def translate_from(self, src_expansion, src_coeff_exprs, dvec):
from sumpy.symbolic import sympy_real_norm_2
k = sp.Symbol(self.kernel.get_base_kernel().helmholtz_k_name)
if isinstance(src_expansion, H2DLocalExpansion):
dvec_len = sympy_real_norm_2(dvec)
bessel_j = sp.Function("bessel_j")
new_center_angle_rel_old_center = sp.atan2(dvec[1], dvec[0])
translated_coeffs = []
for l in self.get_coefficient_identifiers():
translated_coeffs.append(
sum(
src_coeff_exprs[src_expansion.get_storage_index(m)]
* bessel_j(m - l, k * dvec_len)
* sp.exp(sp.I * (m - l) * -new_center_angle_rel_old_center)
for m in src_expansion.get_coefficient_identifiers()
)
)
return translated_coeffs
from sumpy.expansion.multipole import H2DMultipoleExpansion
if isinstance(src_expansion, H2DMultipoleExpansion):
dvec_len = sympy_real_norm_2(dvec)
hankel_1 = sp.Function("hankel_1")
new_center_angle_rel_old_center = sp.atan2(dvec[1], dvec[0])
translated_coeffs = []
for l in self.get_coefficient_identifiers():
translated_coeffs.append(
sum(
(-1) ** l
* hankel_1(m + l, k * dvec_len)
* sp.exp(sp.I * (m + l) * new_center_angle_rel_old_center)
* src_coeff_exprs[src_expansion.get_storage_index(m)]
for m in src_expansion.get_coefficient_identifiers()
)
)
return translated_coeffs
raise RuntimeError(
"do not know how to translate %s to " "local 2D Helmholtz Bessel expansion" % type(src_expansion).__name__
)
def evaluate(self, coeffs, bvec):
from sumpy.symbolic import sympy_real_norm_2
hankel_1 = sp.Function("hankel_1")
bvec_len = sympy_real_norm_2(bvec)
target_angle_rel_center = sp.atan2(bvec[1], bvec[0])
k = sp.Symbol(self.kernel.get_base_kernel().helmholtz_k_name)
return sum(coeffs[self.get_storage_index(l)]
* self.kernel.postprocess_at_target(
hankel_1(l, k * bvec_len)
* sp.exp(sp.I * l * target_angle_rel_center), bvec)
for l in self.get_coefficient_identifiers())
def coefficients_from_source(self, avec, bvec):
from sumpy.symbolic import sympy_real_norm_2
bessel_j = sp.Function("bessel_j")
avec_len = sympy_real_norm_2(avec)
k = sp.Symbol(self.kernel.get_base_kernel().helmholtz_k_name)
# The coordinates are negated since avec points from source to center.
source_angle_rel_center = sp.atan2(-avec[1], -avec[0])
return [self.kernel.postprocess_at_source(
bessel_j(l, k * avec_len) *
sp.exp(sp.I * l * -source_angle_rel_center), avec)
for l in self.get_coefficient_identifiers()]
def translate_from(self, src_expansion, src_coeff_exprs, dvec):
if not isinstance(src_expansion, type(self)):
raise RuntimeError("do not know how to translate %s to "
"multipole 2D Helmholtz Bessel expansion"
% type(src_expansion).__name__)
from sumpy.symbolic import sympy_real_norm_2
dvec_len = sympy_real_norm_2(dvec)
bessel_j = sp.Function("bessel_j")
new_center_angle_rel_old_center = sp.atan2(dvec[1], dvec[0])
k = sp.Symbol(self.kernel.get_base_kernel().helmholtz_k_name)
translated_coeffs = []
for l in self.get_coefficient_identifiers():
translated_coeffs.append(
sum(src_coeff_exprs[src_expansion.get_storage_index(m)]
* bessel_j(m - l, k * dvec_len)
* sp.exp(sp.I * (m - l) * new_center_angle_rel_old_center)
for m in src_expansion.get_coefficient_identifiers()))
return translated_coeffs
