FunctionSpace¶

class dolfin.cpp.function.FunctionSpace(*args)¶

Bases: dolfin.cpp.common.Variable, dolfin.cpp.function.HierarchicalFunctionSpace

This class represents a finite element function space defined by a mesh, a finite element, and a local-to-global mapping of the degrees of freedom (dofmap).

Copy constructor Arguments V (FunctionSpace ) The object to be copied.

Parameters:	FunctionSpace & V (const) –

assign()¶

Assignment operator Arguments V (FunctionSpace ) Another function space.

Parameters:	FunctionSpace & V (const) –
Return type:	const FunctionSpace &

child()¶: Return the child FunctionSpace in the hierarchy

collapse()¶

Collapse a subspace and return a new function space and a map from new to old dofs Arguments collapsed_dofs (std::unordered_map<std::size_t, std::size_t>) The map from new to old dofs. Returns:cpp:any:FunctionSpace The new function space.

Parameters:	std::size_t, std::size_t > & collapsed_dofs (std::unordered_map<) –
Return type:	std::shared_ptr< FunctionSpace >

component()¶

Return component w.r.t. to root superspace, i.e. W.sub(1).sub(0) == [1, 0]. Returns std::vector<std::size_t> The component (w.r.t to root superspace).

Return type:	std::vector< std::size_t >

contains()¶

Check whether V is subspace of this, or this itself Arguments V (FunctionSpace ) The space to be tested for inclusion. Returns bool True if V is contained or equal to this.

Parameters:	FunctionSpace & V (const) –
Return type:	bool

dim()¶

Return global dimension of the function space. Equivalent to dofmap ->global_dimension() Returns std::size_t The dimension of the function space.

Return type:	std::size_t

dofmap()¶

Return dofmap Returns:cpp:any:GenericDofMap The dofmap.

Return type:	std::shared_ptr< const GenericDofMap >

element()¶

Return finite element Returns:cpp:any:FiniteElement The finite element.

Return type:	std::shared_ptr< const FiniteElement >

extract_sub_space()¶

Extract subspace for component Arguments component (std::vector<std::size_t>) The component. Returns:cpp:any:FunctionSpace The subspace.

Parameters:	std::vector< std::size_t > & component (const) –
Return type:	std::shared_ptr< FunctionSpace >

has_cell()¶

Check if function space has given cell Arguments cell (Cell ) The cell. Returns bool True if the function space has the given cell.

Parameters:	Cell & cell (const) –
Return type:	bool

has_element()¶

Check if function space has given element Arguments element (FiniteElement ) The finite element. Returns bool True if the function space has the given element.

Parameters:	FiniteElement & element (const) –
Return type:	bool

interpolate()¶

Interpolate function v into function space, returning the vector of expansion coefficients Arguments expansion_coefficients (GenericVector ) The expansion coefficients. v (GenericFunction ) The function to be interpolated.

Parameters:	& expansion_coefficients (GenericVector) – GenericFunction & v (const) –
Return type:	void

leaf_node()¶: Return the finest FunctionSpace in hierarchy

mesh()¶

Return mesh Returns:cpp:any:Mesh The mesh.

Return type:	std::shared_ptr< const Mesh >

parent()¶: Return the parent FunctionSpace in the hierarchy

print_dofmap()¶

Print dofmap (useful for debugging)

Return type:	void

root_node()¶: Return the coarsest FunctionSpace in hierarchy

set_x()¶

Set dof entries in vector to value*x[i], where [x][i] is the coordinate of the dof spatial coordinate. Parallel layout of vector must be consistent with dof map range This function is typically used to construct the null space of a matrix operator, e.g. rigid body rotations. Arguments vector (GenericVector ) The vector to set. value (double) The value to multiply to coordinate by. component (std::size_t) The coordinate index. mesh (Mesh ) The mesh.

Parameters:	& x (GenericVector) – value (double) – component (std::size_t) –
Return type:	void

sub()¶

Extract subspace for component Arguments component (std::size_t) Index of the subspace. Returns:cpp:any:FunctionSpace The subspace.

Parameters:	component (std::size_t) –
Return type:	std::shared_ptr< FunctionSpace >

tabulate_dof_coordinates()¶

Tabulate the coordinates of all dofs on this process. This function is typically used by preconditioners that require the spatial coordinates of dofs, for example for re-partitioning or nullspace computations. Arguments mesh (Mesh ) The mesh. Returns std::vector<double> The dof coordinates (x0, y0, x1, y1, …)

Return type:	std::vector< double >

thisown¶: The membership flag