while True:
refine_flags = np.zeros(unwarped_mesh.nelements, dtype=bool)
warped_mesh = warp_callable(unwarped_mesh)
# test whether there are invalid values in warped mesh
if not np.isfinite(warped_mesh.vertices).all():
raise FloatingPointError(
"Warped mesh contains non-finite vertices "
"(NaN or Inf)")
for group in warped_mesh.groups:
if not np.isfinite(group.nodes).all():
raise FloatingPointError(
"Warped mesh contains non-finite nodes "
"(NaN or Inf)")
for egrp in warped_mesh.groups:
dim, nunit_nodes = egrp.unit_nodes.shape
interp_err_est_mat = simplex_interp_error_coefficient_estimator_matrix(
egrp.unit_nodes,
egrp.order,
n_tail_orders=1 if warped_mesh.dim > 1 else 2)
vdm_inv = la.inv(
vandermonde(simplex_onb(dim, egrp.order), egrp.unit_nodes))
mapping_coeffs = np.einsum("ij,dej->dei", vdm_inv, egrp.nodes)
mapping_norm_2 = np.sqrt(np.sum(mapping_coeffs**2, axis=-1))
interp_error_coeffs = np.einsum("ij,dej->dei", interp_err_est_mat,
egrp.nodes)
interp_error_norm_2 = np.sqrt(
np.sum(interp_error_coeffs**2, axis=-1))
# max over dimensions
est_rel_interp_error = np.max(interp_error_norm_2 / mapping_norm_2,
axis=0)
refine_flags[
egrp.element_nr_base:
egrp.element_nr_base+egrp.nelements] = \
est_rel_interp_error > est_rel_interp_tolerance
nrefined_elements = np.sum(refine_flags.astype(np.int32))
if nrefined_elements == 0:
break
logger.info(
"warp_and_refine_until_resolved: "
"iteration %d -> splitting %d/%d elements", iteration,
nrefined_elements, unwarped_mesh.nelements)
unwarped_mesh = refiner.refine(refine_flags)
iteration += 1
return unwarped_mesh
def warp_and_refine_until_resolved(
unwarped_mesh_or_refiner, warp_callable, est_rel_interp_tolerance):
"""Given an original ("un-warped") :class:`meshmode.mesh.Mesh` and a
warping function *warp_callable* that takes and returns a mesh and a
tolerance to which the mesh should be resolved by the mapping polynomials,
this function will iteratively refine the *unwarped_mesh* until relative
interpolation error estimates on the warped version are smaller than
*est_rel_interp_tolerance* on each element.
:returns: The refined, un-warped mesh.
.. versionadded:: 2018.1
"""
from modepy.modes import simplex_onb
from modepy.matrices import vandermonde
from modepy.modal_decay import simplex_interp_error_coefficient_estimator_matrix
from meshmode.mesh.refinement import Refiner, RefinerWithoutAdjacency
if isinstance(unwarped_mesh_or_refiner, (Refiner, RefinerWithoutAdjacency)):
refiner = unwarped_mesh_or_refiner
unwarped_mesh = refiner.get_current_mesh()
else:
unwarped_mesh = unwarped_mesh_or_refiner
refiner = Refiner(unwarped_mesh)
iteration = 0
while True:
refine_flags = np.zeros(unwarped_mesh.nelements, dtype=np.bool)
warped_mesh = warp_callable(unwarped_mesh)
# test whether there are invalid values in warped mesh
if not np.isfinite(warped_mesh.vertices).all():
raise FloatingPointError("Warped mesh contains non-finite vertices "
"(NaN or Inf)")
for group in warped_mesh.groups:
if not np.isfinite(group.nodes).all():
raise FloatingPointError("Warped mesh contains non-finite nodes "
"(NaN or Inf)")
for egrp in warped_mesh.groups:
dim, nunit_nodes = egrp.unit_nodes.shape
interp_err_est_mat = simplex_interp_error_coefficient_estimator_matrix(
egrp.unit_nodes, egrp.order,
n_tail_orders=1 if warped_mesh.dim > 1 else 2)
vdm_inv = la.inv(
vandermonde(simplex_onb(dim, egrp.order), egrp.unit_nodes))
mapping_coeffs = np.einsum("ij,dej->dei", vdm_inv, egrp.nodes)
mapping_norm_2 = np.sqrt(np.sum(mapping_coeffs**2, axis=-1))
interp_error_coeffs = np.einsum(
"ij,dej->dei", interp_err_est_mat, egrp.nodes)
interp_error_norm_2 = np.sqrt(np.sum(interp_error_coeffs**2, axis=-1))
# max over dimensions
est_rel_interp_error = np.max(interp_error_norm_2/mapping_norm_2, axis=0)
refine_flags[
egrp.element_nr_base:
egrp.element_nr_base+egrp.nelements] = \
est_rel_interp_error > est_rel_interp_tolerance
nrefined_elements = np.sum(refine_flags.astype(np.int32))
if nrefined_elements == 0:
break
logger.info("warp_and_refine_until_resolved: "
"iteration %d -> splitting %d/%d elements",
iteration, nrefined_elements, unwarped_mesh.nelements)
unwarped_mesh = refiner.refine(refine_flags)
iteration += 1
return unwarped_mesh
