zoomy_core.mesh.lsq_reconstruction

`zoomy_core.mesh.lsq_reconstruction`#

Pure-numpy least-squares reconstruction: monomial bases, Vandermonde matrices, per-cell LSQ stencils and derivatives, used by LSQMesh.

Module Contents#

Functions#

`build_monomial_indices`	Monomial multi-indices up to total `degree` in `dim` dimensions, excluding the constant.
`scale_lsq_derivative`	Factorial scale factors that turn monomial coefficients into derivatives.
`find_derivative_indices`	Positions of the requested derivative multi-indices in the monomial list, as an `(M,)` array (-1 where absent).
`get_polynomial_degree`	Maximum total degree among the monomial multi-indices.
`get_required_monomials_count`	Number of monomials (constant included) of a polynomial of `degree` in `dim` dimensions.
`build_vandermonde`	Vandermonde matrix of the monomials `mon_indices` at the offsets `cell_diffs`.
`expand_neighbors`	Grow a neighbour set by one ring, skipping sentinel indices `>= n_valid`.
`build_vertex_to_cells`	Inverse of `cell_vertices` (shape `(verts_per_cell, n_cells)`): per vertex, the inner cells touching it.
`vertex_one_ring`	Inner cells sharing at least one vertex with cell `ic` (excluding `ic`), sorted.
`compute_gaussian_weights`	Gaussian weights `exp(-(\|dX\|/sigma)^2)` of the offsets `dX`.
`least_squares_reconstruction_local`	Build the per-cell LSQ gradient operators over the vertex-1-ring stencil, with boundary faces as virtual ghost samples at `2(face_center - cell_center)`. The value placed there must be a ghost value (`2u_face - u_cell`).
`compute_derivatives`	Cell-wise derivative estimates of `u` from the mesh LSQ stencil.
`get_physical_boundary_labels`	Map physical-group names of a `.msh` file to their tags via meshio.
`compute_inradius_generic`	Inradius of a cell: the shortest normal distance from its centre to any face.

API#

zoomy_core.mesh.lsq_reconstruction.build_monomial_indices(degree: int, dim: int)#: Monomial multi-indices up to total degree in dim dimensions, excluding the constant.

zoomy_core.mesh.lsq_reconstruction.scale_lsq_derivative(mon_indices)#: Factorial scale factors that turn monomial coefficients into derivatives.

zoomy_core.mesh.lsq_reconstruction.find_derivative_indices(full_monomials_arr, requested_derivs_arr)#: Positions of the requested derivative multi-indices in the monomial list, as an (M,) array (-1 where absent).

zoomy_core.mesh.lsq_reconstruction.get_polynomial_degree(mon_indices)#: Maximum total degree among the monomial multi-indices.

zoomy_core.mesh.lsq_reconstruction.get_required_monomials_count(degree, dim)#: Number of monomials (constant included) of a polynomial of degree in dim dimensions.

zoomy_core.mesh.lsq_reconstruction.build_vandermonde(cell_diffs, mon_indices)#: Vandermonde matrix of the monomials mon_indices at the offsets cell_diffs.

zoomy_core.mesh.lsq_reconstruction.expand_neighbors(neighbors_list, initial_neighbors, n_valid=None)#: Grow a neighbour set by one ring, skipping sentinel indices >= n_valid.

zoomy_core.mesh.lsq_reconstruction.build_vertex_to_cells(cell_vertices, n_inner_cells)#: Inverse of cell_vertices (shape (verts_per_cell, n_cells)): per vertex, the inner cells touching it.

zoomy_core.mesh.lsq_reconstruction.vertex_one_ring(ic, cell_vertices, vertex_to_cells, n_inner_cells)#: Inner cells sharing at least one vertex with cell ic (excluding ic), sorted.

zoomy_core.mesh.lsq_reconstruction.compute_gaussian_weights(dX, sigma=1.0)#: Gaussian weights exp(-(|dX|/sigma)^2) of the offsets dX.

zoomy_core.mesh.lsq_reconstruction.least_squares_reconstruction_local(n_cells, dim, neighbors_list, cell_centers, lsq_degree, n_inner_cells=None, boundary_face_centers=None, cell_boundary_faces=None, cell_vertices=None)#

Build the per-cell LSQ gradient operators over the vertex-1-ring stencil, with boundary faces as virtual ghost samples at 2*(face_center - cell_center). The value placed there must be a ghost value (2*u_face - u_cell).

Args

neighbors_list: face-neighbour table, used only to top up or replace the vertex ring.
boundary_face_centers: (n_boundary_faces, dim); required when cell_boundary_faces is non-empty.
cell_boundary_faces: per cell, the boundary faces it touches.
cell_vertices: (verts_per_cell, n_cells); without it the stencil is the biased face-neighbour expansion.

Returns

(A_glob, neighbors_array, boundary_face_neighbors_array, mon_indices); A_glob is (n_cells, max_neighbors + max_bdy_per_cell, n_monomials), boundary slots are padded with -1.

References

Mavriplis 2003, https://doi.org/10.2514/6.2003-3986

zoomy_core.mesh.lsq_reconstruction.compute_derivatives(u, mesh, derivatives_multi_index=None, *, u_boundary_face)#

Cell-wise derivative estimates of u from the mesh LSQ stencil.