pymor.discretizers.builtin.grids.referenceelements

Module Contents

class pymor.discretizers.builtin.grids.referenceelements.Line

Bases: pymor.discretizers.builtin.grids.interfaces.ReferenceElement

Defines a reference element.

All reference elements have the property that all subentities of a given codimension are of the same type. I.e. a three-dimensional reference element cannot have triangles and rectangles as faces at the same time.

dim

The dimension of the reference element

volume

The volume of the reference element

Methods

center	Coordinates of the barycenter.
mapped_diameter	Return the diameter after transformation.
quadrature	Return quadrature points and weights.
quadrature_info	Return quadrature information.
size	Number of subentities of codimension codim.
sub_reference_element	Returns the reference element of the codim-codim subentities.
subentities	Return subentities.
subentity_embedding	Return subentity embedding.
unit_outer_normals	retval[e] is the unit outer-normal vector to the codim-1 subentity with index e.

center()

Coordinates of the barycenter.

mapped_diameter(A)

Return the diameter after transformation.

The diameter of the reference element after transforming it with the matrix A (vectorized).

quadrature(order=None, npoints=None, quadrature_type='default')

Return quadrature points and weights.

Returns tuple (P, W) where P is an array of quadrature points with corresponding weights W.

The quadrature is of order order or has npoints integration points.

quadrature_info()

Return quadrature information.

Returns a tuple of dicts (O, N) where O[quadrature_type] is a list of orders which are implemented for quadrature_type and N[quadrature_type] is a list of the corresponding numbers of integration points.

size(codim)

Number of subentities of codimension codim.

sub_reference_element(codim)

Returns the reference element of the codim-codim subentities.

subentities(codim, subentity_codim)

Return subentities.

subentities(c,sc)[i,j] is, with respect to the indexing inside the reference element, the index of the j-th codim-subentity_codim subentity of the i-th codim-codim subentity of the reference element.

subentity_embedding(subentity_codim)

Return subentity embedding.

Returns a tuple (A, B) which defines the embedding of the codim-subentity_codim subentities into the reference element.

For subentity_codim > 1', the embedding is by default given recursively via `subentity_embedding(subentity_codim - 1) and sub_reference_element(subentity_codim - 1).subentity_embedding(1) choosing always the superentity with smallest index.

unit_outer_normals()

retval[e] is the unit outer-normal vector to the codim-1 subentity with index e.

class pymor.discretizers.builtin.grids.referenceelements.Point

Bases: pymor.discretizers.builtin.grids.interfaces.ReferenceElement

Defines a reference element.

All reference elements have the property that all subentities of a given codimension are of the same type. I.e. a three-dimensional reference element cannot have triangles and rectangles as faces at the same time.

dim

The dimension of the reference element

volume

The volume of the reference element

Methods

center	Coordinates of the barycenter.
mapped_diameter	Return the diameter after transformation.
quadrature	Return quadrature points and weights.
quadrature_info	Return quadrature information.
size	Number of subentities of codimension codim.
sub_reference_element	Returns the reference element of the codim-codim subentities.
subentities	Return subentities.
subentity_embedding	Return subentity embedding.
unit_outer_normals	retval[e] is the unit outer-normal vector to the codim-1 subentity with index e.

center()

Coordinates of the barycenter.

mapped_diameter(A)

Return the diameter after transformation.

The diameter of the reference element after transforming it with the matrix A (vectorized).

quadrature(order=None, npoints=None, quadrature_type='default')

Return quadrature points and weights.

Returns tuple (P, W) where P is an array of quadrature points with corresponding weights W.

The quadrature is of order order or has npoints integration points.

quadrature_info()

Return quadrature information.

Returns a tuple of dicts (O, N) where O[quadrature_type] is a list of orders which are implemented for quadrature_type and N[quadrature_type] is a list of the corresponding numbers of integration points.

size(codim)

Number of subentities of codimension codim.

sub_reference_element(codim)

Returns the reference element of the codim-codim subentities.

subentities(codim, subentity_codim)

Return subentities.

subentities(c,sc)[i,j] is, with respect to the indexing inside the reference element, the index of the j-th codim-subentity_codim subentity of the i-th codim-codim subentity of the reference element.

subentity_embedding(subentity_codim)

Return subentity embedding.

Returns a tuple (A, B) which defines the embedding of the codim-subentity_codim subentities into the reference element.

For subentity_codim > 1', the embedding is by default given recursively via `subentity_embedding(subentity_codim - 1) and sub_reference_element(subentity_codim - 1).subentity_embedding(1) choosing always the superentity with smallest index.

unit_outer_normals()

retval[e] is the unit outer-normal vector to the codim-1 subentity with index e.

class pymor.discretizers.builtin.grids.referenceelements.Square

Bases: pymor.discretizers.builtin.grids.interfaces.ReferenceElement

Defines a reference element.

All reference elements have the property that all subentities of a given codimension are of the same type. I.e. a three-dimensional reference element cannot have triangles and rectangles as faces at the same time.

dim

The dimension of the reference element

volume

The volume of the reference element

Methods

center	Coordinates of the barycenter.
mapped_diameter	Return the diameter after transformation.
quadrature	Return quadrature points and weights.
quadrature_info	Return quadrature information.
size	Number of subentities of codimension codim.
sub_reference_element	Returns the reference element of the codim-codim subentities.
subentities	Return subentities.
subentity_embedding	Return subentity embedding.
unit_outer_normals	retval[e] is the unit outer-normal vector to the codim-1 subentity with index e.

center()

Coordinates of the barycenter.

mapped_diameter(A)

Return the diameter after transformation.

The diameter of the reference element after transforming it with the matrix A (vectorized).

quadrature(order=None, npoints=None, quadrature_type='default')

Return quadrature points and weights.

Returns tuple (P, W) where P is an array of quadrature points with corresponding weights W.

The quadrature is of order order or has npoints integration points.

quadrature_info()

Return quadrature information.

Returns a tuple of dicts (O, N) where O[quadrature_type] is a list of orders which are implemented for quadrature_type and N[quadrature_type] is a list of the corresponding numbers of integration points.

size(codim)

Number of subentities of codimension codim.

sub_reference_element(codim)

Returns the reference element of the codim-codim subentities.

subentities(codim, subentity_codim)

Return subentities.

subentities(c,sc)[i,j] is, with respect to the indexing inside the reference element, the index of the j-th codim-subentity_codim subentity of the i-th codim-codim subentity of the reference element.

subentity_embedding(subentity_codim)

Return subentity embedding.

Returns a tuple (A, B) which defines the embedding of the codim-subentity_codim subentities into the reference element.

For subentity_codim > 1', the embedding is by default given recursively via `subentity_embedding(subentity_codim - 1) and sub_reference_element(subentity_codim - 1).subentity_embedding(1) choosing always the superentity with smallest index.

unit_outer_normals()

retval[e] is the unit outer-normal vector to the codim-1 subentity with index e.

class pymor.discretizers.builtin.grids.referenceelements.Triangle

Bases: pymor.discretizers.builtin.grids.interfaces.ReferenceElement

Defines a reference element.

All reference elements have the property that all subentities of a given codimension are of the same type. I.e. a three-dimensional reference element cannot have triangles and rectangles as faces at the same time.

dim

The dimension of the reference element

volume

The volume of the reference element

Methods

center	Coordinates of the barycenter.
mapped_diameter	Return the diameter after transformation.
quadrature	Return quadrature points and weights.
quadrature_info	Return quadrature information.
size	Number of subentities of codimension codim.
sub_reference_element	Returns the reference element of the codim-codim subentities.
subentities	Return subentities.
subentity_embedding	Return subentity embedding.
unit_outer_normals	retval[e] is the unit outer-normal vector to the codim-1 subentity with index e.

center()

Coordinates of the barycenter.

mapped_diameter(A)

Return the diameter after transformation.

The diameter of the reference element after transforming it with the matrix A (vectorized).

quadrature(order=None, npoints=None, quadrature_type='default')

Return quadrature points and weights.

Returns tuple (P, W) where P is an array of quadrature points with corresponding weights W.

The quadrature is of order order or has npoints integration points.

quadrature_info()

Return quadrature information.

Returns a tuple of dicts (O, N) where O[quadrature_type] is a list of orders which are implemented for quadrature_type and N[quadrature_type] is a list of the corresponding numbers of integration points.

size(codim)

Number of subentities of codimension codim.

sub_reference_element(codim)

Returns the reference element of the codim-codim subentities.

subentities(codim, subentity_codim)

Return subentities.

subentities(c,sc)[i,j] is, with respect to the indexing inside the reference element, the index of the j-th codim-subentity_codim subentity of the i-th codim-codim subentity of the reference element.

subentity_embedding(subentity_codim)

Return subentity embedding.

Returns a tuple (A, B) which defines the embedding of the codim-subentity_codim subentities into the reference element.

For subentity_codim > 1', the embedding is by default given recursively via `subentity_embedding(subentity_codim - 1) and sub_reference_element(subentity_codim - 1).subentity_embedding(1) choosing always the superentity with smallest index.

unit_outer_normals()

retval[e] is the unit outer-normal vector to the codim-1 subentity with index e.

pymor.discretizers.builtin.grids.referenceelements.line

pymor.discretizers.builtin.grids.referenceelements.point

pymor.discretizers.builtin.grids.referenceelements.square

pymor.discretizers.builtin.grids.referenceelements.triangle