feec.derivatives#

Functions#

block_tostencil(M)

Convert a BlockLinearOperator that contains KroneckerStencilMatrix objects to a BlockLinearOperator that contains StencilMatrix objects

Classes#

Inheritance diagram of psydac.feec.derivatives

`Curl_3D`(Hcurl, Hdiv)	Curl operator in 3D.
`Derivative_1D`(H1, L2)	1D derivative.
`DiffOperator`(domain, codomain, matrix)
`DirectionalDerivativeOperator`(V, W, diffdir, *)	Represents a matrix-free derivative operator in a specific cardinal direction.
`Divergence_2D`(Hdiv, L2)	Divergence operator in 2D.
`Divergence_3D`(Hdiv, L2)	Divergence operator in 3D.
`Gradient_2D`(H1, Hcurl)	Gradient operator in 2D.
`Gradient_3D`(H1, Hcurl)	Gradient operator in 3D.
`ScalarCurl_2D`(Hcurl, L2)	Scalar curl operator in 2D: computes a scalar field from a vector field.
`VectorCurl_2D`(H1, Hdiv)	Vector curl operator in 2D: computes a vector field from a scalar field.

Details#

class DirectionalDerivativeOperator(V, W, diffdir, *, negative=False, transposed=False)[source]#

Bases: LinearOperator

Represents a matrix-free derivative operator in a specific cardinal direction. Can be negated and transposed.

Parameters:

VStencilVectorSpace: The domain of the operator. (or codomain if transposed)
WStencilVectorSpace: The codomain of the operator. (or domain, if transposed) Has to be compatible with the domain, i.e. it has to be equal to it, except for the differentiation direction.
diffdirint: The differentiation direction.
negativebool: If True, this operator is multiplied by -1 after execution. (if False, nothing happens)
transposedbool: If True, this operator represents the transposed derivative operator. Note that then V is the codomain and W is the domain.

property domain#: The domain of the linear operator - an element of Vectorspace

property codomain#: The codomain of the linear operator - an element of Vectorspace

property dtype#

dot(v, out=None)[source]#

Applies the derivative operator on the given StencilVector.

This operation will not allocate any temporary memory unless used in-place. (i.e. only if v is out)

Parameters:

vStencilVector: The input StencilVector. Has to be in the domain space.
outStencilVector | NoneType: The output StencilVector, or None. If given, it has to be in the codomain space.

Returns:

outStencilVector: Either a new allocation (if out is None), or a reference to the parameter out.

tokronstencil()[source]#

Converts this KroneckerDerivativeOperator into a KroneckerStencilMatrix.

Returns:

outKroneckerStencilMatrix: The resulting KroneckerStencilMatrix.

transpose(conjugate=False)[source]#

Transposes this operator. Creates and returns a new object.

Returns:

outDirectionalDerivativeOperator: The transposed operator.

toarray(**kwargs)[source]#

Transforms this operator into a dense matrix.

Returns:

outndarray: The resulting matrix.

tosparse(**kwargs)[source]#

Transforms this operator into a sparse matrix in COO format. Includes padding in both domain and codomain which is optional, if the domain is serial, but mandatory if the domain is parallel.

Parameters:

with_padsBool,optional: If true, then padding in domain and codomain direction is included. Enabled by default.

Returns:

outCOOMatrix: The resulting matrix.

copy()[source]#: Create an identical copy of this operator. Creates and returns a new object.

class DiffOperator(domain, codomain, matrix)[source]#

Bases: object

property matrix#

property domain#

property codomain#

class Derivative_1D(H1, L2)[source]#

Bases: DiffOperator

1D derivative.

Parameters:

H11D TensorFemSpace: Domain of derivative operator.
L21D TensorFemSpace: Codomain of derivative operator.

class Gradient_2D(H1, Hcurl)[source]#

Bases: DiffOperator

Gradient operator in 2D.

Parameters:

H12D TensorFemSpace: Domain of gradient operator.
Hcurl2D VectorFemSpace: Codomain of gradient operator.

class Gradient_3D(H1, Hcurl)[source]#

Bases: DiffOperator

Gradient operator in 3D.

Parameters:

H13D TensorFemSpace: Domain of gradient operator.
Hcurl3D VectorFemSpace: Codomain of gradient operator.

class ScalarCurl_2D(Hcurl, L2)[source]#

Bases: DiffOperator

Scalar curl operator in 2D: computes a scalar field from a vector field.

Parameters:

Hcurl2D VectorFemSpace: Domain of 2D scalar curl operator.
L22D TensorFemSpace: Codomain of 2D scalar curl operator.

class VectorCurl_2D(H1, Hdiv)[source]#

Bases: DiffOperator

Vector curl operator in 2D: computes a vector field from a scalar field. This is sometimes called the ‘rot’ operator.

Parameters:

H12D TensorFemSpace: Domain of 2D vector curl operator.
Hdiv2D VectorFemSpace: Codomain of 2D vector curl operator.

class Curl_3D(Hcurl, Hdiv)[source]#

Bases: DiffOperator

Curl operator in 3D.

Parameters:

Hcurl3D VectorFemSpace: Domain of 3D curl operator.
Hdiv3D VectorFemSpace: Codomain of 3D curl operator.

class Divergence_2D(Hdiv, L2)[source]#

Bases: DiffOperator

Divergence operator in 2D.

Parameters:

Hdiv2D VectorFemSpace: Domain of divergence operator.
L22D TensorFemSpace: Codomain of divergence operator.

class Divergence_3D(Hdiv, L2)[source]#

Bases: DiffOperator

Divergence operator in 3D.

Parameters:

Hdiv3D VectorFemSpace: Domain of divergence operator.
L23D TensorFemSpace: Codomain of divergence operator.

block_tostencil(M)[source]#: Convert a BlockLinearOperator that contains KroneckerStencilMatrix objects to a BlockLinearOperator that contains StencilMatrix objects