Class Field

phi/field/_field.py:51–847

A `Field` represents a discretized physical quantity (like temperature field or velocity field). The sample points and their relation are encoded in the `geometry` property and the corresponding values are stored as one `Tensor` in `values`. The boundary conditions and values outside th

@sliceable
@dataclass(frozen=True)
class Field(metaclass=_FieldType):
    """
    A `Field` represents a discretized physical quantity (like temperature field or velocity field).
    The sample points and their relation are encoded in the `geometry` property and the corresponding values are stored as one `Tensor` in `values`.
    The boundary conditions and values outside the geometry are determined by `boundary`.

    Examples:
        Create a periodic 2D grid, initialized via noise fluctuations.
        >>> Field(UniformGrid(x=32, y=32), values=Noise(), boundary=PERIODIC)

        Create a field on an unstructured mesh loaded from a .gmsh file
        >>> mesh = phi.geom.load_gmsh('cylinder.msh', ('y-', 'x+', 'y+', 'x-', 'cyl+', 'cyl-'))
        >>> Field(mesh, values=vec(x=1, y=0), boundary={'x': ZERO_GRADIENT, 'y': 0, 'cyl': 0})

        Create two cubes and compute a scalar values for each.
        >>> Field(Cuboid(vec(x=[0, 2], y=0), x=1, y=1), values=lambda x,y: x)

    See the `phi.field` module documentation at https://tum-pbs.github.io/PhiFlow/Fields.html
    """

    geometry: Geometry
    """ Discretization `Geometry`. This determines where in space the `values` are sampled as well as their relationship and interpretation. """
    values: Tensor
    """ The sampled values, matching some point set of `geometry`, e.g. center points, see `Geometry.sets`."""
    boundary: Extrapolation = 0.
    """ Boundary conditions describe the values outside of `geometry` and are used by numerical solvers to compute edge values. """

    variable_attrs: Tuple[str, ...] = ('values',)
    """ Which of the three attributes (geometry,values,boundary) should be traced / optimized. See `phiml.math.magic.PhiTreeNode.__variable_attrs__`"""
    value_attrs: Tuple[str, ...] = ('values',)
    """ Which of the three attributes (geometry,values,boundary) are considered values. See `phiml.math.magic.PhiTreeNode.__value_attrs__`"""

    def __post_init__(self):
        math.merge_shapes(self.values, non_batch(self.sampled_elements).non_channel)  # shape check

    @property
    def grid(self) -> UniformGrid:
        """Cast `self.geometry` to a `phi.geom.UniformGrid`."""
        assert isinstance(self.geometry, UniformGrid), f"Geometry is not a UniformGrid but {type(self.geometry)}"
        return self.geometry

    @property
    def mesh(self) -> Mesh:
        """Cast `self.geometry` to a `phi.geom.Mesh`."""
        assert isinstance(self.geometry, Mesh), f"Geometry is not a mesh but {type(self.geometry)}"
        return self.geometry

    @property
    def graph(self) -> Graph:
        """Cast `self.geometry` to a `phi.geom.Graph`."""
        assert isinstance(self.geometry, Graph), f"Geometry is not a mesh but {type(self.geometry)}"
        return self.geometry

    @property
    def faces(self):
        return get_faces(self.geometry, self.boundary)

    @property