# Kernels#

## Kernel interface#

class sumpy.kernel.Kernel(dim)[source]#

Basic kernel interface.

is_complex_valued#
is_translation_invariant#
dim#
get_base_kernel()[source]#

Return the kernel being wrapped by this one, or else self.

replace_base_kernel(new_base_kernel)[source]#

Return the base kernel being wrapped by this one, or else new_base_kernel.

prepare_loopy_kernel(loopy_knl)[source]#

Apply some changes (such as registering function manglers) to the kernel. Return the new kernel.

get_code_transformer()[source]#

Return a function to postprocess the pymbolic expression generated from the result of get_expression() on the way to code generation.

get_expression(dist_vec)[source]#

Return a sympy expression for the kernel.

postprocess_at_source(expr, avec)[source]#

Transform a kernel evaluation or expansion expression in a place where the vector a (something - source) is known. (“something” may be an expansion center or a target.)

The typical use of this function is to apply source-variable derivatives to the kernel.

postprocess_at_target(expr, bvec)[source]#

Transform a kernel evaluation or expansion expression in a place where the vector b (target - something) is known. (“something” may be an expansion center or a target.)

The typical use of this function is to apply target-variable derivatives to the kernel.

Parameters:
get_global_scaling_const()[source]#

Return a global scaling constant of the kernel. Typically, this ensures that the kernel is scaled so that $$\mathcal L(G)(x)=C\delta(x)$$ with a constant of 1, where $$\mathcal L$$ is the PDE operator associated with the kernel. Not to be confused with rscale, which keeps expansion coefficients benignly scaled.

get_args()[source]#

Return list of KernelArgument instances describing extra arguments used by the kernel.

get_source_args()[source]#

Return list of KernelArgument instances describing extra arguments used by kernel in picking up contributions from point sources.

class sumpy.kernel.KernelArgument(loopy_arg)[source]#
loopy_arg#

A loopy.KernelArgument instance describing the type, name, and other features of this kernel argument when passed to a generated piece of code.

## Symbolic kernels#

class sumpy.kernel.ExpressionKernel(dim, expression, global_scaling_const, is_complex_valued)[source]#
expression#

A pymbolic expression depending on variables d_1 through d_N where N equals dim. (These variables match what is returned from pymbolic.primitives.make_sym_vector() with argument “d”.) Any variable that is not d or a SpatialConstant will be viewed as potentially spatially varying.

global_scaling_const#

A constant pymbolic expression for the global scaling of the kernel. Typically, this ensures that the kernel is scaled so that $$\mathcal L(G)(x)=C\delta(x)$$ with a constant of 1, where $$\mathcal L$$ is the PDE operator associated with the kernel. Not to be confused with rscale, which keeps expansion coefficients benignly scaled.

is_complex_valued#
__init__(dim, expression, global_scaling_const, is_complex_valued)[source]#
get_expression(scaled_dist_vec)[source]#

## PDE kernels#

class sumpy.kernel.LaplaceKernel(dim)[source]#
class sumpy.kernel.BiharmonicKernel(dim)[source]#
class sumpy.kernel.HelmholtzKernel(dim, helmholtz_k_name='k', allow_evanescent=False)[source]#
class sumpy.kernel.YukawaKernel(dim, yukawa_lambda_name='lam')[source]#
class sumpy.kernel.StokesletKernel(dim, icomp, jcomp, viscosity_mu='mu', poisson_ratio='0.5')[source]#
class sumpy.kernel.StressletKernel(dim, icomp, jcomp, kcomp, viscosity_mu='mu')[source]#
class sumpy.kernel.ElasticityKernel(dim, icomp, jcomp, viscosity_mu='mu', poisson_ratio='nu')[source]#
class sumpy.kernel.LineOfCompressionKernel(dim=3, axis=2, viscosity_mu='mu', poisson_ratio='nu')[source]#

A kernel for the line of compression or dilatation of constant strength along the axis “axis” from zero to negative infinity. This is used for the explicit solution to half-space Elasticity problem. See [1] for details.

[1]: Mindlin, R.: Force at a Point in the Interior of a Semi-Infinite Solid

https://doi.org/10.1063/1.1745385

## Derivatives#

These objects wrap other kernels and take derivatives of them in the process.

class sumpy.kernel.DerivativeBase(inner_kernel)[source]#
class sumpy.kernel.AxisTargetDerivative(axis, inner_kernel)[source]#
class sumpy.kernel.AxisSourceDerivative(axis, inner_kernel)[source]#
class sumpy.kernel.DirectionalSourceDerivative(inner_kernel, dir_vec_name=None)[source]#
class sumpy.kernel.DirectionalTargetDerivative(inner_kernel, dir_vec_name=None)[source]#

## Transforming kernels#

class sumpy.kernel.KernelMapper[source]#
class sumpy.kernel.KernelCombineMapper[source]#
class sumpy.kernel.KernelIdentityMapper[source]#
class sumpy.kernel.AxisSourceDerivativeRemover[source]#
class sumpy.kernel.AxisTargetDerivativeRemover[source]#
class sumpy.kernel.SourceDerivativeRemover[source]#
class sumpy.kernel.TargetDerivativeRemover[source]#
class sumpy.kernel.TargetPointMultiplier(axis, inner_kernel)[source]#

Wraps a kernel $$G(x, y)$$ and outputs $$x_j G(x, y)$$ where $$x, y$$ are targets and sources respectively.

class sumpy.kernel.DerivativeCounter[source]#