def _get_centers_and_expansion_radii(queue, source, target_discr,
qbx_forced_limit):
"""
:arg queue: a :class:`pyopencl.CommandQueue`.
:arg source: a :class:`pytential.source.LayerPotentialSourceBase`.
:arg target_discr: a :class:`meshmode.discretization.Discretization`.
:arg qbx_forced_limit: an integer (*+1* or *-1*).
:return: a tuple of `(centers, radii)` for each node in *target_discr*.
"""
if source.density_discr is target_discr:
# NOTE: skip expensive target association
centers = bind(
source, sym.expansion_centers(source.ambient_dim,
qbx_forced_limit))(queue)
radii = bind(source, sym.expansion_radii(source.ambient_dim))(queue)
else:
from pytential.qbx.utils import get_interleaved_centers
centers = get_interleaved_centers(queue, source)
radii = bind(
source,
sym.expansion_radii(source.ambient_dim,
granularity=sym.GRANULARITY_CENTER))(queue)
# NOTE: using a very small tolerance to make sure all the stage2
# targets are associated to a center. We can't use the user provided
# source.target_association_tolerance here because it will likely be
# way too small.
target_association_tolerance = 1.0e-1
from pytential.qbx.target_assoc import associate_targets_to_qbx_centers
code_container = source.target_association_code_container
assoc = associate_targets_to_qbx_centers(
source,
code_container.get_wrangler(queue),
[(target_discr, qbx_forced_limit)],
target_association_tolerance=target_association_tolerance)
centers = [
cl.array.take(c, assoc.target_to_center, queue=queue)
for c in centers
]
radii = cl.array.take(radii, assoc.target_to_center, queue=queue)
return centers, radii
def weights_and_area_elements(self):
import pytential.symbolic.primitives as p
from pytential.symbolic.execution import bind
with cl.CommandQueue(self.cl_context) as queue:
# quad_stage2_density_discr is not guaranteed to be usable for
# interpolation/differentiation. Use density_discr to find
# area element instead, then upsample that.
area_element = self.resampler(
queue,
bind(
self.density_discr,
p.area_element(self.ambient_dim, self.dim)
)(queue))
qweight = bind(self.quad_stage2_density_discr, p.QWeight())(queue)
return (area_element.with_queue(queue)*qweight).with_queue(None)
def _norm_inf_op(discr, num_components):
from pytential import sym, bind
if num_components is not None:
from pymbolic.primitives import make_sym_vector
v = make_sym_vector("arg", num_components)
max_arg = sym.abs(v)
else:
max_arg = sym.abs(sym.var("arg"))
return bind(discr, sym.NodeMax(max_arg))
def _norm_op(discr, num_components):
from pytential import sym, bind
if num_components is not None:
from pymbolic.primitives import make_sym_vector
v = make_sym_vector("integrand", num_components)
integrand = sym.real(np.dot(sym.conj(v), v))
else:
integrand = sym.abs(sym.var("integrand"))**2
return bind(discr, sym.integral(integrand))
def _norm_2_op(discr, num_components):
from pytential import sym, bind
if num_components is not None:
from pymbolic.primitives import make_sym_vector
v = make_sym_vector("integrand", num_components)
integrand = sym.real(np.dot(sym.conj(v), v))
else:
integrand = sym.abs(sym.var("integrand"))**2
return bind(discr, sym.integral(discr.ambient_dim, discr.dim, integrand))
def _norm_inf_op(discr, num_components):
from pytential import sym, bind
if num_components is not None:
from pymbolic.primitives import make_sym_vector
v = make_sym_vector("arg", num_components)
max_arg = sym.abs(v)
else:
max_arg = sym.abs(sym.var("arg"))
return bind(discr, sym.NodeMax(max_arg))
def _get_weights_and_area_elements(queue, source, source_discr):
"""
:arg queue: a :class:`pyopencl.CommandQueue`.
:arg source: a :class:`pytential.source.LayerPotentialSourceBase`.
:arg source_discr: a :class:`meshmode.discretization.Discretization`.
:return: quadrature weights for each node in *source_discr*.
"""
if source.quad_stage2_density_discr is source_discr:
waa = source.weights_and_area_elements().with_queue(queue)
else:
# NOTE: copied from `weights_and_area_elements`, but using the
# discretization given by `where` and no interpolation
area = bind(source_discr,
sym.area_element(source.ambient_dim, source.dim))(queue)
qweight = bind(source_discr, sym.QWeight())(queue)
waa = area * qweight
return waa
def map_num_reference_derivative(self, expr):
rec_operand = self.rec(expr.operand)
assert isinstance(rec_operand, np.ndarray)
if self.is_kind_matrix(rec_operand):
raise NotImplementedError("derivatives")
where_discr = self.places[expr.where]
op = sym.NumReferenceDerivative(expr.ref_axes, sym.var("u"))
return bind(where_discr, op)(
self.queue, u=cl.array.to_device(self.queue, rec_operand)).get()
def _get_weights_and_area_elements(queue, source, source_discr):
"""
:arg queue: a :class:`pyopencl.CommandQueue`.
:arg source: a :class:`pytential.source.LayerPotentialSourceBase`.
:arg source_discr: a :class:`meshmode.discretization.Discretization`.
:return: quadrature weights for each node in *source_discr*.
"""
if source.quad_stage2_density_discr is source_discr:
waa = source.weights_and_area_elements().with_queue(queue)
else:
# NOTE: copied from `weights_and_area_elements`, but using the
# discretization given by `where` and no interpolation
area = bind(source_discr,
sym.area_element(source.ambient_dim, source.dim))(queue)
qweight = bind(source_discr, sym.QWeight())(queue)
waa = area * qweight
return waa
def map_num_reference_derivative(self, expr):
rec_operand = self.rec(expr.operand)
assert isinstance(rec_operand, np.ndarray)
if self.is_kind_matrix(rec_operand):
raise NotImplementedError("derivatives")
rec_operand = cl.array.to_device(self.queue, rec_operand)
op = sym.NumReferenceDerivative(ref_axes=expr.ref_axes,
operand=sym.var("u"),
dofdesc=expr.dofdesc)
return bind(self.places, op)(self.queue, u=rec_operand).get()
def map_call(self, expr):
arg, = expr.parameters
rec_arg = self.rec(arg)
if isinstance(rec_arg, np.ndarray) and self.is_kind_matrix(rec_arg):
raise RuntimeError("expression is nonlinear in variable")
if isinstance(rec_arg, np.ndarray):
rec_arg = cl.array.to_device(self.queue, rec_arg)
op = expr.function(sym.var("u"))
result = bind(self.dep_source, op)(self.queue, u=rec_arg)
if isinstance(result, cl.array.Array):
result = result.get()
return result
def map_call(self, expr):
arg, = expr.parameters
rec_arg = self.rec(arg)
if isinstance(rec_arg, np.ndarray) and self.is_kind_matrix(rec_arg):
raise RuntimeError("expression is nonlinear in variable")
if isinstance(rec_arg, np.ndarray):
rec_arg = cl.array.to_device(self.queue, rec_arg)
op = expr.function(sym.var("u"))
result = bind(self.dep_source, op)(self.queue, u=rec_arg)
if isinstance(result, cl.array.Array):
result = result.get()
return result
def _coarsest_quad_resolution(self, last_dim_length="npanels"):
"""This measures the quadrature resolution across the
mesh. In a 1D uniform mesh of uniform 'parametrization speed', it
should be the same as the panel length.
"""
import pytential.qbx.utils as utils
from pytential import sym, bind
with cl.CommandQueue(self.cl_context) as queue:
maxstretch = bind(
self,
sym._simplex_mapping_max_stretch_factor(
self.ambient_dim)
)(queue)
maxstretch = utils.to_last_dim_length(
self.density_discr, maxstretch, last_dim_length)
maxstretch = maxstretch.with_queue(None)
return maxstretch
def _stage2_coarsest_quad_resolution(self, last_dim_length="npanels"):
"""This measures the quadrature resolution across the
mesh. In a 1D uniform mesh of uniform 'parametrization speed', it
should be the same as the panel length.
"""
if last_dim_length != "npanels":
# Not technically required below, but no need to loosen for now.
raise NotImplementedError()
import pytential.qbx.utils as utils
from pytential import sym, bind
with cl.CommandQueue(self.cl_context) as queue:
maxstretch = bind(
self, sym._simplex_mapping_max_stretch_factor(
self.ambient_dim,
where=sym.QBXSourceStage2(sym.DEFAULT_SOURCE))
)(queue)
maxstretch = utils.to_last_dim_length(
self.stage2_density_discr, maxstretch, last_dim_length)
maxstretch = maxstretch.with_queue(None)
return maxstretch
def _integral_op(discr):
from pytential import sym, bind
return bind(discr,
sym.integral(
discr.ambient_dim, discr.dim, sym.var("integrand")))
def _integral_op(discr):
from pytential import sym, bind
return bind(
discr, sym.integral(discr.ambient_dim, discr.dim,
sym.var("integrand")))
def map_node_coordinate_component(self, expr):
where_discr = self.places[expr.where]
op = sym.NodeCoordinateComponent(expr.ambient_axis)
return bind(where_discr, op)(self.queue).get()
def _integral_op(discr):
from pytential import sym, bind
return bind(discr, sym.integral(sym.var("integrand")))
def map_node_coordinate_component(self, expr):
op = sym.NodeCoordinateComponent(expr.ambient_axis,
dofdesc=expr.dofdesc)
return bind(self.places, op)(self.queue).get()
