Expansions

class sumpy.expansion.ExpansionBase(kernel, order, use_rscale=None)

with_kernel(kernel)

__len__()

get_coefficient_identifiers()

Returns the identifiers of the coefficients that actually get stored.

coefficients_from_source(avec, bvec, rscale, sac=None)

Form an expansion from a source point.

Parameters

• avec – vector from source to center.

• bvec – vector from center to target. Not usually necessary, except for line-Taylor expansion.

• sac – a symbolic assignment collection where temporary expressions are stored.

Returns

a list of sympy expressions representing the coefficients of the expansion.

translate_from(src_expansion, src_coeff_exprs, src_rscale, dvec, tgt_rscale, sac=None)

__eq__(other)

Return self==value.

__ne__(other)

Return self!=value.

class sumpy.expansion.LinearPDEBasedExpansionTermsWrangler(order, dim, max_mi=None)

__init__(order, dim, max_mi=None)

Parameters

• order – order of the expansion

• dim – number of dimensions

get_pde_as_diff_op()

Returns the PDE as a sumpy.expansion.diff_op.LinearPDESystemOperator object L where L(u) = 0 is the PDE.

Expansion Factories

class sumpy.expansion.ExpansionFactoryBase

An interface .. automethod:: get_local_expansion_class .. automethod:: get_multipole_expansion_class

class sumpy.expansion.DefaultExpansionFactory

An implementation of ExpansionFactoryBase that gives the ‘best known’ expansion for each kernel.

class sumpy.expansion.VolumeTaylorExpansionFactory

An implementation of ExpansionFactoryBase that uses Volume Taylor expansions for each kernel.

Differential Operators

Differential operator interface

class sumpy.expansion.diff_op.LinearPDESystemOperator(dim, *eqs)

Represents a constant-coefficient linear differential operator of a vector-valued function with dim spatial variables. It is represented by a tuple of immutable dictionaries. The dictionary maps a DerivativeIdentifier to the coefficient. This object is immutable. Optionally supports a time variable as the last variable in the multi-index of the DerivativeIdentifier.

class sumpy.expansion.diff_op.DerivativeIdentifier(mi, vec_idx)

sumpy.expansion.diff_op.make_identity_diff_op(ninput, noutput=1, time_dependent=False)

Returns the identity as a linear PDE system operator. if include_time is true, then the last dimension of the multi-index is time.

Parameters

• ninput – number of spatial variables of the function

• noutput – number of output values of function

• time_dependent – include time as a dimension

sumpy.expansion.diff_op.as_scalar_pde(pde, vec_idx)

Returns a scalar PDE that is satisfied by the vec_idx component of pde.

Parameters

• pde – An instance of LinearPDESystemOperator

• vec_idx – the index of the vector-valued function that we want as a scalar PDE

Local Expansions

class sumpy.expansion.local.VolumeTaylorLocalExpansion(kernel, order, use_rscale=None)

class sumpy.expansion.local.H2DLocalExpansion(kernel, order, use_rscale=None)

class sumpy.expansion.local.Y2DLocalExpansion(kernel, order, use_rscale=None)

class sumpy.expansion.local.LineTaylorLocalExpansion(kernel, order, use_rscale=None)

Multipole Expansions

class sumpy.expansion.multipole.VolumeTaylorMultipoleExpansion(kernel, order, use_rscale=None)

class sumpy.expansion.multipole.H2DMultipoleExpansion(kernel, order, use_rscale=None)

class sumpy.expansion.multipole.Y2DMultipoleExpansion(kernel, order, use_rscale=None)