Class Expression

python/dolfinx/fem/function.py:101–332

An object for evaluating functions of finite element functions. Represents a mathematical expression evaluated at a pre-defined set of points on the reference cell. This class closely follows the concept of a UFC Expression. This functionality can be used to evaluate a gradient of

class Expression(Generic[Scalar]):
    """An object for evaluating functions of finite element functions.

    Represents a mathematical expression evaluated at a pre-defined set
    of points on the reference cell. This class closely follows the
    concept of a UFC Expression.

    This functionality can be used to evaluate a gradient of a Function
    at the quadrature points in all cells. This evaluated gradient can
    then be used as input to a non-FEniCS function that calculates a
    material constitutive model.

    """

    _ufl_expression: ufl.core.expr.Expr
    _argument_space: FunctionSpace | None
    _cpp_object: (
        _cpp.fem.Expression_complex64
        | _cpp.fem.Expression_complex128
        | _cpp.fem.Expression_float32
        | _cpp.fem.Expression_float64
    )
    _code: str

    def __init__(
        self,
        e: ufl.core.expr.Expr,
        X: np.ndarray,
        comm: _MPI.Comm | None = None,
        form_compiler_options: dict | None = None,
        jit_options: dict | None = None,
        dtype: npt.DTypeLike | None = None,
        entity_maps: list[_EntityMap] | None = None,
    ):
        """Create an Expression.

        Args:
            e: UFL expression.
            X: Array of points of shape ``(num_points, tdim)`` on the
                reference element.
            comm: Communicator that the Expression is defined on.
            form_compiler_options: Options used in FFCx compilation of
                this Expression. Run ``ffcx --help`` in the commandline
                to see all available options.
            jit_options: Options controlling JIT compilation of C code.
            dtype: Type of the Expression values. If ``None``,
                the dtype is deduced from the UFL expression.
            entity_maps: Maps between different meshes.

        Note:
            This wrapper is responsible for the FFCx compilation of the
            UFL Expr and attaching the correct data to the underlying
            C++ Expression.
        """
        assert X.ndim < 3
        num_points = X.shape[0] if X.ndim == 2 else 1
        _X = np.reshape(X, (num_points, -1))