Mesh¶

`pynumgeo.mesh` ¶

Mesh container and conversions.

:mod:~pynumgeo.mesh.mesh — the container (:class:Mesh);
:mod:~pynumgeo.mesh.topology — node layout, shape functions and faces of numgeo's elements;
:mod:~pynumgeo.mesh.convert — node permutations from VTK/meshio, gmsh, Abaqus; choice of element types;
:mod:~pynumgeo.mesh.meshio_adapter, :mod:~pynumgeo.mesh.freecad_adapter — meshio and FreeCAD meshes (both optional dependencies, imported when used);
:mod:~pynumgeo.mesh.quality — element orientation (positive Jacobian).

`ImportedMesh(mesh, node_ids, element_ids, ignored=dict())` `dataclass` ¶

A mesh built from another format, with the maps back to the original numbering.

Attributes:

Name	Type	Description
`mesh`	`Mesh`	the numgeo mesh (node labels 1..n when built with `renumber=True`).
`node_ids`	`IntArray`	original id of numgeo node `i + 1` (meshio: point index; FreeCAD: node id).
`element_ids`	`IntArray`	original id of numgeo element `j + 1` in block order (meshio: cell index counted over all cell blocks; FreeCAD: element id).
`ignored`	`dict[str, int]`	cell types left out as lower-dimensional (boundary) cells and how many.

`ElementBlock(type, labels, connectivity, options=list(), comment=None)` `dataclass` ¶

Elements of one type. connectivity[i] are node labels of element labels[i] in numgeo order.

options holds further *Element options as read (e.g. ("BI-QUADRATIC", None)).

`ElementSet(name, kind='list', members=(lambda: np.zeros(0, dtype=np.int64))(), values=list(), internal=False, instance=None, comment=None)` `dataclass` ¶

Bases: _LabelSet

An element set (*Elset): element labels, or a query evaluated by numgeo.

`Mesh()` ¶

Nodes, element blocks, sets and surfaces of a deck (see module docstring).

`node_count` `property` ¶

Number of nodes.

`element_count` `property` ¶

Number of elements over all blocks.

`element_labels` `property` ¶

All element labels in block order.

`add_nodes(coords, labels=None)` ¶

Append nodes; labels default to the next numbers after the current maximum.

`add_elements(type, connectivity, labels=None, *, comment=None)` ¶

Append a block of elements of one type; labels default to the next numbers.

`add_nset(name, members, *, internal=False, comment=None)` ¶

Add a node set given by node labels.

`add_elset(name, members, *, internal=False, comment=None)` ¶

Add an element set given by element labels.

`add_surface(name, rows, type='element', *, comment=None)` ¶

Add a surface: element-based rows (elset, "F1") or node-based rows (nset,).

`nset(name)` ¶

First node set of that name (numgeo also uses the first one).

`elset(name)` ¶

First element set of that name.

`surface(name)` ¶

First surface of that name.

`find_nearest_node(point, candidates=None)` ¶

Label of the node nearest to point as numgeo's find does (first minimum wins).

`check()` ¶

Problems that make numgeo fail or compute wrong results (empty list = fine).

Checks: node labels 1..n in order, unique element labels, connectivity refers to existing nodes, every node used by an element.

`renumbered()` ¶

Copy with node labels 1..n and element labels 1..m (block order).

Returns:

Type	Description
`Mesh`	`(mesh, node_map, element_map)` where `node_map[i]` / `element_map[j]` are the original
`IntArray`	labels of new node `i+1` / element `j+1`.

`summary()` ¶

Counts and names, e.g. for agents (no arrays).

`NodeSet(name, kind='list', members=(lambda: np.zeros(0, dtype=np.int64))(), values=list(), internal=False, instance=None, comment=None)` `dataclass` ¶

Bases: _LabelSet

A node set (*Nset): node labels, or a query evaluated by numgeo (find and variants).

`Surface(name, type='element', rows=list(), comment=None)` `dataclass` ¶

A surface (*Surface).

type="element" rows are (elset, face), type="node" rows (nset,).

`key` `property` ¶

Name as numgeo compares it.

`Topology(name, shape, nnodes, dim, reference, corners, edges, face_centres, centre, vtk_type, meshio_type, source, _n)` `dataclass` ¶

Node layout of one numgeo element topology (independent of the formulation).

Attributes:

Name	Type	Description
`name`	`str`	pynumgeo name (`tri6`, `hex20` ...).
`shape`	`str`	numgeo element shape (`beam`, `triangular`, `rectangular`, `tetrahedral`, `hexahedral`).
`nnodes`	`int`	number of nodes.
`dim`	`int`	dimension of the reference element (1, 2 or 3).
`reference`	`tuple[tuple[float, ...], ...]`	reference coordinates of nodes 1..n in numgeo's natural coordinates (`[-1, 1]` for beam, rectangular and hexahedral shapes, the unit simplex for triangles and tetrahedra).
`corners`	`tuple[int, ...]`	local numbers (1-based) of the corner nodes.
`edges`	`tuple[tuple[int, ...], ...]`	`(a, b)` or `(a, b, mid)` per edge (1-based); for quadratic topologies edge k carries mid node `len(corners) + k`.
`face_centres`	`tuple[int, ...]`	mid-face nodes (hex27 only).
`centre`	`int \| None`	the interior node (quad9, hex27), else `None`.
`vtk_type`	`int`	VTK cell type with the same node layout.
`meshio_type`	`str`	meshio cell type name with the same node layout.
`source`	`str`	numgeo source lines of the shape functions that define the layout.

`order` `property` ¶

Polynomial order of the interpolation along an edge (1 or 2).

`mid_nodes` `property` ¶

All nodes that are not corners (1-based).

`centroid` `property` ¶

Reference coordinates of the element centre (where :mod:~pynumgeo.mesh.quality checks).

`reference_array()` ¶

:attr:reference as a (nnodes, dim) array.

`shape_functions(xi)` ¶

numgeo's shape functions N(1..n) at the natural coordinates xi.

topology("line3").shape_functions([0.0]).tolist() [-0.0, 0.0, 1.0]

`shape_derivatives(xi)` ¶

dN/dxi at xi as a (dim, nnodes) array (exact complex-step derivative of :meth:shape_functions).

topology("quad4").shape_derivatives([0.0, 0.0]).tolist() [[-0.25, 0.25, 0.25, -0.25], [-0.25, -0.25, 0.25, 0.25]]

`build_mesh(node_ids, coords, blocks, *, node_sets=None, element_sets=None, renumber=True, dim=None, ignored=None)` ¶

Build a :class:~pynumgeo.mesh.mesh.Mesh from nodes and element blocks with arbitrary ids.

Parameters:

Name	Type	Description	Default
`node_ids`	`ArrayLike`	original node ids (unique integers).	required
`coords`	`ArrayLike`	`(n, 2 or 3)` coordinates (already scaled to the deck's length unit).	required
`blocks`	`Sequence[tuple[str, ArrayLike, ArrayLike]]`	`(numgeo_type, connectivity, element_ids)`; connectivity in numgeo order with original node ids.	required
`node_sets`	`Mapping[str, ArrayLike] \| None`	name -> original node ids.	`None`
`element_sets`	`Mapping[str, ArrayLike] \| None`	name -> original element ids (of elements in `blocks`).	`None`
`renumber`	`bool`	`True`: keep only the nodes used by the elements and number nodes 1..n in the order of the original ids, elements 1..m in block order (what numgeo needs). `False`: keep all nodes and the original ids as labels (:meth:`Mesh.check` reports what numgeo would reject).	`True`
`dim`	`int \| None`	model dimension (2 or 3); default: the dimension of the element types. For a 2D model a third coordinate must be zero (it is dropped; numgeo ignores it with a warning, `read_nodes_.f90:115-121`).	`None`
`ignored`	`Mapping[str, int] \| None`	passed through to :attr:`ImportedMesh.ignored`.	`None`

Raises:

Type	Description
`ValueError`	unknown or unusable element types, a type that does not fit its cells, non-zero third coordinates in a 2D model, set members that are not part of the mesh.

`from_numgeo(convention, topology_name)` ¶

Inverse of :func:to_numgeo: connectivity_in_convention = numgeo_connectivity[:, q].

from_numgeo("abaqus", "line3").tolist() [0, 2, 1]

`numgeo_element_type(topology_name, dofs, *, ndim=None, axisymmetric=False, reduced=False, variant=None, stem=None, formulation=None)` ¶

The one numgeo element type (lower case, as pynumgeo writes it) for a topology and formulation.

Filters the catalogue as :func:element_type_candidates does; returns the single match.

Raises:

Type	Description
`ValueError`	if no or more than one library entry matches (the message lists the candidates and the tokens that tell them apart).

Examples:

>>> numgeo_element_type("tet10", ["U1", "U2", "U3"])
'u10-solid-3d'
>>> numgeo_element_type("quad4", ["U1", "U2"], variant=["SOLID"], axisymmetric=True, reduced=True)
'u4-solid-ax-red'
>>> numgeo_element_type("tri3", ["U1", "U2", "U3", "R1", "R2", "R3"], ndim=3)
'u3-shell'

`permute(connectivity, convention, topology_name)` ¶

Connectivity rows given in convention order, reordered to numgeo order.

`to_numgeo(convention, topology_name)` ¶

Permutation p (0-based) with numgeo_connectivity = connectivity[:, p].

Derived by matching the reference coordinates of convention with numgeo's (:func:reference_coordinates).

Parameters:

Name	Type	Description	Default
`convention`	`str`	`vtk`, `meshio` (= VTK), `gmsh`, `abaqus` or `numgeo` (identity).	required
`topology_name`	`str`	`line2` ... `hex27`.	required

to_numgeo("vtk", "hex27").tolist() == list(range(27)) True

`femmesh_import(femmesh, element_types, *, length_scale, renumber=True, groups=True, dim=None)` ¶

Like :func:mesh_from_femmesh, also returning the maps to FreeCAD's node and element ids.

`mesh_from_femmesh(femmesh, element_types, *, length_scale, renumber=True, groups=True, dim=None)` ¶

A numgeo mesh from a FreeCAD Fem::FemMesh.

Parameters:

Name	Type	Description	Default
`femmesh`	`FemMeshLike`	the FemMesh (see the module docstring for the API used).	required
`element_types`	`Mapping[str, str]`	topology (`tri6`, `tet10` ...; meshio names are accepted too) -> numgeo element type, e.g. `{"tet10": "u10-solid-3d"}`. Elements of lower dimension than the mapped ones (the edges and faces FreeCAD stores with a volume mesh) are left out.	required
`length_scale`	`float`	factor applied to FreeCAD's coordinates (mm): `1e-3` for a deck in m, `1.0` for a deck in mm. Required — there is no default unit conversion.	required
`renumber`	`bool`	nodes 1..n (in the order of FreeCAD's node ids, unused nodes dropped) and elements 1..m in block order (default); `False` keeps FreeCAD's ids as labels.	`True`
`groups`	`bool`	turn FemMesh groups into sets: node groups and the nodes of lower-dimensional groups become node sets, groups of mapped elements element sets.	`True`
`dim`	`int \| None`	model dimension; default from the element types. A 2D mesh must lie in the x-y plane (z = 0).	`None`

Raises:

Type	Description
`ValueError`	invalid `length_scale`, unmapped elements of the mesh dimension, wedges/pyramids, element types that do not fit the cells, a 2D mesh outside the x-y plane.

`mesh_from_meshio(m, element_types, *, renumber=True, convention='vtk', dim=None)` ¶

A numgeo mesh from a meshio.Mesh.

Parameters:

Name	Type	Description	Default
`m`	`Any`	the meshio mesh (anything with `points`, `cells` (`type`, `data`), optional `point_sets` and `cell_sets`).	required
`element_types`	`Mapping[str, str]`	meshio cell type (or pynumgeo topology name) -> numgeo element type, e.g. `{"triangle6": "u6p3-sat"}`; see :func:`pynumgeo.mesh.convert.numgeo_element_type`.	required
`renumber`	`bool`	drop unused points and label nodes 1..n / elements 1..m (default). With `False` every point is kept with label `index + 1` and elements are labelled `cell index + 1`.	`True`
`convention`	`str`	node order of the cells: `vtk` (meshio's own, default) or `abaqus` (meshio's Abaqus reader keeps Abaqus order) or `gmsh` (raw gmsh order).	`'vtk'`
`dim`	`int \| None`	model dimension; default from the element types. 2D models drop a zero third coordinate.	`None`

Raises:

Type	Description
`ValueError`	see :func:`pynumgeo.mesh.convert.build_mesh`; also for unmapped cells of the mesh dimension.

`mesh_to_meshio(mesh)` ¶

A meshio.Mesh (VTK node order) from a numgeo mesh, e.g. to write VTU/XDMF for inspection.

Node sets become point_sets and element sets cell_sets (list and generate sets; sets that numgeo evaluates itself — find, boundingbox, cylinder — cannot be represented and are left out with a warning). cell_data["numgeo:label"] holds the element labels. Surfaces are not converted.

Raises:

Type	Description
`KeyError`	for an element type that is not in the catalogue.

`meshio_import(m, element_types, *, renumber=True, convention='vtk', dim=None)` ¶

Like :func:mesh_from_meshio, also returning the maps to the meshio numbering.

ImportedMesh.node_ids[i] is the meshio point index of numgeo node i + 1; ImportedMesh.element_ids[j] the index of the cell counted over all cell blocks.

`element_faces(element_type)` ¶

The face table numgeo uses for element-based surfaces of an element type.

This is the catalogue's surface_face_topology of the element type (the selection of src/contacts/contact_.f90:553-610: 2D models by interpolation, 3D models by shape; triangles and quadrilaterals in 3D models are shells with the faces F1 (side of the normal) and F2).

`element_topology(element_type)` ¶

The topology of a numgeo element type (library name or alias, any case).

Raises:

Type	Description
`KeyError`	if the element type is not in the catalogue.

`face_connectivity(element_type, connectivity, face)` ¶

Global node labels of one face of each element (rows of connectivity in numgeo order).

Parameters:

Name	Type	Description	Default
`element_type`	`str`	numgeo element type of the rows.	required
`connectivity`	`ArrayLike`	`(n_elements, nnodes)` node labels in numgeo order.	required
`face`	`str \| int`	`"F1"` ... (or `"S1"` ..., or the number).	required

Returns:

Type	Description
`IntArray`	`(n_elements, n_face_nodes)` node labels in the order of numgeo's face table.

Mesh¶

pynumgeo.mesh ¶

ImportedMesh(mesh, node_ids, element_ids, ignored=dict()) dataclass ¶

ElementBlock(type, labels, connectivity, options=list(), comment=None) dataclass ¶

ElementSet(name, kind='list', members=(lambda: np.zeros(0, dtype=np.int64))(), values=list(), internal=False, instance=None, comment=None) dataclass ¶

Mesh() ¶

node_count property ¶

element_count property ¶

element_labels property ¶

add_nodes(coords, labels=None) ¶

add_elements(type, connectivity, labels=None, *, comment=None) ¶

add_nset(name, members, *, internal=False, comment=None) ¶

add_elset(name, members, *, internal=False, comment=None) ¶

add_surface(name, rows, type='element', *, comment=None) ¶

nset(name) ¶

elset(name) ¶

surface(name) ¶

find_nearest_node(point, candidates=None) ¶

check() ¶

renumbered() ¶

summary() ¶

NodeSet(name, kind='list', members=(lambda: np.zeros(0, dtype=np.int64))(), values=list(), internal=False, instance=None, comment=None) dataclass ¶

Surface(name, type='element', rows=list(), comment=None) dataclass ¶

key property ¶

Topology(name, shape, nnodes, dim, reference, corners, edges, face_centres, centre, vtk_type, meshio_type, source, _n) dataclass ¶

order property ¶

mid_nodes property ¶

centroid property ¶

reference_array() ¶

shape_functions(xi) ¶

shape_derivatives(xi) ¶

build_mesh(node_ids, coords, blocks, *, node_sets=None, element_sets=None, renumber=True, dim=None, ignored=None) ¶

from_numgeo(convention, topology_name) ¶

numgeo_element_type(topology_name, dofs, *, ndim=None, axisymmetric=False, reduced=False, variant=None, stem=None, formulation=None) ¶

permute(connectivity, convention, topology_name) ¶

to_numgeo(convention, topology_name) ¶

femmesh_import(femmesh, element_types, *, length_scale, renumber=True, groups=True, dim=None) ¶

mesh_from_femmesh(femmesh, element_types, *, length_scale, renumber=True, groups=True, dim=None) ¶

mesh_from_meshio(m, element_types, *, renumber=True, convention='vtk', dim=None) ¶

mesh_to_meshio(mesh) ¶

meshio_import(m, element_types, *, renumber=True, convention='vtk', dim=None) ¶

element_faces(element_type) ¶

element_topology(element_type) ¶

face_connectivity(element_type, connectivity, face) ¶

`pynumgeo.mesh` ¶

`ImportedMesh(mesh, node_ids, element_ids, ignored=dict())` `dataclass` ¶

`ElementBlock(type, labels, connectivity, options=list(), comment=None)` `dataclass` ¶

`ElementSet(name, kind='list', members=(lambda: np.zeros(0, dtype=np.int64))(), values=list(), internal=False, instance=None, comment=None)` `dataclass` ¶

`Mesh()` ¶

`node_count` `property` ¶

`element_count` `property` ¶

`element_labels` `property` ¶

`add_nodes(coords, labels=None)` ¶

`add_elements(type, connectivity, labels=None, *, comment=None)` ¶

`add_nset(name, members, *, internal=False, comment=None)` ¶

`add_elset(name, members, *, internal=False, comment=None)` ¶

`add_surface(name, rows, type='element', *, comment=None)` ¶

`nset(name)` ¶

`elset(name)` ¶

`surface(name)` ¶

`find_nearest_node(point, candidates=None)` ¶

`check()` ¶

`renumbered()` ¶

`summary()` ¶

`NodeSet(name, kind='list', members=(lambda: np.zeros(0, dtype=np.int64))(), values=list(), internal=False, instance=None, comment=None)` `dataclass` ¶

`Surface(name, type='element', rows=list(), comment=None)` `dataclass` ¶

`key` `property` ¶

`Topology(name, shape, nnodes, dim, reference, corners, edges, face_centres, centre, vtk_type, meshio_type, source, _n)` `dataclass` ¶

`order` `property` ¶

`mid_nodes` `property` ¶

`centroid` `property` ¶

`reference_array()` ¶

`shape_functions(xi)` ¶

`shape_derivatives(xi)` ¶

`build_mesh(node_ids, coords, blocks, *, node_sets=None, element_sets=None, renumber=True, dim=None, ignored=None)` ¶

`from_numgeo(convention, topology_name)` ¶

`numgeo_element_type(topology_name, dofs, *, ndim=None, axisymmetric=False, reduced=False, variant=None, stem=None, formulation=None)` ¶

`permute(connectivity, convention, topology_name)` ¶

`to_numgeo(convention, topology_name)` ¶

`femmesh_import(femmesh, element_types, *, length_scale, renumber=True, groups=True, dim=None)` ¶

`mesh_from_femmesh(femmesh, element_types, *, length_scale, renumber=True, groups=True, dim=None)` ¶

`mesh_from_meshio(m, element_types, *, renumber=True, convention='vtk', dim=None)` ¶

`mesh_to_meshio(mesh)` ¶

`meshio_import(m, element_types, *, renumber=True, convention='vtk', dim=None)` ¶

`element_faces(element_type)` ¶

`element_topology(element_type)` ¶

`face_connectivity(element_type, connectivity, face)` ¶