pystencils.grids.patch.Patch

class pystencils.grids.patch.Patch(name: str, x_max: tuple[Any, ...], /, *, num_vertices: Iterable[Basic] | None = None, num_cells: Iterable[Basic] | None = None)

class pystencils.grids.patch.Patch(name: str, x_min: tuple[Any, ...], x_max: tuple[Any, ...], /, *, num_vertices: Iterable[Basic] | None = None, num_cells: Iterable[Basic] | None = None)

Cuboid volume of space, discretized by a cartesian grid.

Patches are algebraic objects representing (patches of) simulation domains in pystencils. A patch \(\Omega\) is an \(m\)-dimensional multi-interval \([\ell_1, u_1] \times \cdots \times [\ell_m, u_m]\) given by its lower and upper corners \((\ell_1, \dots, \ell_m)\) and \((u_1, \dots, u_m)\).

Each patch is host to a numerical grid of \(N_1 \times \cdots \times N_m\) vertices (points), with spacings \(h_k = \frac{u_k - \ell_k}{N_k - 1}\) in each dimension. The grid vertices are

\[\mathrm{vertices} (\Omega) = \left\{ (i_k \cdot h_k)_{k = 1, \dots, m} \; \vert \; (i_k = 0, \dots, N_k - 1)_{k = 1, \dots, m} \right\}.\]

The cuboid spaces enclosed by adjacent vertices are the grid’s cells. Each cell encloses a volume \(h_1 \times \cdots \times h_m\) according to the grid spacing; cell \(\mathsf{c}_{\boldsymbol{i}}\) therefore claims the multi-interval

\[\mathsf{c}_{\boldsymbol{i}} = \prod_{k=1}^m [i_k \cdot h_k, (i_k + 1) \cdot h_k].\]

There are one fewer cells than vertices in each dimension; the grid’s cells are therefore

\[\mathrm{cells} (\Omega) = \left\{ \mathsf{c}_{(i_1, \dots, i_m)} \; \vert \; (i_k = 0, \dots, N_k - 2)_{k = 1, \dots, m} \right\}.\]

The Patch class models these patches algebraically, and allows for the definition of fields on its vertex and cell grids. All its attributes are symbolic expressions.

Parameters:

• name (str) – Name of the patch

• x_min – Lower corner \((\ell_1, \dots, \ell_m)\) of the patch. Can be omitted; in this case, the lower corner is set to the origin.

• x_max – Upper corner \((u_1, \dots, u_k)\) of the patch.

• num_vertices (Optional[Iterable[Basic]]) – Number of vertices in each dimension. If given, num_cells is inferred; do not specify both.

• num_cells (Optional[Iterable[Basic]]) – Number of cells in each dimension. If given, num_vertices is inferred; do not specify both.

• corners (tuple[Any, ...])

property name: str

Name of this patch

property dimensionality: int

Dimensionality of this patch

property x_min: ImmutableDenseMatrix

Lower corner as a SymPy matrix

property x_max: ImmutableDenseMatrix

Upper corner as a SymPy matrix

property extents: ImmutableDenseMatrix

Total extents of the patch as a SymPy matrix

property spacing: ImmutableDenseMatrix

Vertex spacing as a SymPy matrix

property num_vertices: ImmutableDenseMatrix

Number of vertices as a SymPy matrix

property num_cells: ImmutableDenseMatrix

Number of cells as a SymPy matrix

property cells: PatchGrid

Proxy indicating the patch’s cell grid; use to associate algebraic fields with the patch’s cells.

property vertices: PatchGrid

Proxy indicating the patch’s vertex grid; use to associate algebraic fields with the patch’s vertices.

vertex(*idcs)

Coordinates of a vertex identified by the given relative indices.

Like for field accesses, indices are interpreted relative to the current iteration point.

Examples

Coordinates of the current vertex:

patch.vertex()

Coordinates of the north-east neighbor vertex on a 2D patch:

patch.vertex(-1, 1)

Return type:

ImmutableDenseMatrix

Parameters:

idcs (SupportsIndex | Basic)

cell_center(*idcs)

Coordinates of the center of a cell identified by the given relative indices.

Like for field accesses, indices are interpreted relative to the current iteration point.

Examples

Coordinates of the current cell’s center:

patch.cell_center()

Coordinates of the center of the north-east neighbor cell on a 2D patch:

patch.cell_center(-1, 1)

Return type:

ImmutableDenseMatrix

Parameters:

idcs (SupportsIndex | Basic)