Common infrastructure¶

exception meshmode.Error¶

exception meshmode.DataUnavailable¶

exception meshmode.FileExistsError¶

Mesh management¶

class meshmode.mesh.MeshElementGroup(order, vertex_indices, nodes, element_nr_base=None, node_nr_base=None, unit_nodes=None, dim=None)¶

A group of elements sharing a common reference element.

order¶

vertex_indices¶: An array (nelements, ref_element.nvertices) of (mesh-wide) vertex indices.

nodes¶: An array of node coordinates with shape (mesh.ambient_dim, nelements, nunit_nodes).

unit_nodes¶: (dim, nunit_nodes)

element_nr_base¶: Lowest element number in this element group.

node_nr_base¶: Lowest node number in this element group.

dim¶: The number of dimensions spanned by the element. Not the ambient dimension, see Mesh.ambient_dim for that.

face_vertex_indices()¶: Return a tuple of tuples indicating which vertices (in mathematically positive ordering) make up each face of an element in this group.

vertex_unit_coordinates()¶: Return an array of shape (nfaces, dim) with the unit coordinates of each vertex.

nfaces¶

__eq__(other)¶: Return self==value.

__ne__(other)¶: Return self!=value.

copy(**kwargs)¶

property dim

face_vertex_indices(): Return a tuple of tuples indicating which vertices (in mathematically positive ordering) make up each face of an element in this group.

join_mesh(element_nr_base, node_nr_base)¶

property nelements¶

property nfaces

property nnodes¶

property nunit_nodes¶

vertex_unit_coordinates(): Return an array of shape (nfaces, dim) with the unit coordinates of each vertex.

class meshmode.mesh.Mesh(vertices, groups, skip_tests=False, node_vertex_consistency_tolerance=None, skip_element_orientation_test=False, nodal_adjacency=None, facial_adjacency_groups=None, boundary_tags=None, vertex_id_dtype=<class 'numpy.int32'>, element_id_dtype=<class 'numpy.int32'>, is_conforming=None)¶

vertices¶: An array of vertex coordinates with shape (ambient_dim, nvertices)

groups¶: A list of MeshElementGroup instances.

nodal_adjacency¶

An instance of NodalAdjacency.

Referencing this attribute may raise meshmode.DataUnavailable.

facial_adjacency_groups¶

A list of mappings from neighbor group IDs to instances of FacialAdjacencyGroup.

facial_adjacency_groups[igrp][ineighbor_group] gives the set of facial adjacency relations between group igrp and ineighbor_group. ineighbor_group and igrp may be identical, or ineighbor_group may be None, in which case an :class:InterPartitionAdjacency group containing boundary faces is returned.

Referencing this attribute may raise meshmode.DataUnavailable.

For example for the mesh in the figure, the following data structure would be present:

[
    {...},  # connectivity for group 0
    {...},  # connectivity for group 1
    {...},  # connectivity for group 2
    {       # connectivity for group 3
        1: FacialAdjacencyGroup(...)  # towards group 1, green
        2: FacialAdjacencyGroup(...)  # towards group 2, pink
        None: FacialAdjacencyGroup(...)  # towards the boundary, orange
    }
]

(Note that element groups are not necessarily contiguous like the figure may suggest.)

boundary_tags¶: A tuple of boundary tag identifiers. BTAG_ALL and BTAG_REALLY_ALL are guranateed to exist.

btag_to_index¶: A mapping that maps boundary tag identifiers to their corresponding index.

vertex_id_dtype¶

element_id_dtype¶

is_conforming¶: True if it is known that all element interfaces are conforming. False if it is known that some element interfaces are non-conforming. None if neither of the two is known.

__eq__(other)¶: Return self==value.

__ne__(other)¶: Return self!=value.

property ambient_dim¶

boundary_tag_bit(boundary_tag)¶

property dim¶

face_id_dtype¶: alias of numpy.int8

property facial_adjacency_groups

get_copy_kwargs(**kwargs)¶

property nelements¶

property nodal_adjacency

nodal_adjacency_init_arg()¶: Returns an ‘nodal_adjacency’ argument that can be passed to a Mesh constructor.

property nvertices¶

class meshmode.mesh.NodalAdjacency(valuedict=None, exclude=None, **kwargs)¶

Describes nodal element adjacency information, i.e. information about elements that touch in at least one point.

neighbors_starts¶

element_id_t [nelements+1]

Use together with neighbors. neighbors_starts[iel] and neighbors_starts[iel+1] together indicate a ranges of element indices neighbors which are adjacent to iel.

neighbors¶

element_id_t []

See neighbors_starts.

__eq__(other)¶: Return self==value.

__ne__(other)¶: Return self!=value.

class meshmode.mesh.FacialAdjacencyGroup(valuedict=None, exclude=None, **kwargs)¶

Describes facial element adjacency information for one MeshElementGroup, i.e. information about elements that share (part of) a face.

Represents (for example) one of the (colored) interfaces between MeshElementGroup instances, or an interface between MeshElementGroup and a boundary. (Note that element groups are not necessarily contiguous like the figure may suggest.)

igroup¶

ineighbor_group¶: ID of neighboring group, or None for boundary faces. If identical to igroup, then this contains the self-connectivity in this group.

elements¶: element_id_t [nfagrp_elements]. elements[i] Group-local element numbers.

element_faces¶: face_id_t [nfagrp_elements]. element_faces[i] indicate what face index of the opposite element indicated in neighbors[iface] touches face number iface of element number iel_grp in this element group.

neighbors¶

element_id_t [nfagrp_elements]. neighbors[i] gives the element number within ineighbor_group of the element opposite elements[i].

If this number is negative, then this indicates that this is a boundary face, and the bits set in -neighbors[i] should be interpreted according to Mesh.boundary_tags.

neighbor_faces¶

face_id_t [nfagrp_elements]. neighbor_faces[i] indicate what face index of the opposite element indicated in neighbors[i] has facial contact with face number element_faces[i] of element number elements[i] in element group igroup.

Zero if neighbors[i] is negative.

__eq__(other)¶: Return self==value.

__ne__(other)¶: Return self!=value.

meshmode.mesh.as_python(mesh, function_name='make_mesh')¶: Return a snippet of Python code (as a string) that will recreate the mesh given as an input parameter.

meshmode.mesh.check_bc_coverage(mesh, boundary_tags, incomplete_ok=False, true_boundary_only=True)¶

Verify boundary condition coverage.

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

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

Parameters

incomplete_ok – Do not report an error if some faces are not covered by the boundary conditions.
true_boundary_only – only verify for faces tagged with BTAG_ALL.

meshmode.mesh.is_boundary_tag_empty(mesh, boundary_tag)¶: Return True if the corresponding boundary tag does not occur as part of mesh.

Predefined Boundary tags¶

class meshmode.mesh.BTAG_NONE¶: A boundary tag representing an empty boundary or volume.

class meshmode.mesh.BTAG_ALL¶

A boundary 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 meshmode.mesh.BTAG_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 meshmode.mesh.BTAG_NO_BOUNDARY¶: A boundary tag indicating that this edge should not fall under TAG_ALL. Among other things, this is used to keep rank boundaries out of BTAG_ALL.

class meshmode.mesh.BTAG_PARTITION(part_nr)¶

A boundary tag indicating that this edge is adjacent to an element of another Mesh. The partition number of the adjacent mesh is given by part_nr.

part_nr¶

New in version 2017.1.

Design of the Data Structure¶

Why does a `Mesh` need to be broken into `MeshElementGroup` instances?¶

Elements can be of different types (e.g. triangle, quadrilateral, tetrahedron, what have you). In addition, elements may vary in the polynomial degree used to represent them (see also below).

All these bits of information could in principle be stored by element, but having large, internally homogeneous groups is a good thing from an efficiency standpoint. (So that you can, e.g., launch one GPU kernel to deal with all order-3 triangles, instead of maybe having to dispatch based on type and size inside the kernel)

What is the difference between ‘vertices’ and ‘nodes’?¶

Nodes exist mainly to represent the (potentially non-affine) deformation of each element, by a one-to-one correspondence with MeshElementGroup.unit_nodes. They are unique to each element. Vertices on the other hand exist to clarify whether or not a point shared by two elements is actually identical (or just happens to be “close”). This is done by assigning (single, globally shared) vertex numbers and having elements refer to them.

Consider the following picture:

Mesh Data Structure¶

class meshmode.mesh.MeshElementGroup(order, vertex_indices, nodes, element_nr_base=None, node_nr_base=None, unit_nodes=None, dim=None)

A group of elements sharing a common reference element.

order

vertex_indices: An array (nelements, ref_element.nvertices) of (mesh-wide) vertex indices.

nodes: An array of node coordinates with shape (mesh.ambient_dim, nelements, nunit_nodes).

unit_nodes: (dim, nunit_nodes)

element_nr_base: Lowest element number in this element group.

node_nr_base: Lowest node number in this element group.

dim: The number of dimensions spanned by the element. Not the ambient dimension, see Mesh.ambient_dim for that.

face_vertex_indices(): Return a tuple of tuples indicating which vertices (in mathematically positive ordering) make up each face of an element in this group.

vertex_unit_coordinates(): Return an array of shape (nfaces, dim) with the unit coordinates of each vertex.

nfaces

__eq__(other): Return self==value.

__ne__(other): Return self!=value.

copy(**kwargs)

property dim

face_vertex_indices(): Return a tuple of tuples indicating which vertices (in mathematically positive ordering) make up each face of an element in this group.

join_mesh(element_nr_base, node_nr_base)

property nelements

property nfaces

property nnodes

property nunit_nodes

vertex_unit_coordinates(): Return an array of shape (nfaces, dim) with the unit coordinates of each vertex.

class meshmode.mesh.Mesh(vertices, groups, skip_tests=False, node_vertex_consistency_tolerance=None, skip_element_orientation_test=False, nodal_adjacency=None, facial_adjacency_groups=None, boundary_tags=None, vertex_id_dtype=<class 'numpy.int32'>, element_id_dtype=<class 'numpy.int32'>, is_conforming=None)

vertices: An array of vertex coordinates with shape (ambient_dim, nvertices)

groups: A list of MeshElementGroup instances.

nodal_adjacency

An instance of NodalAdjacency.

Referencing this attribute may raise meshmode.DataUnavailable.

facial_adjacency_groups

A list of mappings from neighbor group IDs to instances of FacialAdjacencyGroup.

facial_adjacency_groups[igrp][ineighbor_group] gives the set of facial adjacency relations between group igrp and ineighbor_group. ineighbor_group and igrp may be identical, or ineighbor_group may be None, in which case an :class:InterPartitionAdjacency group containing boundary faces is returned.

Referencing this attribute may raise meshmode.DataUnavailable.

For example for the mesh in the figure, the following data structure would be present:

[
    {...},  # connectivity for group 0
    {...},  # connectivity for group 1
    {...},  # connectivity for group 2
    {       # connectivity for group 3
        1: FacialAdjacencyGroup(...)  # towards group 1, green
        2: FacialAdjacencyGroup(...)  # towards group 2, pink
        None: FacialAdjacencyGroup(...)  # towards the boundary, orange
    }
]

(Note that element groups are not necessarily contiguous like the figure may suggest.)

boundary_tags: A tuple of boundary tag identifiers. BTAG_ALL and BTAG_REALLY_ALL are guranateed to exist.

btag_to_index: A mapping that maps boundary tag identifiers to their corresponding index.

vertex_id_dtype

element_id_dtype

is_conforming: True if it is known that all element interfaces are conforming. False if it is known that some element interfaces are non-conforming. None if neither of the two is known.

__eq__(other): Return self==value.

__ne__(other): Return self!=value.

property ambient_dim

boundary_tag_bit(boundary_tag)

property dim

face_id_dtype: alias of numpy.int8

property facial_adjacency_groups

get_copy_kwargs(**kwargs)

property nelements

property nodal_adjacency

nodal_adjacency_init_arg(): Returns an ‘nodal_adjacency’ argument that can be passed to a Mesh constructor.

property nvertices

Mesh generation¶

Curves¶

meshmode.mesh.generation.make_curve_mesh(curve_f, element_boundaries, order, unit_nodes=None, node_vertex_consistency_tolerance=None, return_parametrization_points=False)¶

Parameters

curve_f – A callable representing a parametrization for a curve, accepting a vector of point locations and returning an array of shape (2, npoints).
element_boundaries – a vector of element boundary locations in \([0,1]\), in order. 0 must be the first entry, 1 the last one.
unit_nodes – if given, the unit nodes to use. Must have shape (dim, nnoodes).

Returns

a meshmode.mesh.Mesh, or if return_parametrization_points is True, a tuple (mesh, par_points), where par_points is an array of parametrization points.

Curve parametrizations¶

meshmode.mesh.generation.ellipse(aspect_ratio, t)¶

Parameters: t – the parametrization, runs from [0,1)
Returns: an array of shape (2, npoints)

meshmode.mesh.generation.cloverleaf(t)¶

Parameters: t – the parametrization, runs from [0,1)
Returns: an array of shape (2, npoints)

meshmode.mesh.generation.starfish¶

meshmode.mesh.generation.drop(t)¶

Parameters: t – the parametrization, runs from [0,1)
Returns: an array of shape (2, npoints)

meshmode.mesh.generation.n_gon(n_corners, t)¶

Parameters: t – the parametrization, runs from [0,1)
Returns: an array of shape (2, npoints)

meshmode.mesh.generation.qbx_peanut(t)¶

meshmode.mesh.generation.apple(a, t)¶

Parameters

a – 0 <= a <= 1/2; roundedness: 0 returns a circle, 1/2 returns a cardioid
t – the parametrization, runs from [0,1)

Returns

an array of shape (2, npoints)

class meshmode.mesh.generation.WobblyCircle(coeffs)¶

static random(ncoeffs, seed)¶

__call__(t)¶

Parameters: t – the parametrization, runs from [0,1)
Returns: an array of shape (2, npoints)

Surfaces¶

meshmode.mesh.generation.generate_icosahedron(r, order)¶

meshmode.mesh.generation.generate_icosphere(r, order)¶

meshmode.mesh.generation.generate_torus(r_outer, r_inner, n_outer=20, n_inner=10, order=1)¶

meshmode.mesh.generation.refine_mesh_and_get_urchin_warper(order, m, n, est_rel_interp_tolerance, min_rad=0.2, uniform_refinement_rounds=0)¶

Returns

a tuple (refiner, warp_mesh), where refiner is a meshmode.refinement.Refiner (from which the unwarped mesh may be obtained), and whose meshmode.refinement.Refiner.get_current_mesh() returns a locally-refined meshmode.mesh.Mesh of a sphere and warp_mesh is a callable taking and returning a mesh that warps the unwarped mesh into a smooth shape govered by a spherical harmonic of order (m, n).

Parameters

order – the polynomial order of the returned mesh
est_rel_interp_tolerance – a tolerance for the relative interpolation error estimates on the warped version of the mesh.

meshmode.mesh.generation.generate_urchin(order, m, n, est_rel_interp_tolerance, min_rad=0.2)¶

Returns

a refined meshmode.mesh.Mesh of a smooth shape govered by a spherical harmonic of order (m, n).

Parameters

order – the polynomial order of the returned mesh
est_rel_interp_tolerance – a tolerance for the relative interpolation error estimates on the warped version of the mesh.

Volumes¶

meshmode.mesh.generation.generate_box_mesh(axis_coords, order=1, coord_dtype=<class 'numpy.float64'>, group_factory=None)¶

Create a semi-structured mesh.

Parameters

axis_coords – a tuple with a number of entries corresponding to the number of dimensions, with each entry a numpy array specifying the coordinates to be used along that axis.
group_factory – One of meshmode.mesh.SimplexElementGroup or meshmode.mesh.TensorProductElementGroup.

Changed in version 2017.1: group_factory parameter added.

meshmode.mesh.generation.generate_regular_rect_mesh(a=(0, 0), b=(1, 1), n=(5, 5), order=1)¶

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].

meshmode.mesh.generation.generate_warped_rect_mesh(dim, order, n)¶: Generate a mesh of a warped line/square/cube. Mainly useful for testing functionality with curvilinear meshes.

Mesh input/output¶

class meshmode.mesh.io.ScriptSource(source, extension)¶: New in version 2016.1.

class meshmode.mesh.io.FileSource(filename)¶: New in version 2014.1.

class meshmode.mesh.io.ScriptWithFilesSource(source, filenames, source_name='temp.geo')¶

New in version 2016.1.

source¶: The script code to be fed to gmsh.

filenames¶: The names of files to be copied to the temporary directory where gmsh is run.

meshmode.mesh.io.read_gmsh(filename, force_ambient_dim=None, mesh_construction_kwargs=None)¶

Read a gmsh mesh file from filename and return a meshmode.mesh.Mesh.

Parameters

force_ambient_dim – if not None, truncate point coordinates to this many dimensions.
mesh_construction_kwargs – None or a dictionary of keyword arguments passed to the meshmode.mesh.Mesh constructor.

meshmode.mesh.io.generate_gmsh(source, dimensions=None, order=None, other_options=[], extension='geo', gmsh_executable='gmsh', force_ambient_dim=None, output_file_name='output.msh', mesh_construction_kwargs=None, target_unit=None)¶

Run gmsh on the input given by source, and return a meshmode.mesh.Mesh based on the result.

Parameters

source – an instance of either FileSource or LiteralSource
force_ambient_dim – if not None, truncate point coordinates to this many dimensions.
mesh_construction_kwargs – None or a dictionary of keyword arguments passed to the meshmode.mesh.Mesh constructor.
target_unit – Value of the option Geometry.OCCTargetUnit. Supported values are the strings ‘M’ or ‘MM’.

meshmode.mesh.io.from_meshpy(mesh_info, order=1)¶: Imports a mesh from a meshpy mesh_info data structure, which may be generated by either meshpy.triangle or meshpy_tet.

meshmode.mesh.io.from_vertices_and_simplices(vertices, simplices, order=1, fix_orientation=False)¶

Imports a mesh from a numpy array of vertices and an array of simplices.

Parameters

vertices – An array of vertex coordinates with shape (ambient_dim, nvertices)
simplices – An array (nelements, nvertices) of (mesh-wide) vertex indices.

meshmode.mesh.io.to_json(mesh)¶: Return a JSON-able Python data structure for mesh. The structure directly reflects the Mesh data structure.

Mesh processing¶

meshmode.mesh.processing.find_group_indices(groups, meshwide_elems)¶

Parameters

groups – A list of :class:MeshElementGroup instances that contain meshwide_elems.
meshwide_elems – A :class:numpy.ndarray of mesh-wide element numbers Usually computed by elem + element_nr_base.

Returns

A :class:numpy.ndarray of group numbers that meshwide_elem belongs to.

meshmode.mesh.processing.partition_mesh(mesh, part_per_element, part_num)¶

Parameters

mesh – A meshmode.mesh.Mesh to be partitioned.
part_per_element – A numpy.ndarray containing one integer per element of mesh indicating which part of the partitioned mesh the element is to become a part of.
part_num – The part number of the mesh to return.

Returns

A tuple (part_mesh, part_to_global), where part_mesh is a meshmode.mesh.Mesh that is a partition of mesh, and part_to_global is a numpy.ndarray mapping element numbers on part_mesh to ones in mesh.

New in version 2017.1.

meshmode.mesh.processing.find_volume_mesh_element_orientations(mesh, tolerate_unimplemented_checks=False)¶

Return a positive floating point number for each positively oriented element, and a negative floating point number for each negatively oriented element.

Parameters: tolerate_unimplemented_checks – If True, elements for which no check is available will return NaN.

meshmode.mesh.processing.perform_flips(mesh, flip_flags, skip_tests=False)¶

Parameters: flip_flags – A numpy.ndarray with mesh.nelements entries indicating by their Boolean value whether the element is to be flipped.

meshmode.mesh.processing.find_bounding_box(mesh)¶

Returns: a tuple (min, max), each consisting of a numpy.ndarray indicating the minimal and maximal extent of the geometry along each axis.

meshmode.mesh.processing.merge_disjoint_meshes(meshes, skip_tests=False, single_group=False)¶

meshmode.mesh.processing.map_mesh(mesh, f)¶: Apply the map f to the mesh. f needs to accept and return arrays of shape (ambient_dim, npoints).

meshmode.mesh.processing.affine_map(mesh, A=None, b=None)¶: Apply the affine map f(x)=Ax+b to the geometry of mesh.

Mesh visualization¶

meshmode.mesh.visualization.draw_2d_mesh(mesh, draw_vertex_numbers=True, draw_element_numbers=True, draw_nodal_adjacency=False, draw_face_numbers=False, set_bounding_box=False, **kwargs)¶

meshmode.mesh.visualization.draw_curve(mesh, el_bdry_style='o', el_bdry_kwargs=None, node_style='x-', node_kwargs=None)¶

meshmode.mesh.visualization.write_vertex_vtk_file(mesh, file_name, compressor=None, overwrite=False)¶

meshmode.mesh.visualization.mesh_to_tikz(mesh)¶

Common infrastructure¶

Mesh management¶

Predefined Boundary tags¶

Design of the Data Structure¶

Why does a `Mesh` need to be broken into `MeshElementGroup` instances?¶

What is the difference between ‘vertices’ and ‘nodes’?¶

Mesh Data Structure¶

Mesh generation¶

Curves¶

Curve parametrizations¶

Surfaces¶

Volumes¶

Tools for Iterative Refinement¶

Mesh input/output¶

Mesh processing¶

Mesh refinement¶

Mesh visualization¶

meshmode

Navigation

Related Topics

Common infrastructure¶

Mesh management¶

Predefined Boundary tags¶

Design of the Data Structure¶

Why does a Mesh need to be broken into MeshElementGroup instances?¶

What is the difference between ‘vertices’ and ‘nodes’?¶

Mesh Data Structure¶

Mesh generation¶

Curves¶

Curve parametrizations¶

Surfaces¶

Volumes¶

Tools for Iterative Refinement¶

Mesh input/output¶

Mesh processing¶

Mesh refinement¶

Mesh visualization¶

Why does a `Mesh` need to be broken into `MeshElementGroup` instances?¶