def __init__(self, dim=None, helmholtz_k_name="k", allow_evanescent=False):
"""
:arg helmholtz_k_name: The argument name to use for the Helmholtz
parameter when generating functions to evaluate this kernel.
"""
k = var(helmholtz_k_name)
# Guard against code using the old positional interface.
assert isinstance(allow_evanescent, bool)
if dim == 2:
r = pymbolic_real_norm_2(make_sym_vector("d", dim))
expr = var("hankel_1")(0, k * r)
scaling = var("I") / 4
elif dim == 3:
r = pymbolic_real_norm_2(make_sym_vector("d", dim))
expr = var("exp")(var("I") * k * r) / r
scaling = 1 / (4 * var("pi"))
else:
raise RuntimeError("unsupported dimensionality")
super(HelmholtzKernel, self).__init__(dim,
expression=expr,
global_scaling_const=scaling,
is_complex_valued=True)
self.helmholtz_k_name = helmholtz_k_name
self.allow_evanescent = allow_evanescent
def __init__(self, dim=None, helmholtz_k_name="k",
allow_evanescent=False):
"""
:arg helmholtz_k_name: The argument name to use for the Helmholtz
parameter when generating functions to evaluate this kernel.
"""
k = var(helmholtz_k_name)
# Guard against code using the old positional interface.
assert isinstance(allow_evanescent, bool)
if dim == 2:
r = pymbolic_real_norm_2(make_sym_vector("d", dim))
expr = var("hankel_1")(0, k*r)
scaling = var("I")/4
elif dim == 3:
r = pymbolic_real_norm_2(make_sym_vector("d", dim))
expr = var("exp")(var("I")*k*r)/r
scaling = 1/(4*var("pi"))
elif dim is None:
expr = None
scaling = None
else:
raise RuntimeError("unsupported dimensionality")
ExpressionKernel.__init__(
self,
dim,
expression=expr,
scaling=scaling,
is_complex_valued=True)
self.helmholtz_k_name = helmholtz_k_name
self.allow_evanescent = allow_evanescent
def __init__(self, dim=None, icomp=None, jcomp=None, viscosity_mu_name="mu",
stresslet_vector_name="stresslet_vec"):
"""
:arg viscosity_mu_name: The argument name to use for
dynamic viscosity :math:`\mu` the then generating functions to
evaluate this kernel.
"""
# Mu is unused but kept for consistency with the stokeslet.
if dim == 2:
d = make_sym_vector("d", dim)
n = make_sym_vector(stresslet_vector_name, dim)
r = pymbolic_real_norm_2(d)
expr = (
sum(n[axis]*d[axis] for axis in range(dim))
*
d[icomp]*d[jcomp]/r**4
)
scaling = 1/(var("pi"))
elif dim == 3:
d = make_sym_vector("d", dim)
n = make_sym_vector(stresslet_vector_name, dim)
r = pymbolic_real_norm_2(d)
expr = (
sum(n[axis]*d[axis] for axis in range(dim))
*
d[icomp]*d[jcomp]/r**5
)
scaling = -3/(4*var("pi"))
elif dim is None:
expr = None
scaling = None
else:
raise RuntimeError("unsupported dimensionality")
self.viscosity_mu_name = viscosity_mu_name
self.stresslet_vector_name = stresslet_vector_name
self.icomp = icomp
self.jcomp = jcomp
ExpressionKernel.__init__(
self,
dim,
expression=expr,
scaling=scaling,
is_complex_valued=False)
def __init__(self, dim=None, yukawa_lambda_name="lam"):
"""
:arg yukawa_lambda_name: The argument name to use for the Yukawa
parameter when generating functions to evaluate this kernel.
"""
lam = var(yukawa_lambda_name)
if dim == 2:
r = pymbolic_real_norm_2(make_sym_vector("d", dim))
# http://dlmf.nist.gov/10.27#E8
expr = var("hankel_1")(0, var("I")*lam*r)
scaling_for_K0 = 1/2*var("pi")*var("I") # noqa: N806
scaling = -1/(2*var("pi")) * scaling_for_K0
else:
raise RuntimeError("unsupported dimensionality")
super(YukawaKernel, self).__init__(
dim,
expression=expr,
global_scaling_const=scaling,
is_complex_valued=True)
self.yukawa_lambda_name = yukawa_lambda_name
def get_kernel():
from sumpy.symbolic import pymbolic_real_norm_2
from pymbolic.primitives import make_sym_vector
from pymbolic import var
d = make_sym_vector("d", 3)
r = pymbolic_real_norm_2(d[:-1])
# r3d = pymbolic_real_norm_2(d)
#expr = var("log")(r3d)
log = var("log")
sqrt = var("sqrt")
a = d[-1]
expr = log(r)
expr = log(sqrt(r**2 + a**2))
expr = log(sqrt(r + a**2))
#expr = log(sqrt(r**2 + a**2))-a**2/2/(r**2+a**2)
#expr = 2*log(sqrt(r**2 + a**2))
scaling = 1 / (2 * var("pi"))
from sumpy.kernel import ExpressionKernel
return ExpressionKernel(dim=3,
expression=expr,
global_scaling_const=scaling,
is_complex_valued=False)
def get_kernel():
from sumpy.symbolic import pymbolic_real_norm_2
from pymbolic.primitives import make_sym_vector
from pymbolic import var
d = make_sym_vector("d", 3)
r = pymbolic_real_norm_2(d[:-1])
# r3d = pymbolic_real_norm_2(d)
#expr = var("log")(r3d)
log = var("log")
sqrt = var("sqrt")
a = d[-1]
expr = log(r)
expr = log(sqrt(r**2 + a**2))
expr = log(sqrt(r + a**2))
#expr = log(sqrt(r**2 + a**2))-a**2/2/(r**2+a**2)
#expr = 2*log(sqrt(r**2 + a**2))
scaling = 1/(2*var("pi"))
from sumpy.kernel import ExpressionKernel
return ExpressionKernel(
dim=3,
expression=expr,
global_scaling_const=scaling,
is_complex_valued=False)
def __init__(self, dim=None, yukawa_lambda_name="lam"):
"""
:arg yukawa_lambda_name: The argument name to use for the Yukawa
parameter when generating functions to evaluate this kernel.
"""
lam = var(yukawa_lambda_name)
if dim == 2:
r = pymbolic_real_norm_2(make_sym_vector("d", dim))
# http://dlmf.nist.gov/10.27#E8
expr = var("hankel_1")(0, var("I")*lam*r)
scaling_for_K0 = 1/2*var("pi")*var("I") # noqa: N806
scaling = -1/(2*var("pi")) * scaling_for_K0
else:
raise RuntimeError("unsupported dimensionality")
super(YukawaKernel, self).__init__(
dim,
expression=expr,
global_scaling_const=scaling,
is_complex_valued=True)
self.yukawa_lambda_name = yukawa_lambda_name
def __init__(self, dim=None):
# See (Kress LIE, Thm 6.2) for scaling
if dim == 2:
r = pymbolic_real_norm_2(make_sym_vector("d", dim))
expr = var("log")(r)
scaling = 1 / (-2 * var("pi"))
elif dim == 3:
r = pymbolic_real_norm_2(make_sym_vector("d", dim))
expr = 1 / r
scaling = 1 / (4 * var("pi"))
else:
raise NotImplementedError("unsupported dimensionality")
super(LaplaceKernel, self).__init__(dim,
expression=expr,
global_scaling_const=scaling,
is_complex_valued=False)
def __init__(self, dim=None):
# See (Kress LIE, Thm 6.2) for scaling
if dim == 2:
r = pymbolic_real_norm_2(make_sym_vector("d", dim))
expr = var("log")(r)
scaling = 1/(-2*var("pi"))
elif dim == 3:
r = pymbolic_real_norm_2(make_sym_vector("d", dim))
expr = 1/r
scaling = 1/(4*var("pi"))
else:
raise NotImplementedError("unsupported dimensionality")
super(LaplaceKernel, self).__init__(
dim,
expression=expr,
global_scaling_const=scaling,
is_complex_valued=False)
def __init__(self, dim, icomp, jcomp, viscosity_mu_name="mu"):
"""
:arg viscosity_mu_name: The argument name to use for
dynamic viscosity :math:`\mu` the then generating functions to
evaluate this kernel.
"""
mu = var(viscosity_mu_name)
if dim == 2:
d = make_sym_vector("d", dim)
r = pymbolic_real_norm_2(d)
expr = (
-var("log")(r)*(1 if icomp == jcomp else 0)
+
d[icomp]*d[jcomp]/r**2
)
scaling = 1/(4*var("pi")*mu)
elif dim == 3:
d = make_sym_vector("d", dim)
r = pymbolic_real_norm_2(d)
expr = (
(1/r)*(1 if icomp == jcomp else 0)
+
d[icomp]*d[jcomp]/r**3
)
scaling = -1/(8*var("pi")*mu)
elif dim is None:
expr = None
scaling = None
else:
raise RuntimeError("unsupported dimensionality")
self.viscosity_mu_name = viscosity_mu_name
self.icomp = icomp
self.jcomp = jcomp
ExpressionKernel.__init__(
self,
dim,
expression=expr,
scaling=scaling,
is_complex_valued=False)
def __init__(self, dim, icomp, jcomp, viscosity_mu_name="mu"):
r"""
:arg viscosity_mu_name: The argument name to use for
dynamic viscosity :math:`\mu` the then generating functions to
evaluate this kernel.
"""
mu = var(viscosity_mu_name)
if dim == 2:
d = make_sym_vector("d", dim)
r = pymbolic_real_norm_2(d)
expr = (
-var("log")(r)*(1 if icomp == jcomp else 0)
+ # noqa: W504
d[icomp]*d[jcomp]/r**2
)
scaling = -1/(4*var("pi")*mu)
elif dim == 3:
d = make_sym_vector("d", dim)
r = pymbolic_real_norm_2(d)
expr = (
(1/r)*(1 if icomp == jcomp else 0)
+ # noqa: W504
d[icomp]*d[jcomp]/r**3
)
scaling = -1/(8*var("pi")*mu)
elif dim is None:
expr = None
scaling = None
else:
raise RuntimeError("unsupported dimensionality")
self.viscosity_mu_name = viscosity_mu_name
self.icomp = icomp
self.jcomp = jcomp
super(StokesletKernel, self).__init__(
dim,
expression=expr,
global_scaling_const=scaling,
is_complex_valued=False)
def __init__(self, dim=None, icomp=None, jcomp=None, kcomp=None,
viscosity_mu_name="mu"):
r"""
:arg viscosity_mu_name: The argument name to use for
dynamic viscosity :math:`\mu` the then generating functions to
evaluate this kernel.
"""
# Mu is unused but kept for consistency with the stokeslet.
if dim == 2:
d = make_sym_vector("d", dim)
r = pymbolic_real_norm_2(d)
expr = (
d[icomp]*d[jcomp]*d[kcomp]/r**4
)
scaling = 1/(var("pi"))
elif dim == 3:
d = make_sym_vector("d", dim)
r = pymbolic_real_norm_2(d)
expr = (
d[icomp]*d[jcomp]*d[kcomp]/r**5
)
scaling = 3/(4*var("pi"))
elif dim is None:
expr = None
scaling = None
else:
raise RuntimeError("unsupported dimensionality")
self.viscosity_mu_name = viscosity_mu_name
self.icomp = icomp
self.jcomp = jcomp
self.kcomp = kcomp
super(StressletKernel, self).__init__(
dim,
expression=expr,
global_scaling_const=scaling,
is_complex_valued=False)
def __init__(self, dim=None, icomp=None, jcomp=None, kcomp=None,
viscosity_mu_name="mu"):
r"""
:arg viscosity_mu_name: The argument name to use for
dynamic viscosity :math:`\mu` the then generating functions to
evaluate this kernel.
"""
# Mu is unused but kept for consistency with the stokeslet.
if dim == 2:
d = make_sym_vector("d", dim)
r = pymbolic_real_norm_2(d)
expr = (
d[icomp]*d[jcomp]*d[kcomp]/r**4
)
scaling = 1/(var("pi"))
elif dim == 3:
d = make_sym_vector("d", dim)
r = pymbolic_real_norm_2(d)
expr = (
d[icomp]*d[jcomp]*d[kcomp]/r**5
)
scaling = 3/(4*var("pi"))
elif dim is None:
expr = None
scaling = None
else:
raise RuntimeError("unsupported dimensionality")
self.viscosity_mu_name = viscosity_mu_name
self.icomp = icomp
self.jcomp = jcomp
self.kcomp = kcomp
super(StressletKernel, self).__init__(
dim,
expression=expr,
global_scaling_const=scaling,
is_complex_valued=False)
def __init__(self, dim=None):
# See (Kress LIE, Thm 6.2) for scaling
if dim == 2:
r = pymbolic_real_norm_2(make_sym_vector("d", dim))
expr = var("log")(r)
scaling = 1/(-2*var("pi"))
elif dim == 3:
r = pymbolic_real_norm_2(make_sym_vector("d", dim))
expr = 1/r
scaling = 1/(4*var("pi"))
elif dim is None:
expr = None
scaling = None
else:
raise RuntimeError("unsupported dimensionality")
ExpressionKernel.__init__(
self,
dim,
expression=expr,
scaling=scaling,
is_complex_valued=False)
def get_kernel():
from sumpy.symbolic import pymbolic_real_norm_2
from pymbolic.primitives import (make_sym_vector, Variable as var)
r = pymbolic_real_norm_2(make_sym_vector("d", 3))
expr = var("log")(r)
scaling = 1/(2*var("pi"))
from sumpy.kernel import ExpressionKernel
return ExpressionKernel(
dim=3,
expression=expr,
scaling=scaling,
is_complex_valued=False)
def __init__(self, dim=None):
r = pymbolic_real_norm_2(make_sym_vector("d", dim))
if dim == 2:
expr = r**2 * var("log")(r)
scaling = 1 / (8 * var("pi"))
elif dim == 3:
expr = r
scaling = 1 # FIXME: Unknown
else:
raise RuntimeError("unsupported dimensionality")
super(BiharmonicKernel, self).__init__(dim,
expression=expr,
global_scaling_const=scaling,
is_complex_valued=False)
def __init__(self, dim=None):
r = pymbolic_real_norm_2(make_sym_vector("d", dim))
if dim == 2:
expr = r**2 * var("log")(r)
scaling = 1/(8*var("pi"))
elif dim == 3:
expr = r
scaling = 1 # FIXME: Unknown
else:
raise RuntimeError("unsupported dimensionality")
super(BiharmonicKernel, self).__init__(
dim,
expression=expr,
global_scaling_const=scaling,
is_complex_valued=False)
def __init__(self, dim=None):
# See https://arxiv.org/abs/1202.1811
r = pymbolic_real_norm_2(make_sym_vector("d", dim))
if dim == 2:
expr = r**2 * (var("log")(r) - 1)
scaling = -1 / (8 * var("pi"))
elif dim == 3:
expr = r
scaling = 1 / (8 * var("pi"))
else:
raise RuntimeError("unsupported dimensionality")
super(BiharmonicKernel, self).__init__(dim,
expression=expr,
global_scaling_const=scaling,
is_complex_valued=False)
def __init__(self, dim=None, yukawa_lambda_name="lam"):
"""
:arg yukawa_lambda_name: The argument name to use for the Yukawa
parameter when generating functions to evaluate this kernel.
"""
lam = var(yukawa_lambda_name)
# NOTE: The Yukawa kernel is given by [1]
# -1/(2 pi)**(n/2) * (lam/r)**(n/2-1) * K(n/2-1, lam r)
# where K is a modified Bessel function of the second kind.
#
# [1] https://en.wikipedia.org/wiki/Green%27s_function
# [2] http://dlmf.nist.gov/10.27#E8
# [3] https://dlmf.nist.gov/10.47#E2
# [4] https://dlmf.nist.gov/10.49
r = pymbolic_real_norm_2(make_sym_vector("d", dim))
if dim == 2:
# NOTE: transform K(0, lam r) into a Hankel function using [2]
expr = var("hankel_1")(0, var("I")*lam*r)
scaling_for_K0 = var("pi")/2*var("I") # noqa: N806
scaling = -1/(2*var("pi")) * scaling_for_K0
elif dim == 3:
# NOTE: to get the expression, we do the following and simplify
# 1. express K(1/2, lam r) as a modified spherical Bessel function
# k(0, lam r) using [3] and use expression for k(0, lam r) from [4]
# 2. or use (AS 10.2.17) directly
expr = var("exp")(-lam*r) / r
scaling = -1/(4 * var("pi")**2)
else:
raise RuntimeError("unsupported dimensionality")
super(YukawaKernel, self).__init__(
dim,
expression=expr,
global_scaling_const=scaling,
is_complex_valued=True)
self.yukawa_lambda_name = yukawa_lambda_name
def __init__(self, dim=None):
r = pymbolic_real_norm_2(make_sym_vector("d", dim))
if dim == 2:
# Ref: Farkas, Peter. Mathematical foundations for fast algorithms
# for the biharmonic equation. Technical Report 765,
# Department of Computer Science, Yale University, 1990.
expr = r**2 * var("log")(r)
scaling = 1 / (8 * var("pi"))
elif dim == 3:
# Ref: Jiang, Shidong, Bo Ren, Paul Tsuji, and Lexing Ying.
# "Second kind integral equations for the first kind Dirichlet problem
# of the biharmonic equation in three dimensions."
# Journal of Computational Physics 230, no. 19 (2011): 7488-7501.
expr = r
scaling = -1 / (8 * var("pi"))
else:
raise RuntimeError("unsupported dimensionality")
super().__init__(dim,
expression=expr,
global_scaling_const=scaling,
is_complex_valued=False)
