sktopt.mesh

This package provides mesh utilities and task domain definitions.

Bases: object

Container for storing finite element and optimization-related data used in topology optimization tasks.

This class holds material properties, boundary condition information, designable and non-designable element indices, as well as force vectors and volume data for each element. It is typically constructed using LinearElasticity.from_defaults.

basis

Finite element basis object associated with the mesh and function space.

Type:: skfem.Basis

dirichlet_dofs

Degrees of freedom constrained by Dirichlet (displacement) boundary conditions.

Type:: np.ndarray

dirichlet_elements

Elements that contain Dirichlet boundary points.

Type:: np.ndarray

neumann_elements

Elements that contain the force application points.

Type:: np.ndarray

force

External force vector(s) applied to the system. A list is used when multiple load cases are present.

Type:: np.ndarray or list of np.ndarray

design_elements

Indices of elements that are considered designable in the optimization.

Type:: np.ndarray

free_dofs

Degrees of freedom that are not fixed by boundary conditions.

Type:: np.ndarray

free_elements

Elements associated with the free degrees of freedom.

Type:: np.ndarray

all_elements

Array of all element indices in the mesh.

Type:: np.ndarray

fixed_elements

Elements excluded from the design domain.

Type:: np.ndarray

dirichlet_neumann_elements

Union of Dirichlet and force elements. Useful for identifying constrained and loaded regions.

Type:: np.ndarray

elements_volume

Volume of each finite element, used in volume constraints and integration.

Type:: np.ndarray

Bases: FEMDomain

Container for storing finite element and optimization-related data used in topology optimization tasks.

This class holds material properties, boundary condition information, designable and non-designable element indices, as well as force vectors and volume data for each element. It is typically constructed using LinearElasticity.from_defaults.

E

Young’s modulus of the base material.

Type:: float

nu

Poisson’s ratio of the base material.

Type:: float

classmethod from_facets(basis: CellBasis, dirichlet_facets_ids: ndarray | list[ndarray], dirichlet_dir: Literal['u^1', 'u^2', 'u^3', 'all'] | list[Literal['u^1', 'u^2', 'u^3', 'all']], force_facets_ids: ndarray | list[ndarray], force_dir_type: str | list[str], force_value: float | list[float], design_elements: ndarray, E: float, nu: float) → LinearElasticity

Create a TaskConfig from facet-based boundary-condition specifications.

This constructor allows you to specify Dirichlet and Neumann boundaries directly via facet indices (rather than node indices). It will internally:

Convert dirichlet_facets_ids into the corresponding Dirichlet node set.
Resolve Dirichlet DOFs from those nodes and dirichlet_dir.
Convert force_facets_ids into the corresponding force node set.
Assemble the Neumann (surface) load vector(s) using
assemble_surface_forces.
Forward all data to TaskConfig.neumann_ to build the final config.

Parameters:

E (float) – Young’s modulus.
nu (float) – Poisson’s ratio.
basis (skfem.Basis) – Finite-element space providing mesh and DOFs.
dirichlet_facets_ids (np.ndarray or list[np.ndarray]) – Indices of facets subject to Dirichlet boundary conditions. If a list is given, each entry corresponds to a boundary region.
dirichlet_dir (_lit_bc or list[_lit_bc]) – Direction specifier(s) for Dirichlet constraints. _lit_bc = Literal[‘u^1’, ‘u^2’, ‘u^3’, ‘all’] - ‘all’ fixes all displacement components. - ‘u^1’, ‘u^2’, ‘u^3’ fix the respective component only.
force_facets_ids (np.ndarray or list[np.ndarray]) – Indices of facets subject to Neumann (surface) forces. A list denotes multiple load regions.
force_dir_type (str or list[str]) – Direction specifier(s) for each force region. _lit_force = Literal[‘u^1’, ‘u^2’, ‘u^3’] Indicates along which component the surface load is applied.
force_value (float or list[float]) – Magnitude(s) of the surface forces, one per region if multiple.
design_elements (np.ndarray) – Element indices initially considered designable. Force-touching elements will be excluded downstream.

Returns:

A fully initialized TaskConfig, equivalent to what TaskConfig.neumann_ produces but constructed from facet-based specifications.

Return type:

TaskConfig

class sktopt.mesh.LinearHeatConduction(basis: skfem.assembly.basis.cell_basis.CellBasis, dirichlet_nodes: numpy.ndarray | list[numpy.ndarray] | None, dirichlet_dofs: numpy.ndarray | list[numpy.ndarray] | None, dirichlet_elements: numpy.ndarray | None, dirichlet_values: float | list[float] | None, neumann_nodes: numpy.ndarray | list[numpy.ndarray] | None, neumann_elements: numpy.ndarray | None, neumann_dir_type: str | list[str] | None, neumann_values: float | list[float] | None, robin_facets_ids: numpy.ndarray | list[numpy.ndarray] | None, robin_nodes: numpy.ndarray | list[numpy.ndarray] | None, robin_elements: numpy.ndarray | None, robin_coefficient: float | list[float] | None, robin_bc_value: float | list[float] | None, design_robin_boundary: bool | None, design_elements: numpy.ndarray, free_dofs: numpy.ndarray, free_elements: numpy.ndarray, all_elements: numpy.ndarray, fixed_elements: numpy.ndarray, dirichlet_neumann_elements: numpy.ndarray, elements_volume: numpy.ndarray, k: float, robin_bilinear: list | None = None, robin_linear: list | None = None, objective: Literal['compliance'] = 'compliance'): Bases: FEMDomain