warp.fem.ShapeFunction

class warp.fem.ShapeFunction

Interface class for defining scalar-valued shape functions over a single element.

Methods

make_element_inner_weight()	Create a device function returning the value of the shape function associated to a given node at given coordinates.
make_element_inner_weight_gradient()	Create a device function returning the gradient of the shape function associated to a given node at given coordinates.
make_node_coords_in_element()	Create a device function returning the coordinates of each node.
make_node_dual_weight()	Create a device function returning the reference-space dual weight of each node.
make_node_quadrature_weight()	Create a device function returning the weight of each node when used as a quadrature point over the element.
make_trace_node_quadrature_weight()	Create a device function returning the weight of each node when used as a quadrature point over the element boundary.

Attributes

name	Unique name encoding all parameters defining the shape function
value	Value type of the shape function.
ORDER	Maximum degree of the polynomials used to define the shape function.
NODES_PER_ELEMENT	Number of shape function nodes.

ORDER: int

Maximum degree of the polynomials used to define the shape function.

NODES_PER_ELEMENT: int

Number of shape function nodes.

class Value(*values)

Scalar = 0

Scalar-valued shape function.

CovariantVector = 1

Covariant vector-valued shape function.

ContravariantVector = 2

Contravariant vector-valued shape function.

value: Value = 0

Value type of the shape function.

property name: str

Unique name encoding all parameters defining the shape function

make_node_coords_in_element()

Create a device function returning the coordinates of each node.

make_node_quadrature_weight()

Create a device function returning the weight of each node when used as a quadrature point over the element.

make_trace_node_quadrature_weight()

Create a device function returning the weight of each node when used as a quadrature point over the element boundary.

make_element_inner_weight()

Create a device function returning the value of the shape function associated to a given node at given coordinates.

make_element_inner_weight_gradient()

Create a device function returning the gradient of the shape function associated to a given node at given coordinates.

make_node_dual_weight()

Create a device function returning the reference-space dual weight of each node.

The degree of freedom of node i reproducing a reference-space value v is v * d_i for scalar-valued shape functions, or dot(v, d_i) for vector-valued ones, with d_i the returned dual weight. For vector-valued shape functions, d_i is aligned with the edge tangent (covariant) or side normal (contravariant) associated to the node, and scaled such that dot(d_i, w_i) = 1, with w_i the node weight at the node coordinates.

The default implementation returns 1 / w_i for scalar-valued shape functions, and must be overridden for vector-valued ones.