pygeon.discretizations.fem.mat_l2 module

Module for the discretizations of the matrix L2 space.

class pygeon.discretizations.fem.mat_l2.MatPwConstants(keyword='unitary_data')[source]

Bases: VecPwConstants

A class representing the discretization using matrix piecewise constant functions.

poly_order = 0

Polynomial degree of the basis functions

tensor_order = 2

Matrix-valued discretization

__init__(keyword='unitary_data')[source]

Initialize the matrix discretization class. The base discretization class is pg.PwConstants.

Parameters:

keyword (str) – The keyword for the matrix discretization class. Default is pg.UNITARY_DATA.

Returns:

None

class pygeon.discretizations.fem.mat_l2.MatPwLinears(keyword='unitary_data')[source]

Bases: VecPwLinears

A class representing the discretization using matrix piecewise linear functions.

poly_order = 1

Polynomial degree of the basis functions

tensor_order = 2

Matrix-valued discretization

__init__(keyword='unitary_data')[source]

Initialize the matrix discretization class. The base discretization class is pg.PwLinears.

Parameters:

keyword (str) – The keyword for the matrix discretization class. Default is pg.UNITARY_DATA.

Returns:

None

assemble_trace_matrix(sd)[source]

Assembles and returns the trace matrix for the matrix-valued piecewise linears.

Parameters:

sd (pg.Grid) – The grid.

Returns:

The trace matrix obtained from the discretization.

Return type:

sps.csc_array

assemble_asym_matrix(sd)[source]

Assembles and returns the asymmetry matrix for the matrix-valued piecewise linears.

Parameters:

sd (pg.Grid) – The grid.

Returns:

The asymmetry matrix obtained from the discretization.

Return type:

sps.csc_array

class pygeon.discretizations.fem.mat_l2.MatPwQuadratics(keyword='unitary_data')[source]

Bases: VecPwQuadratics

A class representing the discretization using matrix piecewise quadratic functions.

poly_order = 2

Polynomial degree of the basis functions

tensor_order = 2

Matrix-valued discretization

__init__(keyword='unitary_data')[source]

Initialize the matrix discretization class. The base discretization class is pg.PwQuadratics.

Parameters:

keyword (str) – The keyword for the matrix discretization class. Default is pg.UNITARY_DATA.

Returns:

None

assemble_trace_matrix(sd)[source]

Assembles and returns the trace matrix for the matrix-valued piecewise quadratics.

Parameters:

sd (pg.Grid) – The grid.

Returns:

The trace matrix obtained from the discretization.

Return type:

sps.csc_array

assemble_asym_matrix(sd)[source]

Assembles and returns the asymmetry matrix for the matrix-valued piecewise quadratics.

Parameters:

sd (pg.Grid) – The grid.

Returns:

The asymmetry matrix obtained from the discretization.

Return type:

sps.csc_array