liblaf.apple.jax.fem.element

Classes:

• Element –

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

• ElementTetra –

Element

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

References

1. felupe.Element

Returned by:

• Reference Liblaf apple jax
  •  jax
    •  Geometry  element
    •  GeometryTriangle  element
    •  Region  element
  • fem
    •  fem
      •  Geometry  element
      •  GeometryTriangle  element
      •  Region  element
    • geometry  geometry
      •  Geometry  element
      •  GeometryTriangle  element
    • region  region  Region  element

Methods:

• function –

  Return the shape functions at given coordinates.

• gradient –
• hessian –

Attributes:

• cells (Integer[Array, ' points']) –
• dim (int) –
• n_points (int) –
• points (Float[Array, 'points dim']) –
• quadrature (Scheme) –

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

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

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

def hessian(self, coords: Float[Array, " dim"]) -> Float[Array, "points dim dim"]:
    return jax.hessian(self.function)(coords)

ElementTetra

Bases: Element

              flowchart TD
              liblaf.apple.jax.fem.element.ElementTetra[ElementTetra]
              liblaf.apple.jax.fem.element._element.Element[Element]

                              liblaf.apple.jax.fem.element._element.Element --> liblaf.apple.jax.fem.element.ElementTetra
                


              click liblaf.apple.jax.fem.element.ElementTetra href "" "liblaf.apple.jax.fem.element.ElementTetra"
              click liblaf.apple.jax.fem.element._element.Element href "" "liblaf.apple.jax.fem.element._element.Element"
            

Returned by:

• Reference Liblaf apple jax
  •  jax  GeometryTetra  element
  • fem
    •  fem  GeometryTetra  element
    • geometry  geometry  GeometryTetra  element

Methods:

• function –

  Return the shape functions at given coordinates.

• gradient –
• hessian –

Attributes:

• cells (Integer[Array, ' points']) –
• dim (int) –
• n_points (int) –
• points (Float[Array, 'points=4 dim=3']) –
• quadrature (QuadratureTetra) –

cells property

cells: Integer[Array, ' points']

dim property

dim: int

n_points property

n_points: int

points property

points: Float[Array, 'points=4 dim=3']

quadrature property

quadrature: QuadratureTetra

function

function(
    coords: Float[Array, "dim=3"],
) -> Float[Array, "points=4"]

Return the shape functions at given coordinates.

Source code in src/liblaf/apple/jax/fem/element/_tetra.py

@override
def function(self, coords: Float[Array, "dim=3"]) -> Float[Array, "points=4"]:
    coords = jnp.asarray(coords)
    r, s, t = coords
    return jnp.asarray([1.0 - r - s - t, r, s, t], float)

gradient

gradient(
    coords: Float[Array, "dim=3"],
) -> Float[Array, "points=4 dim=3"]

Source code in src/liblaf/apple/jax/fem/element/_tetra.py

@override
def gradient(self, coords: Float[Array, "dim=3"]) -> Float[Array, "points=4 dim=3"]:
    return jnp.asarray([[-1, -1, -1], [1, 0, 0], [0, 1, 0], [0, 0, 1]], float)

hessian

hessian(
    coords: Float[Array, "dim=3"],
) -> Float[Array, "points=4 dim=3 dim=3"]

Source code in src/liblaf/apple/jax/fem/element/_tetra.py

@override
def hessian(
    self, coords: Float[Array, "dim=3"]
) -> Float[Array, "points=4 dim=3 dim=3"]:
    return jnp.zeros((4, 3, 3), float)