sofia.field.field

class sofia.field.field.Field(name, domain, *args, **kwargs)

Bases: Expr

Symbolic field living on Domain.

as_dummy(name=None)

Return the expression with any objects having structurally bound symbols replaced with unique, canonical symbols within the object in which they appear and having only the default assumption for commutativity being True. When applied to a symbol a new symbol having only the same commutativity will be returned.

Examples

>>> from sympy import Integral, Symbol
>>> from sympy.abc import x
>>> r = Symbol('r', real=True)
>>> Integral(r, (r, x)).as_dummy()
Integral(_0, (_0, x))
>>> _.variables[0].is_real is None
True
>>> r.as_dummy()
_r

Notes

Any object that has structurally bound variables should have a property, bound_symbols that returns those symbols appearing in the object.

class sofia.field.field.VectorField(name: str | Symbol, domain: Domain, staggered: str | tuple[Staggered, ...] | None = None, **kwargs)
class sofia.field.field.VectorField(*terms: Vector, **options)

Bases: VectorAdd

A vector field composed of one scalar Field per axis.

It is a sympy vector so it can be used in any vector expression.

Parameters:

  • name – Each component field is named f”{name}_{axis}” (where axis is “x”, “y” or “z”).

  • domain – Domain the component fields live on.

  • staggered – Where the components sit within a cell on a Grid. This can be given either as a Staggered per component or as the string “faces”, which means each component lives on the face normal to its axis.

  • **kwargs – Forwarded to every component Field.

Examples

>>> from sofia import Grid
>>> G = Grid(ndim=2, name="G")
>>> u = VectorField("u", G)
>>> u
u_x*global.ihat + u_y*global.jhat
>>> u.fields
(u_x, u_y)
>>> [f.staggered for f in VectorField("m", G, staggered="faces").fields]
[XFACE, YFACE]
>>> u << 0
CodeBlock(
EvalAssignment(u_x, 0),
EvalAssignment(u_y, 0)
)
property fields: tuple[Field, ...]

The scalar field of each component.

assignments(other) → dict[Field, Expr]

Return the value each component field gets when other is assigned.

class sofia.field.field.TensorField(name: str | Symbol, domain: Domain, symmetric: bool = False, staggered: str | tuple[tuple[Staggered | None, ...], ...] | None = None, **kwargs)
class sofia.field.field.TensorField(*terms: Dyadic, **options)

Bases: DyadicAdd

An order 2 tensor field (dyadic) composed of one scalar Field per pair of axes.

It is a sympy dyadic, so it can be used in any dyadic expression.

Parameters:

  • name – Each component field is named f”{name}_{a}{b}” (e.g. T_xy).

  • domain – Domain the component fields live on.

  • symmetric – Use one field for T_ab and T_ba, so the tensor is symmetric by construction.

  • staggered – Where the components sit within a cell on a Grid. This can be given either as one Staggered per component, as rows (staggered[a][b] for component T_ab), or as the string “mac”, which puts the diagonal components at cell centers and the off-diagonal ones on the edges.

  • **kwargs – Forwarded to every component Field.

Examples

>>> from sofia import Grid
>>> G = Grid(ndim=2, name="G")
>>> T = TensorField("T", G)
>>> T.fields
(T_xx, T_xy, T_yx, T_yy)
>>> T.dot(G.unit_vectors[0])
T_xx*global.ihat + T_yx*global.jhat
>>> S = TensorField("S", G, symmetric=True)
>>> S.fields
(S_xx, S_xy, S_yy)
>>> S << 2
CodeBlock(
EvalAssignment(S_xx, 2),
EvalAssignment(S_xy, 2),
EvalAssignment(S_yy, 2)
)
property fields: tuple[Field, ...]

The distinct component fields.

property symmetric: bool

Whether T_ab and T_ba are the same field for every pair of axes.

assignments(other) → dict[Field, Expr]

Return the value each component field gets when other is assigned.

sofia.field.field.component_fields(symbols) → tuple

Return symbols as a tuple, with vector and tensor fields split into fields.

sofia.field.field.fields(names: str, domain: Domain, **kwargs: object) → tuple[Field, ...]

Create one or more Fields on a shared domain.

Equivalent to sympy.symbols(), but for Fields. Always returns a tuple for better type support.

Parameters:

  • names – Field names, comma- or whitespace-separated; see sympy.symbols().

  • domain – Domain the fields live on.

  • **kwargs – Forwarded to the Field subclass registered for domain.

Returns:

A tuple of the created Field(s).

Return type:

tuple[Field, …]

Examples

>>> (u,) = fields("u", domain=Grid(ndim=1))
>>> v, w = fields("v w", domain=Grid(ndim=2))