pymor.grids package

Submodules

_unstructured module

boundaryinfos module

class pymor.grids.boundaryinfos.AllDirichletBoundaryInfo(grid)[source]

Bases: pymor.grids.interfaces.BoundaryInfoInterface

BoundaryInfo where the boundary type ‘dirichlet’ is attached to each boundary entity.

Methods

AllDirichletBoundaryInfo mask
BoundaryInfoInterface check_boundary_types, dirichlet_boundaries, dirichlet_mask, neumann_boundaries, neumann_mask, no_boundary_type_mask, robin_boundaries, robin_mask, unique_boundary_type_mask
CacheableInterface cached_method_call, disable_caching, enable_caching
ImmutableInterface generate_sid, with_, __setattr__
BasicInterface disable_logging, enable_logging, has_interface_name, implementor_names, implementors

Attributes

BoundaryInfoInterface boundary_types, cache_region, has_dirichlet, has_neumann, has_robin
CacheableInterface sid_ignore
ImmutableInterface add_with_arguments, sid, with_arguments
BasicInterface logger, logging_disabled, name, uid
class pymor.grids.boundaryinfos.BoundaryInfoFromIndicators(grid, indicators, assert_unique_type=None, assert_some_type=None)[source]

Bases: pymor.grids.interfaces.BoundaryInfoInterface

BoundaryInfo where the boundary types are determined by indicator functions.

Parameters

grid
The Grid to which the BoundaryInfo is associated.
indicators
Dict where each key is a boundary type and the corresponding value is a boolean valued function defined on the analytical domain which indicates if a point belongs to a boundary of the given boundary type (the indicator functions must be vectorized).

Methods

BoundaryInfoFromIndicators mask
BoundaryInfoInterface check_boundary_types, dirichlet_boundaries, dirichlet_mask, neumann_boundaries, neumann_mask, no_boundary_type_mask, robin_boundaries, robin_mask, unique_boundary_type_mask
CacheableInterface cached_method_call, disable_caching, enable_caching
ImmutableInterface generate_sid, with_, __setattr__
BasicInterface disable_logging, enable_logging, has_interface_name, implementor_names, implementors

Attributes

BoundaryInfoInterface boundary_types, cache_region, has_dirichlet, has_neumann, has_robin
CacheableInterface sid_ignore
ImmutableInterface add_with_arguments, sid, with_arguments
BasicInterface logger, logging_disabled, name, uid
class pymor.grids.boundaryinfos.EmptyBoundaryInfo(grid)[source]

Bases: pymor.grids.interfaces.BoundaryInfoInterface

BoundaryInfo with no boundary types attached to any boundary.

Methods

EmptyBoundaryInfo mask
BoundaryInfoInterface check_boundary_types, dirichlet_boundaries, dirichlet_mask, neumann_boundaries, neumann_mask, no_boundary_type_mask, robin_boundaries, robin_mask, unique_boundary_type_mask
CacheableInterface cached_method_call, disable_caching, enable_caching
ImmutableInterface generate_sid, with_, __setattr__
BasicInterface disable_logging, enable_logging, has_interface_name, implementor_names, implementors

Attributes

BoundaryInfoInterface boundary_types, cache_region, has_dirichlet, has_neumann, has_robin
CacheableInterface sid_ignore
ImmutableInterface add_with_arguments, sid, with_arguments
BasicInterface logger, logging_disabled, name, uid
class pymor.grids.boundaryinfos.SubGridBoundaryInfo(subgrid, grid, grid_boundary_info, new_boundary_type=None)[source]

Bases: pymor.grids.interfaces.BoundaryInfoInterface

Derives a BoundaryInfo for a SubGrid.

Parameters

subrid
The SubGrid for which a BoundaryInfo is created.
grid
The parent Grid.
grid_boundary_info
The BoundaryInfo of the parent Grid from which to derive the BoundaryInfo
new_boundary_type
The boundary type which is assigned to the new boundaries of subgrid. If None, no boundary type is assigned.

Methods

SubGridBoundaryInfo mask
BoundaryInfoInterface check_boundary_types, dirichlet_boundaries, dirichlet_mask, neumann_boundaries, neumann_mask, no_boundary_type_mask, robin_boundaries, robin_mask, unique_boundary_type_mask
CacheableInterface cached_method_call, disable_caching, enable_caching
ImmutableInterface generate_sid, with_, __setattr__
BasicInterface disable_logging, enable_logging, has_interface_name, implementor_names, implementors

Attributes

BoundaryInfoInterface boundary_types, cache_region, has_dirichlet, has_neumann, has_robin
CacheableInterface sid_ignore
ImmutableInterface add_with_arguments, sid, with_arguments
BasicInterface logger, logging_disabled, name, uid

constructions module

pymor.grids.constructions.flatten_grid(grid)[source]

This method is used by our visualizers to render n-dimensional grids which cannot be embedded into R^n by duplicating vertices which would have to be mapped to multiple points at once (think of grids on rectangular domains with identified edges).

Parameters

grid
The Grid to flatten.

Returns

subentities
The subentities(0, grid.dim) relation for the flattened grid.
coordinates
The coordinates of the codim-grid.dim entities.
entity_map
Maps the indices of the codim-grid.dim entities of the flattened grid to the indices of the corresponding entities in the original grid.

defaultimpl module

class pymor.grids.defaultimpl.AffineGridDefaultImplementations[source]

Bases: object

Provides default implementations for AffineGrids.

class pymor.grids.defaultimpl.ConformalTopologicalGridDefaultImplementations[source]

Bases: object

Provides default informations for ConformalTopologicalGrids.

class pymor.grids.defaultimpl.ReferenceElementDefaultImplementations[source]

Bases: object

Provides default implementations for ReferenceElements.

gmsh module

class pymor.grids.gmsh.GmshBoundaryInfo(grid, sections)[source]

Bases: pymor.grids.interfaces.BoundaryInfoInterface

BoundaryInfo for a GmshGrid.

Parameters

grid
The corresponding GmshGrid.
sections
Parsed sections of the MSH-file as returned by load_gmsh.

Methods

GmshBoundaryInfo mask
BoundaryInfoInterface check_boundary_types, dirichlet_boundaries, dirichlet_mask, neumann_boundaries, neumann_mask, no_boundary_type_mask, robin_boundaries, robin_mask, unique_boundary_type_mask
CacheableInterface cached_method_call, disable_caching, enable_caching
ImmutableInterface generate_sid, with_, __setattr__
BasicInterface disable_logging, enable_logging, has_interface_name, implementor_names, implementors

Attributes

BoundaryInfoInterface boundary_types, cache_region, has_dirichlet, has_neumann, has_robin
CacheableInterface sid_ignore
ImmutableInterface add_with_arguments, sid, with_arguments
BasicInterface logger, logging_disabled, name, uid
class pymor.grids.gmsh.GmshGrid(sections)[source]

Bases: pymor.grids.unstructured.UnstructuredTriangleGrid

An UnstructuredTriangleGrid built from an existing Gmsh MSH-file.

Parameters

sections
Parsed sections of the MSH-file as returned by load_gmsh.

Methods

UnstructuredTriangleGrid embeddings, size, subentities, visualize
AffineGridInterface bounding_box, centers, diameters, integration_elements, jacobian_inverse_transposed, quadrature_points, unit_outer_normals, volumes, volumes_inverse
ConformalTopologicalGridInterface boundaries, boundary_mask, neighbours, superentities, superentity_indices
CacheableInterface cached_method_call, disable_caching, enable_caching
ImmutableInterface generate_sid, with_, __setattr__
BasicInterface disable_logging, enable_logging, has_interface_name, implementor_names, implementors

Attributes

UnstructuredTriangleGrid dim, reference_element
ConformalTopologicalGridInterface cache_region
CacheableInterface sid_ignore
ImmutableInterface add_with_arguments, sid, with_arguments
BasicInterface logger, logging_disabled, name, uid
pymor.grids.gmsh.load_gmsh(gmsh_file)[source]

Parse a Gmsh file and create a corresponding GmshGrid and GmshBoundaryInfo.

Parameters

gmsh_file
File handle of the Gmsh MSH-file.

Returns

grid
The generated GmshGrid.
boundary_info
The generated GmshBoundaryInfo.

interfaces module

class pymor.grids.interfaces.AffineGridInterface[source]

Bases: pymor.grids.defaultimpl.AffineGridDefaultImplementations, pymor.grids.interfaces.ConformalTopologicalGridInterface

Topological grid with geometry where each codim-0 entity is affinely mapped to the same ReferenceElement.

The grid is completely determined via the subentity relation given by subentities and the embeddings given by embeddings. In addition, only size and reference_element have to be implemented. Cached default implementations for all other methods are provided by AffineGridDefaultImplementations.

Methods

AffineGridInterface bounding_box, centers, diameters, embeddings, integration_elements, jacobian_inverse_transposed, quadrature_points, reference_element, subentities, unit_outer_normals, volumes, volumes_inverse
ConformalTopologicalGridInterface boundaries, boundary_mask, neighbours, size, superentities, superentity_indices
CacheableInterface cached_method_call, disable_caching, enable_caching
ImmutableInterface generate_sid, with_, __setattr__
BasicInterface disable_logging, enable_logging, has_interface_name, implementor_names, implementors

Attributes

ConformalTopologicalGridInterface cache_region, dim
CacheableInterface sid_ignore
ImmutableInterface add_with_arguments, sid, with_arguments
BasicInterface logger, logging_disabled, name, uid
bounding_box()[source]

returns a (2, dim)-shaped array containing lower/upper bounding box coordinates.

centers(codim)[source]

retval[e] is the barycenter of the codim-codim entity with global index e.

diameters(codim)[source]

retval[e] is the diameter of the codim-codim entity with global index e.

embeddings(codim)[source]

Returns tuple (A, B) where A[e] and B[e] are the linear part and the translation part of the map from the reference element of e to e.

For codim > 0, we provide a default implementation by taking the embedding of the codim-1 parent entity e_0 of e with lowest global index and composing it with the subentity_embedding of e into e_0 determined by the reference element.

integration_elements(codim)[source]

retval[e] is given as sqrt(det(A^T*A)), where A = embeddings(codim)[0][e].

jacobian_inverse_transposed(codim)[source]

retval[e] is the transposed (pseudo-)inverse of the Jacobian of embeddings(codim)[e].

quadrature_points(codim, order=None, npoints=None, quadrature_type='default')[source]

retval[e] is an array of quadrature points in global coordinates for the codim-codim entity with global index e.

The quadrature is of order order or has npoints integration points. To integrate a function f over e one has to form

np.dot(f(quadrature_points(codim, order)[e]), reference_element(codim).quadrature(order)[1]) *
integration_elements(codim)[e].  # NOQA
reference_element(codim)[source]

The ReferenceElement of the codim-codim entities.

subentities(codim, subentity_codim)[source]

retval[e,s] is the global index of the s-th codim-subentity_codim subentity of the codim-codim entity with global index e.

The ordering of subentities(0, subentity_codim)[e] has to correspond, w.r.t. the embedding of e, to the local ordering inside the reference element.

For codim > 0, we provide a default implementation by calculating the subentities of e as follows:

  1. Find the codim-1 parent entity e_0 of e with minimal global index
  2. Lookup the local indices of the subentities of e inside e_0 using the reference element.
  3. Map these local indices to global indices using subentities(codim - 1, subentity_codim).

This procedures assures that subentities(codim, subentity_codim)[e] has the right ordering w.r.t. the embedding determined by e_0, which agrees with what is returned by embeddings(codim)

unit_outer_normals()[source]

retval[e,i] is the unit outer normal to the i-th codim-1 subentity of the codim-0 entitiy with global index e.

volumes(codim)[source]

retval[e] is the (dim-codim)-dimensional volume of the codim-codim entity with global index e.

volumes_inverse(codim)[source]

retval[e] = 1 / volumes(codim)[e].

class pymor.grids.interfaces.AffineGridWithOrthogonalCentersInterface[source]

Bases: pymor.grids.interfaces.AffineGridInterface

AffineGrid with an additional orthogonal_centers method.

Methods

AffineGridWithOrthogonalCentersInterface orthogonal_centers
AffineGridInterface bounding_box, centers, diameters, embeddings, integration_elements, jacobian_inverse_transposed, quadrature_points, reference_element, subentities, unit_outer_normals, volumes, volumes_inverse
ConformalTopologicalGridInterface boundaries, boundary_mask, neighbours, size, superentities, superentity_indices
CacheableInterface cached_method_call, disable_caching, enable_caching
ImmutableInterface generate_sid, with_, __setattr__
BasicInterface disable_logging, enable_logging, has_interface_name, implementor_names, implementors

Attributes

ConformalTopologicalGridInterface cache_region, dim
CacheableInterface sid_ignore
ImmutableInterface add_with_arguments, sid, with_arguments
BasicInterface logger, logging_disabled, name, uid
orthogonal_centers()[source]

retval[e] is a point inside the codim-0 entity with global index e such that the line segment from retval[e] to retval[e2] is always orthogonal to the codim-1 entity shared by the codim-0 entities with global index e and e2.

(This is mainly useful for gradient approximation in finite volume schemes.)

class pymor.grids.interfaces.BoundaryInfoInterface[source]

Bases: pymor.core.cache.CacheableInterface

Provides boundary types for the boundaries of a given ConformalTopologicalGrid.

For every boundary type and codimension a mask is provided, marking grid entities of the respective type and codimension by their global index.

Methods

BoundaryInfoInterface check_boundary_types, dirichlet_boundaries, dirichlet_mask, mask, neumann_boundaries, neumann_mask, no_boundary_type_mask, robin_boundaries, robin_mask, unique_boundary_type_mask
CacheableInterface cached_method_call, disable_caching, enable_caching
ImmutableInterface generate_sid, with_, __setattr__
BasicInterface disable_logging, enable_logging, has_interface_name, implementor_names, implementors

Attributes

BoundaryInfoInterface boundary_types, cache_region, has_dirichlet, has_neumann, has_robin
CacheableInterface sid_ignore
ImmutableInterface add_with_arguments, sid, with_arguments
BasicInterface logger, logging_disabled, name, uid
boundary_types

set of all boundary types the grid has.

mask(boundary_type, codim)[source]

retval[i] is True if the codim-codim entity of global index i is associated to the boundary type boundary_type.

no_boundary_type_mask(codim)[source]

retval[i] is True if the codim-codim entity of global index i is associated to no boundary type.

unique_boundary_type_mask(codim)[source]

retval[i] is True if the codim-codim entity of global index i is associated to one and only one boundary type.

class pymor.grids.interfaces.ConformalTopologicalGridInterface[source]

Bases: pymor.grids.defaultimpl.ConformalTopologicalGridDefaultImplementations, pymor.core.cache.CacheableInterface

A topological grid without hanging nodes.

The grid is completely determined via the subentity relation given by subentities. In addition, only size has to be implemented, cached default implementations for all other methods are provided by ConformalTopologicalGridDefaultImplementations.

Methods

ConformalTopologicalGridInterface boundaries, boundary_mask, neighbours, size, subentities, superentities, superentity_indices
CacheableInterface cached_method_call, disable_caching, enable_caching
ImmutableInterface generate_sid, with_, __setattr__
BasicInterface disable_logging, enable_logging, has_interface_name, implementor_names, implementors

Attributes

ConformalTopologicalGridInterface cache_region, dim
CacheableInterface sid_ignore
ImmutableInterface add_with_arguments, sid, with_arguments
BasicInterface logger, logging_disabled, name, uid
dim

The dimension of the grid.

boundaries(codim)[source]

Returns the global indices of all codim-codim boundary entities.

By definition, a codim-1 entity is a boundary entity if it has only one codim-0 superentity. For codim != 1, a codim-codim entity is a boundary entity if it has a codim-1 sub/super-entity.

boundary_mask(codim)[source]

retval[e] is true iff the codim-codim entity with global index e is a boundary entity.

By definition, a codim-1 entity is a boundary entity if it has only one codim-0 superentity. For codim != 1, a codim-codim entity is a boundary entity if it has a codim-1 sub/super-entity.

neighbours(codim, neighbour_codim, intersection_codim=None)[source]

retval[e,n] is the global index of the n-th codim-neighbour_codim entitiy of the codim-codim entity e that shares with e a subentity of codimension intersection_codim.

If intersection_codim == None, it is set to codim + 1 if codim == neighbour_codim and to min(codim, neighbour_codim) otherwise.

The default implementation is to compute the result from subentities(codim, intersection_codim) and superentities(intersection_codim, neihbour_codim).

size(codim)[source]

The number of entities of codimension codim.

subentities(codim, subentity_codim)[source]

retval[e,s] is the global index of the s-th codim-subentity_codim subentity of the codim-codim entity with global index e.

Only subentities(codim, codim+1) has to be implemented; a default implementation is provided which evaluates subentities(codim, subentity_codim) by computing the transitive closure of subentities(codim, codim+1).

superentities(codim, superentity_codim)[source]

retval[e,s] is the global index of the s-th codim-superentity_codim superentity of the codim-codim entity with global index e.

retval[e] is sorted by global index.

The default implementation is to compute the result from subentities(superentity_codim, codim).

superentity_indices(codim, superentity_codim)[source]

retval[e,s] is the local index of the codim-codim entity e in the codim-superentity_codim superentity superentities(codim, superentity_codim)[e,s].

class pymor.grids.interfaces.ReferenceElementInterface[source]

Bases: pymor.grids.defaultimpl.ReferenceElementDefaultImplementations, pymor.core.cache.CacheableInterface

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.

Methods

ReferenceElementInterface center, mapped_diameter, quadrature, quadrature_info, quadrature_types, size, sub_reference_element, subentities, subentity_embedding, unit_outer_normals, __call__
CacheableInterface cached_method_call, disable_caching, enable_caching
ImmutableInterface generate_sid, with_, __setattr__
BasicInterface disable_logging, enable_logging, has_interface_name, implementor_names, implementors

Attributes

ReferenceElementInterface cache_region, dim, volume
CacheableInterface sid_ignore
ImmutableInterface add_with_arguments, sid, with_arguments
BasicInterface logger, logging_disabled, name, uid
dim

The dimension of the reference element

volume

The volume of the reference element

__call__(codim)[source]

Returns the reference element of the codim-codim subentities.

center()[source]

Coordinates of the barycenter.

mapped_diameter(A)[source]

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

quadrature(order=None, npoints=None, quadrature_type='default')[source]

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()[source]

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)[source]

Number of subentities of codimension codim.

sub_reference_element(codim)[source]

Returns the reference element of the codim-codim subentities.

subentities(codim, subentity_codim)[source]

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)[source]

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()[source]

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

oned module

class pymor.grids.oned.OnedGrid(domain=(0, 1), num_intervals=4, identify_left_right=False)[source]

Bases: pymor.grids.interfaces.AffineGridWithOrthogonalCentersInterface

One-dimensional Grid on an interval.

Parameters

domain
Tuple (left, right) containing the left and right boundary of the domain.
num_intervals
The number of codim-0 entities.

Methods

OnedGrid bounding_box, embeddings, orthogonal_centers, size, subentities, visualize
AffineGridInterface centers, diameters, integration_elements, jacobian_inverse_transposed, quadrature_points, unit_outer_normals, volumes, volumes_inverse
ConformalTopologicalGridInterface boundaries, boundary_mask, neighbours, superentities, superentity_indices
CacheableInterface cached_method_call, disable_caching, enable_caching
ImmutableInterface generate_sid, with_, __setattr__
BasicInterface disable_logging, enable_logging, has_interface_name, implementor_names, implementors

Attributes

OnedGrid dim, reference_element
ConformalTopologicalGridInterface cache_region
CacheableInterface sid_ignore
ImmutableInterface add_with_arguments, sid, with_arguments
BasicInterface logger, logging_disabled, name, uid
visualize(U, codim=2, **kwargs)[source]

Visualize scalar data associated to the grid as a patch plot.

Parameters

U
NumPy array of the data to visualize. If U.dim == 2 and len(U) > 1, the data is visualized as a time series of plots. Alternatively, a tuple of NumPy arrays can be provided, in which case a subplot is created for each entry of the tuple. The lengths of all arrays have to agree.
codim
The codimension of the entities the data in U is attached to (either 0 or 2).
kwargs
See visualize_patch

rect module

class pymor.grids.rect.RectGrid(num_intervals=(2, 2), domain=([0, 0], [1, 1]), identify_left_right=False, identify_bottom_top=False)[source]

Bases: pymor.grids.interfaces.AffineGridWithOrthogonalCentersInterface

Basic implementation of a rectangular Grid on a rectangular domain.

The global face, edge and vertex indices are given as follows

x1
^
|

6--10---7--11---8
|       |       |
3   2   4   3   5
|       |       |
3---8---4---9---5
|       |       |
0   0   1   1   2
|       |       |
0---6---1---7---2  --> x0

Parameters

num_intervals
Tuple (n0, n1) determining a grid with n0 x n1 codim-0 entities.
domain
Tuple (ll, ur) where ll defines the lower left and ur the upper right corner of the domain.

Methods

RectGrid bounding_box, embeddings, global_to_structured, orthogonal_centers, size, structured_to_global, subentities, vertex_coordinates, visualize
AffineGridInterface centers, diameters, integration_elements, jacobian_inverse_transposed, quadrature_points, unit_outer_normals, volumes, volumes_inverse
ConformalTopologicalGridInterface boundaries, boundary_mask, neighbours, superentities, superentity_indices
CacheableInterface cached_method_call, disable_caching, enable_caching
ImmutableInterface generate_sid, with_, __setattr__
BasicInterface disable_logging, enable_logging, has_interface_name, implementor_names, implementors

Attributes

RectGrid dim, reference_element
ConformalTopologicalGridInterface cache_region
CacheableInterface sid_ignore
ImmutableInterface add_with_arguments, sid, with_arguments
BasicInterface logger, logging_disabled, name, uid
global_to_structured(codim)[source]

Returns an array which maps global codim-codim indices to structured indices.

I.e. if GTS = global_to_structured(codim) and STG = structured_to_global(codim), then STG[GTS[:, 0], GTS[:, 1]] == numpy.arange(size(codim)).

structured_to_global(codim)[source]

Returns an NumPy array which maps structured indices to global codim-codim indices.

In other words structured_to_global(codim)[i, j] is the global index of the i-th in x0-direction and j-th in x1-direction codim-codim entity of the grid.

vertex_coordinates(dim)[source]

Returns an array of the x_dim coordinates of the grid vertices.

I.e.

centers(2)[structured_to_global(2)[i, j]] == np.array([vertex_coordinates(0)[i], vertex_coordinates(1)[j]])
visualize(U, codim=2, **kwargs)[source]

Visualize scalar data associated to the grid as a patch plot.

Parameters

U
NumPy array of the data to visualize. If U.dim == 2 and len(U) > 1, the data is visualized as a time series of plots. Alternatively, a tuple of NumPy arrays can be provided, in which case a subplot is created for each entry of the tuple. The lengths of all arrays have to agree.
codim
The codimension of the entities the data in U is attached to (either 0 or 2).
kwargs
See visualize_patch

referenceelements module

class pymor.grids.referenceelements.Line[source]

Bases: pymor.grids.interfaces.ReferenceElementInterface

Methods

Line center, mapped_diameter, quadrature, quadrature_info, size, sub_reference_element, subentities, subentity_embedding, unit_outer_normals
ReferenceElementInterface quadrature_types, __call__
CacheableInterface cached_method_call, disable_caching, enable_caching
ImmutableInterface generate_sid, with_, __setattr__
BasicInterface disable_logging, enable_logging, has_interface_name, implementor_names, implementors

Attributes

Line dim, volume
ReferenceElementInterface cache_region
CacheableInterface sid_ignore
ImmutableInterface add_with_arguments, sid, with_arguments
BasicInterface logger, logging_disabled, name, uid
class pymor.grids.referenceelements.Point[source]

Bases: pymor.grids.interfaces.ReferenceElementInterface

Methods

Point center, mapped_diameter, quadrature, quadrature_info, size, sub_reference_element, subentities, subentity_embedding, unit_outer_normals
ReferenceElementInterface quadrature_types, __call__
CacheableInterface cached_method_call, disable_caching, enable_caching
ImmutableInterface generate_sid, with_, __setattr__
BasicInterface disable_logging, enable_logging, has_interface_name, implementor_names, implementors

Attributes

Point dim, volume
ReferenceElementInterface cache_region
CacheableInterface sid_ignore
ImmutableInterface add_with_arguments, sid, with_arguments
BasicInterface logger, logging_disabled, name, uid
class pymor.grids.referenceelements.Square[source]

Bases: pymor.grids.interfaces.ReferenceElementInterface

Methods

Square center, mapped_diameter, quadrature, quadrature_info, size, sub_reference_element, subentities, subentity_embedding, unit_outer_normals
ReferenceElementInterface quadrature_types, __call__
CacheableInterface cached_method_call, disable_caching, enable_caching
ImmutableInterface generate_sid, with_, __setattr__
BasicInterface disable_logging, enable_logging, has_interface_name, implementor_names, implementors

Attributes

Square dim, volume
ReferenceElementInterface cache_region
CacheableInterface sid_ignore
ImmutableInterface add_with_arguments, sid, with_arguments
BasicInterface logger, logging_disabled, name, uid
class pymor.grids.referenceelements.Triangle[source]

Bases: pymor.grids.interfaces.ReferenceElementInterface

Methods

Triangle center, mapped_diameter, quadrature, quadrature_info, size, sub_reference_element, subentities, subentity_embedding, unit_outer_normals
ReferenceElementInterface quadrature_types, __call__
CacheableInterface cached_method_call, disable_caching, enable_caching
ImmutableInterface generate_sid, with_, __setattr__
BasicInterface disable_logging, enable_logging, has_interface_name, implementor_names, implementors

Attributes

Triangle dim, volume
ReferenceElementInterface cache_region
CacheableInterface sid_ignore
ImmutableInterface add_with_arguments, sid, with_arguments
BasicInterface logger, logging_disabled, name, uid

subgrid module

class pymor.grids.subgrid.SubGrid(grid, entities)[source]

Bases: pymor.grids.interfaces.AffineGridInterface

A subgrid of a Grid.

Given a Grid and a list of codim-0 entities we construct the minimal subgrid of the grid, containing all the given entities.

Parameters

grid
Grid of which a subgrid is to be created.
entities
NumPy array of global indices of the codim-0 entities which are to be contained in the subgrid.

Methods

SubGrid embeddings, indices_from_parent_indices, parent_indices, size, subentities
AffineGridInterface bounding_box, centers, diameters, integration_elements, jacobian_inverse_transposed, quadrature_points, unit_outer_normals, volumes, volumes_inverse
ConformalTopologicalGridInterface boundaries, boundary_mask, neighbours, superentities, superentity_indices
CacheableInterface cached_method_call, disable_caching, enable_caching
ImmutableInterface generate_sid, with_, __setattr__
BasicInterface disable_logging, enable_logging, has_interface_name, implementor_names, implementors

Attributes

SubGrid parent_grid, reference_element
ConformalTopologicalGridInterface cache_region, dim
CacheableInterface sid_ignore
ImmutableInterface add_with_arguments, sid, with_arguments
BasicInterface logger, logging_disabled, name, uid
parent_grid

The Grid from which the subgrid was constructed. Subgrid only stores a weakref to the grid, so accessing this property might return None if the original grid has been destroyed.

indices_from_parent_indices(ind, codim)[source]

Maps a NumPy array of indicies of codim-codim entites of the parent grid to indicies of the subgrid.

Raises

ValueError
Not all provided indices correspond to entities contained in the subgrid.
parent_indices(codim)[source]

retval[e] is the index of the e-th codim-codim entity in the parent grid.

tria module

class pymor.grids.tria.TriaGrid(num_intervals=(2, 2), domain=([0, 0], [1, 1]), identify_left_right=False, identify_bottom_top=False)[source]

Bases: pymor.grids.interfaces.AffineGridWithOrthogonalCentersInterface

Basic implementation of a triangular grid on a rectangular domain.

The global face, edge and vertex indices are given as follows

6---------10----------7---------11----------8
| \                 / | \                 / |
|    22   10    18    |    23   11    19    |
|       \     /       |       \     /       |
3    14   11     6    4    15   12     7    5
|       /     \       |       /     \       |
|    14    2    26    |    15    3    27    |
| /                 \ | /                 \ |
3----------8----------4----------9----------5
| \                 / | \                 / |
|    20    8    16    |    21    9    17    |
|       \     /       |       \     /       |
0    12    9     4    1    13   10     5    2
|       /     \       |       /     \       |
|    12    0    24    |    13    1    25    |
| /                 \ | /                 \ |
0----------6----------1----------7----------2

Parameters

num_intervals
Tuple (n0, n1) determining a grid with n0 x n1 codim-0 entities.
domain
Tuple (ll, ur) where ll defines the lower left and ur the upper right corner of the domain.

Methods

TriaGrid bounding_box, embeddings, orthogonal_centers, size, subentities, visualize
AffineGridInterface centers, diameters, integration_elements, jacobian_inverse_transposed, quadrature_points, unit_outer_normals, volumes, volumes_inverse
ConformalTopologicalGridInterface boundaries, boundary_mask, neighbours, superentities, superentity_indices
CacheableInterface cached_method_call, disable_caching, enable_caching
ImmutableInterface generate_sid, with_, __setattr__
BasicInterface disable_logging, enable_logging, has_interface_name, implementor_names, implementors

Attributes

TriaGrid dim, reference_element
ConformalTopologicalGridInterface cache_region
CacheableInterface sid_ignore
ImmutableInterface add_with_arguments, sid, with_arguments
BasicInterface logger, logging_disabled, name, uid
visualize(U, codim=2, **kwargs)[source]

Visualize scalar data associated to the grid as a patch plot.

Parameters

U
NumPy array of the data to visualize. If U.dim == 2 and len(U) > 1, the data is visualized as a time series of plots. Alternatively, a tuple of NumPy arrays can be provided, in which case a subplot is created for each entry of the tuple. The lengths of all arrays have to agree.
codim
The codimension of the entities the data in U is attached to (either 0 or 2).
kwargs
See visualize_patch

unstructured module

class pymor.grids.unstructured.UnstructuredTriangleGrid(vertices, faces)[source]

Bases: pymor.grids.interfaces.AffineGridInterface

A generic unstructured, triangular grid.

Parameters

vertices
A (num_vertices, 2)-shaped NumPy array containing the coordinates of all vertices in the grid. The row numbers in the array will be the global indices of the given vertices (codim 2 entities).
faces
A (num_faces, 3)-shaped NumPy array containing the global indices of the vertices which define a given triangle in the grid. The row numbers in the array will be the global indices of the given triangles (codim 0 entities).

Methods

UnstructuredTriangleGrid embeddings, size, subentities, visualize
AffineGridInterface bounding_box, centers, diameters, integration_elements, jacobian_inverse_transposed, quadrature_points, unit_outer_normals, volumes, volumes_inverse
ConformalTopologicalGridInterface boundaries, boundary_mask, neighbours, superentities, superentity_indices
CacheableInterface cached_method_call, disable_caching, enable_caching
ImmutableInterface generate_sid, with_, __setattr__
BasicInterface disable_logging, enable_logging, has_interface_name, implementor_names, implementors

Attributes

UnstructuredTriangleGrid dim, reference_element
ConformalTopologicalGridInterface cache_region
CacheableInterface sid_ignore
ImmutableInterface add_with_arguments, sid, with_arguments
BasicInterface logger, logging_disabled, name, uid
visualize(U, codim=2, **kwargs)[source]

Visualize scalar data associated to the grid as a patch plot.

Parameters

U
NumPy array of the data to visualize. If U.dim == 2 and len(U) > 1, the data is visualized as a time series of plots. Alternatively, a tuple of NumPy arrays can be provided, in which case a subplot is created for each entry of the tuple. The lengths of all arrays have to agree.
codim
The codimension of the entities the data in U is attached to (either 0 or 2).
kwargs
See visualize_patch