Mesh Data Structure

Tags

class hedge.mesh.TAG_NONE

A boundary or volume tag representing an empty boundary or volume.

class hedge.mesh.TAG_ALL

A boundary or volume tag representing the entire boundary or volume.

In the case of the boundary, TAG_ALL does not include rank boundaries, or, more generally, anything tagged with TAG_NO_BOUNDARY.

class hedge.mesh.TAG_REALLY_ALL

A boundary tag representing the entire boundary.

Unlike TAG_ALL, this includes rank boundaries, or, more generally, everything tagged with TAG_NO_BOUNDARY.

class hedge.mesh.TAG_NO_BOUNDARY

A boundary tag indicating that this edge should not fall under TAG_ALL.

class hedge.mesh.TAG_RANK_BOUNDARY(rank)

A boundary tag indicating the boundary with a neighboring rank.

rank

Element Types

class hedge.mesh.Element

id

vertex_indices

bounding_box(vertices)

centroid(vertices)

map

inverse_map

face_normals

face_jacobians

Meshes

class hedge.mesh.Mesh(valuedict=None, exclude=[, 'self'], **kwargs)

Information about the geometry and connectivity of a finite element mesh. (Note: no information about the discretization is stored here.)

Variable points:  

list of Pylinear vectors of node coordinates

Variable elements:  

list of Element instances

Variable interfaces:  

a list of pairs:

((element instance 1, face index 1), (element instance 2, face index 2))

enumerating elements bordering one another. The relation “element 1 touches element 2” is always reflexive, but this list will only contain one entry per element pair.

Variable tag_to_boundary:  

a mapping of the form:

boundary_tag -> [(element instance, face index)])

The boundary tag TAG_NONE always refers to an empty boundary. The boundary tag TAG_ALL always refers to the entire boundary.

Variable tag_to_elements:  

a mapping of the form element_tag -> [element instances]

The element tag TAG_NONE always refers to an empty domain. The element tag TAG_ALL always refers to the entire domain.

Variable periodicity:  

A list of tuples (minus_tag, plus_tag) or None indicating the tags of the boundaries to be matched together as periodic. There is one tuple per axis, so that for example a 3D mesh has three tuples.

Variable periodic_opposite_faces:  

a mapping of the form:

(face_vertex_indices) ->

(opposite_face_vertex_indices), axis

This maps a face to its periodicity-induced opposite.

Variable periodic_opposite_vertices:  

a mapping of the form:

vertex_index -> [(opposite_vertex_index, axis), ...]

This maps one vertex to a list of its periodicity-induced opposites.

both_interfaces()

bounding_box()

dimensions

element_adjacency_graph()

Return a dictionary mapping each element id to a list of adjacent element ids.

class hedge.mesh.ConformalMesh

Bases: hedge.mesh.Mesh

A mesh whose elements’ faces exactly match up with one another.

See Mesh for attributes provided by this class.

__init__()

reordered_by()

reordered()

hedge.mesh.make_conformal_mesh(points, elements, boundary_tagger=None, element_tagger=None, periodicity=None, _is_rankbdry_face=None)

Construct a simplical mesh.

Face indices follow the convention for the respective element, such as Triangle or Tetrahedron, in this module.

Parameters:

• points – an iterable of vertex coordinates, given as vectors.
• elements – an iterable of tuples of indices into points, giving element endpoints.
• boundary_tagger – a function that takes the arguments (set_of_face_vertex_indices, element, face_number, all_vertices) It returns a list of tags that apply to this surface.
• element_tagger – a function that takes the arguments (element, all_vertices) and returns the a list of tags that apply to that element.
• periodicity – either None or is a list of tuples just like the one documented for the periodicity member of class Mesh.
• _is_rankbdry_face – an implementation detail, should not be used from user code. It is a function returning whether a given face identified by (element instance, face_nr) is cut by a parallel mesh partition.

hedge.mesh.check_bc_coverage(mesh, bc_tags, incomplete_ok=False)

Verify boundary condition coverage.

Given a list of boundary tags as bc_tags, this function verifies that

1. the union of all these boundaries gives the complete boundary, 1. all these boundaries are disjoint.

Parameter:incomplete_ok – Do not report an error if some faces are not covered by the boundary conditions.

Mesh Generation

1D Meshes

hedge.mesh.make_1d_mesh(points, left_tag=None, right_tag=None, periodic=False, boundary_tagger=None, element_tagger=None)

hedge.mesh.make_uniform_1d_mesh(a, b, el_count, left_tag=None, right_tag=None, periodic=False, boundary_tagger=None)

2D Meshes

hedge.mesh.make_regular_rect_mesh(a=(0, 0), b=(1, 1), n=(5, 5), periodicity=None, boundary_tagger=function)

Create a semi-structured rectangular mesh.

Parameters:

• a – the lower left hand point of the rectangle
• b – the upper right hand point of the rectangle
• n – a tuple of integers indicating the total number of points on [a,b].
• periodicity – either None, or a tuple of bools specifying whether the mesh is to be periodic in x and y.

hedge.mesh.make_centered_regular_rect_mesh(a=(0, 0), b=(1, 1), n=(5, 5), periodicity=None, post_refine_factor=1, boundary_tagger=function)

Create a semi-structured rectangular mesh.

Parameters:

• a – the lower left hand point of the rectangle
• b – the upper right hand point of the rectangle
• n – a tuple of integers indicating the total number of points on [a,b].
• periodicity – either None, or a tuple of bools specifying whether the mesh is to be periodic in x and y.

hedge.mesh.make_regular_square_mesh(a=-0.5, b=0.5, n=5, periodicity=None, boundary_tagger=function)

Create a semi-structured square mesh.

Parameters:

• a – the lower x and y coordinate of the square
• b – the upper x and y coordinate of the square
• n – integer indicating the total number of points on [a,b].
• periodicity – either None, or a tuple of bools specifying whether the mesh is to be periodic in x and y.

hedge.mesh.make_rect_mesh(a=(0, 0), b=(1, 1), max_area=None, boundary_tagger=function, periodicity=None, subdivisions=None, refine_func=None)

Create an unstructured rectangular mesh.

Parameters:

• a – the lower left hand point of the rectangle
• b – the upper right hand point of the rectangle
• max_area – maximum area of each triangle.
• periodicity – either None, or a tuple of bools specifying whether the mesh is to be periodic in x and y.
• subdivisions – If not None, this is a 2-tuple specifying the number of facet subdivisions in X and Y.
• refine_func – A refinement function as taken by meshpy.triangle.build().

hedge.mesh.make_regular_rect_mesh(a=(0, 0), b=(1, 1), n=(5, 5), periodicity=None, boundary_tagger=function)

Create a semi-structured rectangular mesh.

Parameters:

• a – the lower left hand point of the rectangle
• b – the upper right hand point of the rectangle
• n – a tuple of integers indicating the total number of points on [a,b].
• periodicity – either None, or a tuple of bools specifying whether the mesh is to be periodic in x and y.

hedge.mesh.make_square_mesh(a=-0.5, b=0.5, max_area=0.004, boundary_tagger=function)

Create an unstructured square mesh.

Parameters:

• a – the lower x and y coordinate of the square
• b – the upper x and y coordinate of the square
• max_area – maximum area of each triangle

hedge.mesh.make_disk_mesh(r=0.5, faces=50, max_area=0.004, boundary_tagger=function)

3D Meshes

hedge.mesh.make_ball_mesh(r=0.5, subdivisions=10, max_volume=None, boundary_tagger=function)

hedge.mesh.make_cylinder_mesh(radius=0.5, height=1, radial_subdivisions=10, height_subdivisions=1, max_volume=None, periodic=False, boundary_tagger=function)

hedge.mesh.make_box_mesh(a=(0, 0, 0), b=(1, 1, 1), max_volume=None, periodicity=None, boundary_tagger=function, return_meshpy_mesh=False)

Return a mesh for a brick from the origin to dimensions.

max_volume specifies the maximum volume for each tetrahedron. periodicity is either None, or a triple of bools, indicating whether periodic BCs are to be applied along that axis. See make_conformal_mesh() for the meaning of boundary_tagger.

A few stock boundary tags are provided for easy application of boundary conditions, namely plus_[xyz] and minus_[xyz] tag the appropriate faces of the brick.