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:

f_i the value of the ith node’s degrees-of-freedom (dof)
N_i(x) the weight associated to the node at x
L(x) local linear transformation from node-space to world-space

Parameters:: basis (BasisSpace)

__init__(basis)[source]#

Parameters:: basis (BasisSpace)

Methods

`__init__`(basis)
`divergence_valid`()	Whether divergence of this field can be computed.
`dof_value`(space_value, node_weight, ...)	Computes the projection of a world-space value onto the basis of a single degree of freedom :param - space_value: world-space value :param - node_weight: weight associated to the node, as given per the basis space :param - local_value_map: data encoding local transformation from node space to world space, as given per local_map_value_(inn\|out)er
`gradient_valid`()	Whether gradient operator can be computed.
`local_value_map_inner`(elt_arg, ...)	Builds the local value map transforming from node to world space
`local_value_map_outer`(elt_arg, ...)	Builds the local value map transforming vector-valued from node to world space
`make_field`([space_partition])	Creates 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, ...)
`space_gradient`(dof_value, ...)	Assembles the world-space gradient of the function space :param - dof_value: node value in the degrees-of-freedom basis :param - node_weight_gradient: gradient of the weight associated to the node, either w.r.t element or world space :param - local_value_map: data encoding local transformation from node space to world space, as given per local_map_value_(inn\|out)er
`space_value`(dof_value, node_weight, ...)	Assembles the world-space value of the function space :param - dof_value: node value in the degrees-of-freedom basis :param - node_weight: weight associated to the node, as given per the basis space :param - local_value_map: data encoding local transformation from node space to world space, as given per local_map_value_(inn\|out)er
`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

dtype: type#: Value type of the interpolation functions

dof_dtype: type#: Data type of the degrees of freedom of each node

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

Return type:: int

property topology: SpaceTopology[source]#: Underlying geometry

property basis: BasisSpace[source]#: Underlying basis space

property geometry: Geometry[source]#: Underlying geometry

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

property dimension: int[source]#: Function space embedding dimension

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

property name[source]#

trace()[source]#

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

Return type:: FunctionSpace

make_field(space_partition=None)[source]#

Creates 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