Operator

tatva.operator.Operator

Operator(mesh: Mesh, element: Element, batch_size: int | None = None)

A class that provides an Operator for finite element method (FEM) assembly.

Parameters:

• mesh

  (Mesh) –

  The mesh containing the elements and nodes.

• element

  (Element) –

  The element type used for the finite element method.

Provides several operators for evaluating and integrating functions over the mesh, such as integrate, eval, and grad. These operators can be used to compute integrals, evaluate functions at quadrature points, and compute gradients of functions at quadrature points.

Example

from tatva import Mesh, Tri3, Operator mesh = Mesh.unit_square(10, 10) # Create a mesh element = Tri3() # Define an element type operator = Operator(mesh, element) nodal_values = jnp.array(...) # Nodal values at the mesh nodes energy = operator.integrate(energy_density)(nodal_values)

Methods:

• map –

  Maps a function over the elements and quad points of the mesh.

• map_over_elements –

  Maps a function over the elements of the mesh.

• integrate –

  Integrate a nodal_array, quad_array, or numeric value over the mesh.

• integrate_per_element –

  Integrate a nodal_array, quad_array, or numeric value over the mesh. Returning the

• eval –

  Evaluates the nodal values at the quadrature points.

• grad –

  Computes the gradient of the nodal values at the quad points.

• interpolate –

  Interpolates nodal values to a set of points in the physical space.

map

map(func: MappableOverElementsAndQuads[P, RT], *, element_quantity: Sequence[int] = ()) -> MappedCallable[P, RT]

Maps a function over the elements and quad points of the mesh.

Returns a function that takes values at nodal points (globally) and returns the vmapped result over the elements and quad points.

Parameters:

• func

  (MappableOverElementsAndQuads[P, RT]) –

  The function to map over the elements and quadrature points.

• element_quantity

  (Sequence[int], default: () ) –

  Indices of the arguments of func that are quantities defined per element. The rest of the arguments are assumed to be defined at nodal points.

map_over_elements

map_over_elements(func: Callable[P, RT], *, element_quantity: Sequence[int] = ()) -> MappedCallable[P, RT]

Maps a function over the elements of the mesh.

Returns a function that takes values at nodal points (globally) and returns the vmapped result over the elements.

Parameters:

• func

  (Callable[P, RT]) –

  The function to map over the elements.

• element_quantity

  (Sequence[int], default: () ) –

  Indices of the arguments of func that are quantities defined per element. The rest of the arguments are assumed to be defined at nodal points.

integrate

integrate(arg: Array | Numeric) -> jax.Array

Integrate a nodal_array, quad_array, or numeric value over the mesh.

Parameters:

• arg

  (Array | Numeric) –

  An array of nodal values (shape: (n_nodes, n_values)), an array of quadrature values (shape: (n_elements, n_quad_points, n_values)), or a numeric value (float or int).

Returns:

• Array –

  The integral of the nodal values or quadrature values over the mesh.

integrate_per_element

integrate_per_element(arg: Array | Numeric) -> jax.Array

Integrate a nodal_array, quad_array, or numeric value over the mesh. Returning the integral per element.

Parameters:

• arg

  (Array | Numeric) –

  An array of nodal values (shape: (n_nodes, n_values)), an array of quadrature values (shape: (n_elements, n_quad_points, n_values)), or a numeric value (float or int).

Returns:

• Array –

  A jax.Array where each element contains the integral of the values in the

• Array –

  element (shape: (n_elements, n_values)).

eval

eval(nodal_values: Array) -> jax.Array

Evaluates the nodal values at the quadrature points.

Parameters:

• nodal_values

  (Array) –

  The nodal values at the element's nodes (shape: (n_nodes, n_values))

Returns:

• Array –

  A jax.Array with the values of the nodal values at each quadrature point of

• Array –

  each element (shape: (n_elements, n_quad_points, n_values)).

grad

grad(nodal_values: Array) -> jax.Array

Computes the gradient of the nodal values at the quad points.

Parameters:

• nodal_values

  (Array) –

  The nodal values at the element's nodes (shape: (n_nodes, n_values))

Returns:

• Array –

  A jax.Array with the gradient of the nodal values at each quadrature point

• Array –

  of each element (shape: (n_elements, n_quad_points, n_values, n_dim)).

interpolate

interpolate(arg: Array, points: Array) -> jax.Array

Interpolates nodal values to a set of points in the physical space.

Parameters:

• arg

  (Array) –

  The nodal values to interpolate.

• points

  (Array) –

  The points to interpolate the function or nodal values to.

Returns:

• Array –

  A jax.Array with the interpolated values at the given points.