pymor.discretizers.builtin.grids.referenceelements

Module Contents

Classes

Point	Defines a reference element.
Line	Defines a reference element.
Square	Defines a reference element.
Triangle	Defines a reference element.

Attributes

point
line
square
triangle

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

size(self, codim)

Number of subentities of codimension codim.

subentities(self, codim, subentity_codim)

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(self, subentity_codim)

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.

sub_reference_element(self, codim)

Returns the reference element of the codim-codim subentities.

unit_outer_normals(self)

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

center(self)

Coordinates of the barycenter.

mapped_diameter(self, A)

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

quadrature_info(self)

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.

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

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.

pymor.discretizers.builtin.grids.referenceelements.point

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

size(self, codim)

Number of subentities of codimension codim.

subentities(self, codim, subentity_codim)

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(self, subentity_codim)

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.

sub_reference_element(self, codim)

Returns the reference element of the codim-codim subentities.

unit_outer_normals(self)

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

center(self)

Coordinates of the barycenter.

mapped_diameter(self, A)

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

quadrature_info(self)

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.

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

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.

pymor.discretizers.builtin.grids.referenceelements.line

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

size(self, codim)

Number of subentities of codimension codim.

subentities(self, codim, subentity_codim)

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(self, subentity_codim)

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.

sub_reference_element(self, codim)

Returns the reference element of the codim-codim subentities.

unit_outer_normals(self)

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

center(self)

Coordinates of the barycenter.

mapped_diameter(self, A)

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

quadrature_info(self)

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.

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

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.

pymor.discretizers.builtin.grids.referenceelements.square

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

size(self, codim)

Number of subentities of codimension codim.

subentities(self, codim, subentity_codim)

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(self, subentity_codim)

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.

sub_reference_element(self, codim)

Returns the reference element of the codim-codim subentities.

unit_outer_normals(self)

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

center(self)

Coordinates of the barycenter.

mapped_diameter(self, A)

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

quadrature_info(self)

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.

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

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.

pymor.discretizers.builtin.grids.referenceelements.triangle