puncturedfem.GlobalFunctionSpace

Global function space V_p(T) on a planar mesh T of degree p.

Attributes:

Name	Type	Description
mesh	PlanarMesh	Planar mesh
deg	int	Degree of polynomial space
quad_dict	QuadDict	Dictionary of quadrature rules
num_funs	int	Number of functions in the space
num_vert_funs	int	Number of vertex functions
num_edge_funs	int	Number of edge functions
num_bubb_funs	int	Number of bubble functions
edge_spaces	list[EdgeSpace]	List of edge spaces
edge_fun_cumsum	list[int]	Cumulative sum of the number of edge functions
cell_dofs	list[list[GlobalKey]]	List of lists of global keys for each cell

__init__(mesh, deg, quad_dict, verbose=True)

Initialize a GlobalFunctionSpace object.

Parameters:

Name	Type	Description	Default
mesh	PlanarMesh	Planar mesh	required
deg	int	Degree of polynomial space	required
quad_dict	dict[str, Quad]	Dictionary of quadrature rules	required
verbose	bool, optional	If True, print progress bars, by default True	True

__str__()

Return a string representation of the global function space.

build_edge_spaces(verbose=True)

Build the Edge spaces for each edge in the mesh.

Parameters:

Name	Type	Description	Default
verbose	bool, optional	If True, print progress bars, by default True	True

build_local_function_space(cell_idx, verbose=True, compute_interior_values=True, compute_interior_gradient=True)

Build the local function space V_p(K) for a MeshCell K.

Parameters:

Name	Type	Description	Default
cell_idx	int	Index of the cell K in the mesh	required
verbose	bool, optional	If True, print progress bars, by default True	True
compute_interior_values	bool, optional	If True, compute the values of interior functions, by default True	True

fun_is_on_boundary(key)

Return True if a global function is on the boundary.

Parameters:

Name	Type	Description	Default
key	GlobalKey	Global key of the function	required

get_global_idx(key, abs_cell_idx)

Return the global index of a local function.

Parameters:

Name	Type	Description	Default
key	GlobalKey	Local key of the function	required
abs_cell_idx	int	Absolute cell index	required

Returns:

Type	Description
int	Global index of the function

set_deg(deg)

Set the degree of the polynomial space.

Parameters:

Name	Type	Description	Default
deg	int	Degree of polynomial space	required

set_mesh(mesh)

Set the mesh.

Parameters:

Name	Type	Description	Default
mesh	PlanarMesh	Planar mesh	required