pygeon.discretizations.vec_discretization module

Module for the vector discretization class.

class pygeon.discretizations.vec_discretization.VecDiscretization(keyword='unitary_data')[source]

Bases: Discretization

A class representing a vectorized discretization for a given base discretization. The base needs to be specified in the __init__ function.

base_discr: The scalar discretization method.

ndof(sd)[source]

Returns the number of degrees of freedom associated to the method. In this case, it returns the product of the number of nodes and the dimension of the grid.

Parameters:: sd (pg.Grid) – The grid or a subclass.
Returns:: The number of degrees of freedom.
Return type:: int

assemble_mass_matrix(sd, data=None)[source]

Assembles and returns the mass matrix.

Parameters:

sd (pg.Grid) – The grid.
data (dict | None) – Optional data for the assembly.

Returns:

The mass matrix obtained from the discretization.

Return type:

sps.csc_array

assemble_diff_matrix(sd)[source]

Assembles the matrix corresponding to the differential operator.

Parameters:: sd (pg.Grid) – Grid object or a subclass.
Returns:: The differential matrix.
Return type:: sps.csc_array

assemble_stiff_matrix(sd, data=None)[source]

Assembles the stiffness matrix.

Parameters:: sd (pg.Grid) – Grid object or a subclass.
Returns:: The differential matrix.
Return type:: sps.csc_array

assemble_lumped_matrix(sd, data=None)[source]

Assembles the lumped mass matrix given by the row sums on the diagonal.

Parameters:

sd (pg.Grid) – Grid object or a subclass.
data (dict | None) – Dictionary with physical parameters for scaling.

Returns:

The lumped mass matrix.

Return type:

sps.csc_array

proj_to_PwPolynomials(sd)[source]

Construct the matrix for projecting a vector function to a piecewise vector space.

Parameters:: sd (pg.Grid) – The grid on which to construct the matrix.
Returns:: The matrix representing the projection.
Return type:: sps.csc_array

interpolate(sd, func)[source]

Interpolates a function onto the finite element space

Parameters:

sd (pg.Grid) – Grid, or a subclass.
func (Callable) – A function that returns the function values at coordinates.

Returns:

The values of the degrees of freedom

Return type:

np.ndarray

eval_at_cell_centers(sd)[source]

Assembles the matrix for evaluating the discretization at the cell centers.

Parameters:: sd (pg.Grid) – Grid object or a subclass.
Returns:: The evaluation matrix.
Return type:: sps.csc_array

assemble_nat_bc(sd, func, b_faces)[source]

Assembles the natural boundary condition vector, equal to zero.

Parameters:

sd (pg.Grid) – The grid object.
func (Callable[[np.ndarray], np.ndarray]) – The function defining the natural boundary condition.
b_faces (np.ndarray) – The array of boundary faces.

Returns:

The assembled natural boundary condition vector.

Return type:

np.ndarray

assemble_broken_div_matrix(sd)[source]

Assembles the broken, element-wise divergence operator. This operator is only implemented for vector-valued functions.

Parameters:: sd (pg.Grid) – The grid object.
Returns:: The divergence matrix.
Return type:: sps.csc_array

assemble_broken_curl_matrix(sd)[source]

Assembles the broken, element-wise curl operator. This operator is only implemented for vector-valued functions.

Parameters:: sd (pg.Grid) – The grid object.
Returns:: The curl matrix.
Return type:: sps.csc_array

vectorize(dim, matrix)[source]

Vectorizes the given matrix by repeating it for each dimension of the grid.

Parameters:

dim (int) – Number of vector components.
matrix (sps.csc_array) – The matrix to be vectorized.

Returns:

The vectorized matrix.

Return type:

sps.csc_array