warp.fem.FunctionSpace#

class warp.fem.FunctionSpace(basis)[source]#

Interface class for function spaces, i.e. geometry + interpolation basis.

The value of a function f at a position x is generally computed as

f(x) = L(x)[sum_i f_i N_i(x)]

with:

__init__(basis)[source]#

Methods

`__init__`(basis)
`divergence_valid`()	Whether divergence of this field can be computed.
`dof_value`(space_value, node_weight, ...)	Compute the projection of a world-space value onto the basis of a single degree of freedom.
`gradient_valid`()	Whether gradient operator can be computed.
`local_value_map_inner`(elt_arg, ...)	Build the local value map transforming from node to world space.
`local_value_map_outer`(elt_arg, ...)	Build the local value map transforming vector-valued from node to world space.
`make_field`([space_partition])	Create a zero-initialized discrete field over the function space holding values for all degrees of freedom of nodes in a space partition.
`node_basis_element`(dof_coord)	Basis element for node degrees of freedom.
`node_count`()	Number of nodes in the interpolation basis.
`space_divergence`(dof_value, ...)	Assemble the world-space divergence of the function space.
`space_gradient`(dof_value, ...)	Assemble the world-space gradient of the function space.
`space_value`(dof_value, node_weight, ...)	Assemble the world-space value of the function space.
`trace`()	Trace of the function space over lower-dimensional elements of the geometry.
`value_basis_element`(dof_coord)	Basis element for the function space values.

Attributes

`basis`	Underlying basis space.
`degree`	Maximum polynomial degree of the underlying basis.
`dimension`	Function space embedding dimension.
`element_kind`	Kind of element the function space is expressed over.
`geometry`	Underlying geometry.
`name`
`topology`	Underlying geometry.
`dtype`	Value type of the interpolation functions.
`dof_dtype`	Data type of the degrees of freedom of each node.
`weight_dtype`	Data type of the shape functions associated to each node.
`LocalValueMap`	Type of the local map for transforming vector-valued functions from reference to world space.
`VALUE_DOF_COUNT`	Number of degrees of freedom per value, as a Warp constant.
`NODE_DOF_COUNT`	Number of degrees of freedom per node, as a Warp constant.
`ORDER`	Polynomial degree of the function space, used to determine integration order.

weight_dtype: type#: Data type of the shape functions associated to each node.

LocalValueMap: type#: Type of the local map for transforming vector-valued functions from reference to world space.

VALUE_DOF_COUNT: int#: Number of degrees of freedom per value, as a Warp constant.

NODE_DOF_COUNT: int#: Number of degrees of freedom per node, as a Warp constant.

ORDER: int#: Polynomial degree of the function space, used to determine integration order.

node_count()[source]#

Number of nodes in the interpolation basis.

property element_kind: ElementKind[source]#: Kind of element the function space is expressed over.

property degree: int[source]#: Maximum polynomial degree of the underlying basis.

Trace of the function space over lower-dimensional elements of the geometry.

make_field(space_partition=None)[source]#

Create a zero-initialized discrete field over the function space holding values for all degrees of freedom of nodes in a space partition.

Parameters:: space_partition – If provided, the subset of nodes to consider