sofia.field.grid_field

class sofia.field.grid_field.IndexedGridField(base, *args, **kw_args)

Bases: Indexed

class sofia.field.grid_field.GridField(name: str, domain: Grid, staggered: Staggered = Center, discretisation_order: int = 0, axes: Tuple | tuple[Symbol | int, ...] = None, _shifts: Tuple | tuple[Symbol | float | int, ...] | None = None)

Bases: Field

Symbolic representation of a field living on a structured grid.

A GridField is a symbol that carries the information needed to discretise expressions it appears in: the grid it is defined on, which of the grid axes it varies along, where within a cell its values sit, and how far it is shifted from its natural location.

Parameters:

  • name – Name of the field, used for its symbolic and generated-code names.

  • domain – The Grid the field is defined on.

  • staggered – Location of the field values within a cell, as a Staggered member. Defaults to Staggered.CENTER.

  • discretisation_order – Order of accuracy for derivatives and interpolation of this field. Must be even. The default of 0 means the order of domain is used instead.

  • axes – Grid axes the field varies along, given as indices or coordinates. Defaults to all of them. Passing a subset gives a field of lower dimensionality than the grid; passing () gives a scalar.

Examples

>>> import sympy as sp
>>> from sofia import Grid, Field, Staggered

>>> G = Grid(ndim=2)
>>> u = Field("u", domain=G)

>>> u.shape
(G.Nx, G.Ny)
>>> u.axes
(0, 1)
>>> Field("v", domain=G, axes=(G.x,)).shape
(G.Nx,)
>>> Field("dt", domain=G, axes=()).shape
()

Shifts:

>>> u.s(1, 0).shifts
(1, 0)
>>> u.s(1, 0).s(2, 0).shifts
(3, 0)
>>> u.s(j=-1).shifts
(0, -1)
fractional_offset(wrt) → Expr

Combine shift and staggered offset of a field.

class sofia.field.grid_field.GridFieldLocus(grid: Grid, axes: Tuple, shifts: Tuple)

Bases: Locus

property shifts: Tuple

Tuple of (half-)integer shifts.