Common infrastructure¶

exception meshmode.Error¶

exception meshmode.DataUnavailable¶

exception meshmode.FileExistsError¶

Mesh management¶

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, **kwargs)¶

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.

is_affine¶: A bool flag that is True if the local-to-global parametrization of all the elements in the group is affine.

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.

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

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

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)¶

ambient_dim¶

dim¶

vertices¶: None or an array of vertex coordinates with shape (ambient_dim, nvertices). If None, vertices are not known for this mesh.

nvertices¶

groups¶: A list of MeshElementGroup instances.

nelements¶

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 InterPartitionAdjacencyGroup 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 geometrically contiguous like the figure may suggest.)

boundary_tags¶: A list of boundary tag identifiers. BTAG_ALL and BTAG_REALLY_ALL are guaranteed to exist.

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

Note

Elements of boundary_tags that do not cover any part of the boundary will not be keys in this dictionary.

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.

copy(**kwargs)¶

__eq__(other)¶: Return self==value.

__ne__(other)¶: Return self!=value.

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.

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

Describes boundary adjacency information of elements in one MeshElementGroup.

igroup¶: The group number of this group.

ineighbor_group¶: None for boundary faces.

elements¶: Group-local element numbers. Element element_id_dtype elements[i] and face face_id_dtype element_faces[i] is connected to neighbor element element_id_dtype partition_neighbors[i] with face face_id_dtype global_neighbor_faces[i]. The partition number it connects to is neighbor_partitions[i].

element_faces¶: face_id_dtype element_faces[i] gives the face of element_id_dtype elements[i] that is connected to partition_neighbors[i].

neighbors¶: Since this is a boundary, element_id_dtype neighbors[i] is interpreted as a boundary tag. -neighbors[i] should be interpreted according to :class:Mesh.boundary_tags.

partition_neighbors¶

element_id_dtype partition_neighbors[i] gives the volume element number within the neighboring partition of the element connected to element_id_dtype elements[i] (which is a boundary element index). Use ~meshmode.mesh.processing.find_group_indices to find the group that the element belongs to, then subtract element_nr_base to find the element of the group.

If partition_neighbors[i] is negative, elements[i] is on a true boundary and is not connected to any other :class:Mesh.

neighbor_faces¶

face_id_dtype global_neighbor_faces[i] gives face index within the neighboring partition of the face connected to element_id_dtype elements[i]

If neighbor_partitions[i] is negative, elements[i] is on a true boundary and is not connected to any other :class:Mesh.

neighbor_partitions¶

neighbor_partitions[i] gives the partition number that elements[i] is connected to.

If neighbor_partitions[i] is negative, elements[i] is on a true boundary and is not connected to any other :class:Mesh.

New in version 2017.1.

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, BTAG_ALL does not include rank boundaries, or, more generally, anything tagged with BTAG_NO_BOUNDARY.

In the case of a mesh representing an element-wise subset of another, BTAG_ALL does not include boundaries induced by taking the subset. Instead, these boundaries will be tagged with BTAG_INDUCED_BOUNDARY.

class meshmode.mesh.BTAG_REALLY_ALL¶

A boundary tag representing the entire boundary.

Unlike BTAG_ALL, this includes rank boundaries, or, more generally, everything tagged with BTAG_NO_BOUNDARY.

In the case of a mesh representing an element-wise subset of another, this tag includes boundaries induced by taking the subset, or, more generally, everything tagged with BTAG_INDUCED_BOUNDARY

class meshmode.mesh.BTAG_NO_BOUNDARY¶: A boundary tag indicating that this edge should not fall under BTAG_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.

class meshmode.mesh.BTAG_INDUCED_BOUNDARY¶: When a Mesh is created as an element-by-element subset of another (as, for example, when using the Firedrake interop features while passing restrict_to_boundary), boundaries may arise where there were none in the original mesh. This boundary tag is used to indicate such boundaries.

Mesh generation¶

Curves¶

meshmode.mesh.generation.make_curve_mesh(curve_f: Callable[[numpy.ndarray], numpy.ndarray], element_boundaries: numpy.ndarray, order: int, *, unit_nodes: Optional[numpy.ndarray] = None, node_vertex_consistency_tolerance: Optional[Union[float, bool]] = None, closed: bool = True, return_parametrization_points: bool = False)¶

Parameters

curve_f – 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.
order – order of the (simplex) elements. If unit_nodes is also provided, the orders should match.
unit_nodes – if given, the unit nodes to use. Must have shape (2, nnodes).
node_vertex_consistency_tolerance – passed to the Mesh constructor. If False, no checks are performed.
closed – if True, the curve is assumed closed and the first and last of the element_boundaries must match.
return_parametrization_points – if True, the parametrization points at which all the nodes in the mesh were evaluated are also returned.

Returns

a 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.circle(t: numpy.ndarray)¶

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

meshmode.mesh.generation.ellipse(aspect_ratio: float, t: numpy.ndarray)¶

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

meshmode.mesh.generation.cloverleaf(t: numpy.ndarray)¶

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

meshmode.mesh.generation.starfish¶

meshmode.mesh.generation.drop(t: numpy.ndarray)¶

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

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

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

meshmode.mesh.generation.qbx_peanut(t: numpy.ndarray)¶

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

meshmode.mesh.generation.apple(a: float, t: numpy.ndarray)¶

Parameters

a – roundness parameter in \([0, 1/2]\), where \(0\) gives a circle and \(1/2\) gives a cardioid.
t – the parametrization, runs from \([0, 1)\).

Returns

an array of shape (2, t.size).

class meshmode.mesh.generation.WobblyCircle(coeffs: numpy.ndarray)¶

static random(ncoeffs: int, seed: int)¶

__call__(t: numpy.ndarray)¶

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

class meshmode.mesh.generation.NArmedStarfish(n_arms: int, amplitude: float)¶

Inherits from WobblyCircle.

__call__(t: numpy.ndarray)¶

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

Surfaces¶

meshmode.mesh.generation.generate_icosahedron(r: float, order: int, *, node_vertex_consistency_tolerance: Optional[Union[float, bool]] = None, unit_nodes: Optional[numpy.ndarray] = None)¶

meshmode.mesh.generation.generate_icosphere(r: float, order: int, *, uniform_refinement_rounds: int = 0, node_vertex_consistency_tolerance: Optional[Union[float, bool]] = None, unit_nodes: Optional[numpy.ndarray] = None)¶

Parameters

r – radius of the sphere.
order – order of the (simplex) elements. If unit_nodes is also provided, the orders should match.
uniform_refinement_rounds – number of uniform refinement rounds to perform after the initial mesh was created.
node_vertex_consistency_tolerance – passed to the Mesh constructor. If False, no checks are performed.
unit_nodes – if given, the unit nodes to use. Must have shape (3, nnodes).

meshmode.mesh.generation.generate_torus(r_major: float, r_minor: float, n_major: int = 20, n_minor: int = 10, order: int = 1, node_vertex_consistency_tolerance: Optional[Union[float, bool]] = None, unit_nodes: Optional[numpy.ndarray] = None)¶

Generate a torus.

_images/torus.png — Shown: A torus with major circle (magenta) and minor circle (red). Source: https://commons.wikimedia.org/wiki/File:Torus_cycles.svg (public domain image by Krishnavedala).¶

The torus is obtained as the image of the parameter domain \((u, v) \in [0, 2\pi) \times [0, 2 \pi)\) under the map

\[\begin{split}\begin{align} x &= \cos(u) (r_\text{major} + r_\text{minor} \cos(v)) \\ y &= \sin(u) (r_\text{major} + r_\text{minor} \sin(v)) \\ z &= r_\text{minor} \sin(v) \end{align}\end{split}\]

where \(r_\text{major}\) and \(r_\text{minor}\) are the radii of the major and minor circles, respectively. The parameter domain is tiled with \(n_\text{major} \times n_\text{minor}\) contiguous rectangles, and then each rectangle is subdivided into two triangles.

Parameters

r_major – radius of the major circle.
r_minor – radius of the minor circle.
n_major – number of rectangles along major circle.
n_minor – number of rectangles along minor circle.
order – order of the (simplex) elements. If unit_nodes is also provided, the orders should match.
node_vertex_consistency_tolerance – passed to the Mesh constructor. If False, no checks are performed.
unit_nodes – if given, the unit nodes to use. Must have shape (3, nnodes).

Returns

a Mesh of a torus.

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

Parameters

order – order of the (simplex) elements.
m – order of the spherical harmonic \(Y^m_n\).
n – order of the spherical harmonic \(Y^m_n\).
est_rel_interp_tolerance – a tolerance for the relative interpolation error estimates on the warped version of the mesh.

Returns

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

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

Parameters

order – order of the (simplex) elements. If unit_nodes is also provided, the orders should match.
m – order of the spherical harmonic \(Y^m_n\).
n – order of the spherical harmonic \(Y^m_n\).
est_rel_interp_tolerance – a tolerance for the relative interpolation error estimates on the warped version of the mesh.

Returns

a refined Mesh of a smooth shape covered by a spherical harmonic of order \((m, n)\).

meshmode.mesh.generation.generate_surface_of_revolution(get_radius: Callable[[numpy.ndarray, numpy.ndarray], numpy.ndarray], height_discr: numpy.ndarray, angle_discr: numpy.ndarray, order: int, *, node_vertex_consistency_tolerance: Optional[Union[float, bool]] = None, unit_nodes: Optional[numpy.ndarray] = None)¶

Return a cylinder aligned with the “height” axis aligned with the Z axis.

Parameters

get_radius – A callable function that takes in a 1D array of heights and a 1D array of angles and returns a 1D array of radii.
height_discr – A discretization of [0, 2*pi).
angle_discr – A discretization of [0, 2*pi).
order – order of the (simplex) elements. If unit_nodes is also provided, the orders should match.
node_vertex_consistency_tolerance – passed to the Mesh constructor. If False, no checks are performed.
unit_nodes – if given, the unit nodes to use. Must have shape (3, nnodes).

Volumes¶

meshmode.mesh.generation.generate_box_mesh(axis_coords, order=1, coord_dtype=<class 'numpy.float64'>, group_cls=None, boundary_tag_to_face=None, mesh_type=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_cls – One of meshmode.mesh.SimplexElementGroup or meshmode.mesh.TensorProductElementGroup.
boundary_tag_to_face –
an optional dictionary for tagging boundaries. The keys correspond to custom boundary tags, with the values giving a list of the faces on which they should be applied in terms of coordinate directions (+x, -x, +y, -y, +z, -z, +w, -w).

For example:
```
boundary_tag_to_face={"bdry_1": ["+x", "+y"], "bdry_2": ["-x"]}
```
mesh_type –
In two dimensions with non-tensor-product elements, mesh_type may be set to "X" to generate this type of mesh:
```
_______
|\   /|
| \ / |
|  X  |
| / \ |
|/   \|
^^^^^^^
```
instead of the default:
```
_______
|\    |
| \   |
|  \  |
|   \ |
|    \|
^^^^^^^
```
Specifying a value other than None for all other mesh dimensionalities and element types is an error.

Changed in version 2017.1: group_factory parameter added.

Changed in version 2020.1: boundary_tag_to_face parameter added.

Changed in version 2020.3: group_factory deprecated and renamed to group_cls.

meshmode.mesh.generation.generate_regular_rect_mesh(a=(0, 0), b=(1, 1), *, nelements_per_axis=None, npoints_per_axis=None, order=1, boundary_tag_to_face=None, group_cls=None, mesh_type=None, n=None)¶

Create a semi-structured rectangular mesh with equispaced elements.

Parameters

a – the lower left hand point of the rectangle.
b – the upper right hand point of the rectangle.
nelements_per_axis – an optional tuple of integers indicating the number of elements along each axis.
npoints_per_axis – an optional tuple of integers indicating the number of points along each axis.
order – the mesh element order.
boundary_tag_to_face – an optional dictionary for tagging boundaries. See generate_box_mesh().
group_cls – see generate_box_mesh().
mesh_type – see generate_box_mesh().

Note

Specify only one of nelements_per_axis and npoints_per_axis.

meshmode.mesh.generation.generate_warped_rect_mesh(dim, order, *, nelements_side=None, npoints_side=None, group_cls=None, n=None)¶: Generate a mesh of a warped 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=None, 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 gmsh_interop.reader.FileSource or gmsh_interop.reader.ScriptSource
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 meshmode.mesh.Mesh data structure.

Mesh processing¶

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

Parameters

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

Returns

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

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

Parameters

mesh – A 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 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.flip_simplex_element_group(vertices, grp, grp_flip_flags)¶

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

Parameters: flip_flags – A numpy.ndarray with meshmode.mesh.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.split_mesh_groups(mesh, element_flags, return_subgroup_mapping=False)¶

Split all the groups in mesh according to the values of element_flags. The element flags are expected to be integers defining, for each group, how the elements are to be split into subgroups. For example, a single-group mesh with flags:

element_flags = [0, 0, 0, 42, 42, 42, 0, 0, 0, 41, 41, 41]

will create three subgroups. The integer flags need not be increasing or contiguous and can repeat across different groups (i.e. they are group-local).

Parameters: element_flags – a numpy.ndarray with nelements entries indicating how the elements in a group are to be split.
Returns: a Mesh where each group has been split according to flags in element_flags. If return_subgroup_mapping is True, it also returns a mapping of (group_index, subgroup) -> new_group_index.

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: Optional[Union[numbers.Real, numpy.ndarray]] = None, b: Optional[Union[numbers.Real, numpy.ndarray]] = None)¶: Apply the affine map \(f(x) = A x + b\) to the geometry of mesh.

meshmode.mesh.processing.rotate_mesh_around_axis(mesh, *, theta: numbers.Real, axis: Optional[numpy.ndarray] = None)¶

Rotate the mesh by theta radians around the axis axis.

Parameters: axis – a (not necessarily unit) vector. By default, the rotation is performed around the \(z\) axis.

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)¶

meshmode.mesh.visualization.vtk_visualize_mesh(actx, mesh, filename, vtk_high_order=True)¶

Common infrastructure¶

Mesh management¶

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¶

Predefined Boundary tags¶

Mesh generation¶

Curves¶

Curve parametrizations¶

Surfaces¶

Volumes¶

Tools for Iterative Refinement¶

Mesh input/output¶

Mesh processing¶

Mesh refinement¶

Mesh visualization¶

Common infrastructure¶

Mesh management¶

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¶

Predefined Boundary tags¶

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?¶