warp.fem.BasisSpace

class warp.fem.BasisSpace(topology)

Interface class for defining shape functions over a geometry.

A basis space is a component of a function space, and is responsible for defining the node positions and their weights over individual elements of the geometry. The connectivity pattern between elements of geometry is defined by the SpaceTopology. The actual valuation of the space is defined by the FunctionSpace, allowing to reuse a single basis space for multiple value types (e.g, scalar, vector, or tensor).

See also: make_polynomial_basis_space(), make_collocated_function_space()

Methods

basis_arg_value(device)
fill_basis_arg(arg, device)	Fill the arguments to be passed to basis-related device functions
make_element_inner_weight()	Create a device function returning inner element shape weights.
make_element_inner_weight_gradient()	Create a device function returning gradients of inner element weights.
make_element_outer_weight()	Create a device function returning outer element shape weights.
make_element_outer_weight_gradient()	Create a device function returning gradients of outer element weights.
make_node_coords_in_element()	Create a device function returning node coordinates within an element.
make_node_dual_weight()	Create a device function returning the dual weight of each element node.
make_node_quadrature_weight()	Create a device function returning node quadrature weights.
make_node_sample()	Create a device function locating an element node's physical anchor.
make_trace_node_quadrature_weight()	Create a device function returning trace node quadrature weights.
node_positions([out])	Return a temporary array containing the world position for each node.
trace()	Return a trace basis space on lower-dimensional elements.

Attributes

BasisArg
geometry	Underlying geometry of the basis space
moves_node_samples	Whether make_node_sample() may return another element than the one it is given.
supports_nodal_assembly	Whether nodal assembly may assume a diagonal node coupling.
supports_nodal_quadrature	Whether this basis may supply nodal quadrature points and weights.
topology	Underlying topology of the basis space
value	Value type for the underlying shape functions
weight_gradient_type	Data type of node weight gradients returned by the basis.
weight_type	Data type of node weights returned by the basis.

Parameters:

topology (SpaceTopology)

supports_nodal_assembly = True

Whether nodal assembly may assume a diagonal node coupling.

supports_nodal_quadrature = True

Whether this basis may supply nodal quadrature points and weights.

moves_node_samples = False

Whether make_node_sample() may return another element than the one it is given.

BasisArg = <warp._src.codegen.Struct object>

property topology: SpaceTopology

Underlying topology of the basis space

property geometry: Geometry

Underlying geometry of the basis space

property value: Value

Value type for the underlying shape functions

basis_arg_value(device)

fill_basis_arg(arg, device)

Fill the arguments to be passed to basis-related device functions

node_positions(out=None)

Return a temporary array containing the world position for each node.

Parameters:

out (array | None)

Return type:

array

make_node_coords_in_element()

Create a device function returning node coordinates within an element.

make_node_sample()

Create a device function locating an element node’s physical anchor.

The result is an element index, in-element coordinates, and the same node’s local slot on that element. Constrained spaces may return a different element containing the independent master node.

make_node_quadrature_weight()

Create a device function returning node quadrature weights.

make_element_inner_weight()

Create a device function returning inner element shape weights.

make_element_outer_weight()

Create a device function returning outer element shape weights.

make_element_inner_weight_gradient()

Create a device function returning gradients of inner element weights.

make_element_outer_weight_gradient()

Create a device function returning gradients of outer element weights.

make_trace_node_quadrature_weight()

Create a device function returning trace node quadrature weights.

make_node_dual_weight()

Create a device function returning the dual weight of each element node.

The dual weight d of a node extracts its degree of freedom from a node-space value v reproduced by the basis at the node location, as v * d for scalar-valued bases or dot(v, d) for vector-valued bases.

The default implementation returns the inverse of the node weight at the node location, which is only valid for scalar-valued bases whose node weights vanish at the other nodes. See ShapeFunction.make_node_dual_weight().

trace()

Return a trace basis space on lower-dimensional elements.

Return type:

TraceBasisSpace

property weight_type

Data type of node weights returned by the basis.

property weight_gradient_type

Data type of node weight gradients returned by the basis.