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liblaf.apple.jax.fem ¤

Modules:

Classes:

Element ¤

Base-class for a finite element which provides methods for plotting.

References
  1. felupe.Element
Returned by:

Methods:

Attributes:

cells property ¤

cells: Integer[Array, ' points']

dim property ¤

dim: int

n_points property ¤

n_points: int

points property ¤

points: Float[Array, 'points dim']

quadrature property ¤

quadrature: Scheme

function ¤

function(
    coords: Float[Array, " dim"],
) -> Float[Array, " points"]

Return the shape functions at given coordinates.

Source code in src/liblaf/apple/jax/fem/element/_element.py 
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def function(self, coords: Float[Array, " dim"]) -> Float[Array, " points"]:
    """Return the shape functions at given coordinates."""
    raise NotImplementedError

gradient ¤

gradient(
    coords: Float[Array, " dim"],
) -> Float[Array, "points dim"]
Source code in src/liblaf/apple/jax/fem/element/_element.py 
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def gradient(self, coords: Float[Array, " dim"]) -> Float[Array, "points dim"]:
    return jax.jacobian(self.function)(coords)

hessian ¤

hessian(
    coords: Float[Array, " dim"],
) -> Float[Array, "points dim dim"]
Source code in src/liblaf/apple/jax/fem/element/_element.py 
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def hessian(self, coords: Float[Array, " dim"]) -> Float[Array, "points dim dim"]:
    return jax.hessian(self.function)(coords)

Geometry ¤

Parameters:

Returned by: Used by:

Methods:

Attributes:

cell_data property ¤

cell_data: DataSetAttributes

cells property ¤

cells: Integer[Array, 'c a']

cells_global property ¤

cells_global: Integer[Array, 'c a']

element property ¤

element: Element

mesh class-attribute instance-attribute ¤

mesh: DataSet = field()

n_cells property ¤

n_cells: int

point_data property ¤

point_data: DataSetAttributes

point_id property ¤

point_id: Integer[Array, 'p J']

points property ¤

points: Float[Array, 'p J']

from_pyvista classmethod ¤

from_pyvista(mesh: DataObject) -> Geometry
Source code in src/liblaf/apple/jax/fem/geometry/_geometry.py 
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@classmethod
def from_pyvista(cls, mesh: pv.DataObject) -> Geometry:
    from ._tetra import GeometryTetra
    from ._triangle import GeometryTriangle

    if isinstance(mesh, pv.PolyData):
        return GeometryTriangle.from_pyvista(mesh)
    if isinstance(mesh, pv.UnstructuredGrid):
        return GeometryTetra.from_pyvista(mesh)
    raise NotImplementedError

GeometryTetra ¤

Bases: Geometry


              flowchart TD
              liblaf.apple.jax.fem.GeometryTetra[GeometryTetra]
              liblaf.apple.jax.fem.geometry._geometry.Geometry[Geometry]

                              liblaf.apple.jax.fem.geometry._geometry.Geometry --> liblaf.apple.jax.fem.GeometryTetra
                


              click liblaf.apple.jax.fem.GeometryTetra href "" "liblaf.apple.jax.fem.GeometryTetra"
              click liblaf.apple.jax.fem.geometry._geometry.Geometry href "" "liblaf.apple.jax.fem.geometry._geometry.Geometry"

Parameters:

  • mesh ¤

    (UnstructuredGrid) –

Methods:

Attributes:

cell_data property ¤

cell_data: DataSetAttributes

cells property ¤

cells: Integer[Array, 'c a']

cells_global property ¤

cells_global: Integer[Array, 'c a']

element property ¤

element: ElementTetra

mesh class-attribute instance-attribute ¤

mesh: UnstructuredGrid = field()

n_cells property ¤

n_cells: int

point_data property ¤

point_data: DataSetAttributes

point_id property ¤

point_id: Integer[Array, 'p J']

points property ¤

points: Float[Array, 'p J']

from_pyvista classmethod ¤

from_pyvista(mesh: UnstructuredGrid) -> Self
Source code in src/liblaf/apple/jax/fem/geometry/_tetra.py 
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@override
@classmethod
def from_pyvista(cls, mesh: pv.UnstructuredGrid) -> Self:  # pyright: ignore[reportIncompatibleMethodOverride]
    self: Self = cls(mesh=mesh)
    return self

GeometryTriangle ¤

Bases: Geometry


              flowchart TD
              liblaf.apple.jax.fem.GeometryTriangle[GeometryTriangle]
              liblaf.apple.jax.fem.geometry._geometry.Geometry[Geometry]

                              liblaf.apple.jax.fem.geometry._geometry.Geometry --> liblaf.apple.jax.fem.GeometryTriangle
                


              click liblaf.apple.jax.fem.GeometryTriangle href "" "liblaf.apple.jax.fem.GeometryTriangle"
              click liblaf.apple.jax.fem.geometry._geometry.Geometry href "" "liblaf.apple.jax.fem.geometry._geometry.Geometry"

Parameters:

  • mesh ¤

    (PolyData) –

Methods:

Attributes:

cell_data property ¤

cell_data: DataSetAttributes

cells property ¤

cells: Integer[Array, 'c a']

cells_global property ¤

cells_global: Integer[Array, 'c a']

element property ¤

element: Element

mesh class-attribute instance-attribute ¤

mesh: PolyData = field()

n_cells property ¤

n_cells: int

point_data property ¤

point_data: DataSetAttributes

point_id property ¤

point_id: Integer[Array, 'p J']

points property ¤

points: Float[Array, 'p J']

from_pyvista classmethod ¤

from_pyvista(mesh: PolyData) -> Self
Source code in src/liblaf/apple/jax/fem/geometry/_triangle.py 
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@override
@classmethod
def from_pyvista(cls, mesh: pv.PolyData) -> Self:  # pyright: ignore[reportIncompatibleMethodOverride]
    mesh = mesh.triangulate()  # pyright: ignore[reportAssignmentType]
    self: Self = cls(mesh=mesh)
    return self

Region ¤

Parameters:

  • geometry ¤

    (Geometry) –

  • quadrature ¤

    (Scheme) –

  • h ¤

    (Float[Array, 'q a'], default: None ) –

  • dhdr ¤

    (Float[Array, 'q a J'], default: None ) –

  • dXdr ¤

    (Float[Array, 'c q J J'], default: None ) –

  • drdX ¤

    (Float[Array, 'c q J J'], default: None ) –

  • dV ¤

    (Float[Array, 'c q'], default: None ) –

  • dhdX ¤

    (Float[Array, 'c q a J'], default: None ) –
Used by:

Methods:

Attributes:

cell_data property ¤

cell_data: DataSetAttributes

cells property ¤

cells: Integer[Array, 'c a']

cells_global property ¤

cells_global: Integer[Array, 'c a']

dV class-attribute instance-attribute ¤

dV: Float[Array, 'c q'] = array(default=None)

dXdr class-attribute instance-attribute ¤

dXdr: Float[Array, 'c q J J'] = array(default=None)

dhdX class-attribute instance-attribute ¤

dhdX: Float[Array, 'c q a J'] = array(default=None)

dhdr class-attribute instance-attribute ¤

dhdr: Float[Array, 'q a J'] = array(default=None)

drdX class-attribute instance-attribute ¤

drdX: Float[Array, 'c q J J'] = array(default=None)

element property ¤

element: Element

geometry class-attribute instance-attribute ¤

geometry: Geometry = field()

h class-attribute instance-attribute ¤

h: Float[Array, 'q a'] = array(default=None)

mesh property ¤

mesh: DataSet

n_cells property ¤

n_cells: int

point_data property ¤

point_data: DataSetAttributes

points property ¤

points: Float[Array, 'p J']

quadrature class-attribute instance-attribute ¤

quadrature: Scheme = field()

compute_grad ¤

compute_grad() -> None
Source code in src/liblaf/apple/jax/fem/region/_region.py 
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def compute_grad(self) -> None:
    h: Float[Array, "q a"] = jnp.stack(
        [self.element.function(q) for q in self.quadrature.points]
    )
    dhdr: Float[Array, "q a J"] = jnp.stack(
        [self.element.gradient(q) for q in self.quadrature.points]
    )
    dXdr: Float[Array, "c q J J"] = einops.einsum(
        self.points[self.cells], dhdr, "c a I, q a J -> c q I J"
    )
    drdX: Float[Array, "c q J J"] = jnp.linalg.inv(dXdr)
    dV: Float[Array, "c q"] = (
        jnp.linalg.det(dXdr) * self.quadrature.weights[jnp.newaxis, :]
    )
    if jnp.any(dV <= 0):
        logger.warning("dV <= 0")
    dhdX: Float[Array, "c q a J"] = einops.einsum(
        dhdr, drdX, "q a I, c q I J -> c q a J"
    )
    self.h = h
    self.dhdr = dhdr
    self.dXdr = dXdr
    self.drdX = drdX
    self.dV = dV
    self.dhdX = dhdX

deformation_gradient ¤

deformation_gradient(
    u: Float[Array, "p J"],
) -> Float[Array, "c q J J"]
Source code in src/liblaf/apple/jax/fem/region/_region.py 
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def deformation_gradient(self, u: Float[Array, "p J"]) -> Float[Array, "c q J J"]:
    grad: Float[Array, "c q J J"] = self.gradient(u)
    F: Float[Array, "c q J J"] = (
        grad + jnp.identity(3)[jnp.newaxis, jnp.newaxis, ...]
    )
    return F

from_geometry classmethod ¤

from_geometry(
    geometry: Geometry,
    *,
    grad: bool = False,
    quadrature: Scheme | None = None,
) -> Self
Source code in src/liblaf/apple/jax/fem/region/_region.py 
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@classmethod
def from_geometry(
    cls, geometry: Geometry, *, grad: bool = False, quadrature: Scheme | None = None
) -> Self:
    if quadrature is None:
        quadrature = geometry.element.quadrature
    self: Self = cls(geometry=geometry, quadrature=quadrature)
    if grad:
        self.compute_grad()
    return self

from_pyvista classmethod ¤

from_pyvista(
    mesh: DataObject,
    *,
    grad: bool = False,
    quadrature: Scheme | None = None,
) -> Self
Source code in src/liblaf/apple/jax/fem/region/_region.py 
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@classmethod
def from_pyvista(
    cls,
    mesh: pv.DataObject,
    *,
    grad: bool = False,
    quadrature: Scheme | None = None,
) -> Self:
    geometry: Geometry = Geometry.from_pyvista(mesh)
    self: Self = cls.from_geometry(geometry, grad=grad, quadrature=quadrature)
    return self

gradient ¤

gradient(
    u: Float[Array, " points *shape"],
) -> Float[Array, "c q *shape J"]
Source code in src/liblaf/apple/jax/fem/region/_region.py 
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def gradient(
    self, u: Float[Array, " points *shape"]
) -> Float[Array, "c q *shape J"]:
    result: Float[Array, "c q *shape J"] = einops.einsum(
        self.scatter(u), self.dhdX, "c a ..., c q a J -> c q ... J"
    )
    return result

integrate ¤

integrate(
    a: Float[Array, "c q *shape"],
) -> Float[Array, " c *shape"]
Source code in src/liblaf/apple/jax/fem/region/_region.py 
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def integrate(self, a: Float[Array, "c q *shape"]) -> Float[Array, " c *shape"]:
    return einops.einsum(a, self.dV, "c q ..., c q -> c ...")

scatter ¤

scatter(
    u: Float[Array, " points *shape"],
) -> Float[Array, "c a *shape"]
Source code in src/liblaf/apple/jax/fem/region/_region.py 
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def scatter(self, u: Float[Array, " points *shape"]) -> Float[Array, "c a *shape"]:
    return u[self.cells_global]

Scheme ¤

Parameters:

  • points ¤

    (Float[Array, 'q J']) –

  • weights ¤

    (Float[Array, q]) –
Returned by: Used by:

Methods:

Attributes:

dim property ¤

dim: int

n_points property ¤

n_points: int

points class-attribute instance-attribute ¤

points: Float[Array, 'q J'] = array()

weights class-attribute instance-attribute ¤

weights: Float[Array, ' q'] = array()

from_felupe classmethod ¤

from_felupe(scheme: Scheme) -> Self
Source code in src/liblaf/apple/jax/fem/quadrature/_scheme.py 
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@classmethod
def from_felupe(cls, scheme: felupe.quadrature.Scheme) -> Self:
    return cls(
        points=jnp.asarray(scheme.points), weights=jnp.asarray(scheme.weights)
    )