porepy.numerics.fem.rt0 module
- class RT0(keyword)[source]
Bases:
DualElliptic- Parameters
keyword (str) –
- discretize(sd, data)[source]
Discretize a second order elliptic equation using a RT0-P0 method.
We assume the following two sub-dictionaries to be present in the data dictionary:
- parameter_dictionary, storing all parameters.
Stored in data[pp.PARAMETERS][self.keyword].
- matrix_dictionary, for storage of discretization matrices.
Stored in data[pp.DISCRETIZATION_MATRICES][self.keyword]
- deviation_from_plane_tol: The geometrical tolerance, used in the check to
rotate 2d and 1d grids.
- parameter_dictionary contains the entries:
- second_order_tensor: (pp.SecondOrderTensor) Permeability defined
cell-wise. This is the effective permeability, including any aperture scalings etc.
- matrix_dictionary will be updated with the following entries:
- mass: sps.csc_matrix (sd.num_faces, sd.num_faces)
The mass matrix.
- div: sps.csc_matrix (sd.num_cells, sd.num_faces)
The divergence matrix.
Optional parameter:
- is_tangential: Whether the lower-dimensional permeability tensor has been
rotated to the fracture plane. Defaults to False and stored in the data dictionary.
- static faces_to_cell(pt, coord, f_centers, f_normals, dim, R)[source]
Construct a local matrix that evaluate a RT0 solution in a give point (cell center).
Parameters
pt: the point where to evaluate the field, usually cell center coord: the vertices of the simplex f_centers: the centre of the faces ordered following coord f_normals: the normal of the faces ordered as f_centers dim: the spatial dimension
- static massHdiv(inv_K, c_volume, coord, sign, dim, HB)[source]
Compute the local mass Hdiv matrix using the mixed vem approach.
Parameters
- Kndarray (sd.dim, sd.dim)
Permeability of the cell.
- c_volumescalar
Cell volume.
- signarray (num_faces_of_cell)
+1 or -1 if the normal is inward or outward to the cell.
Return
- out: ndarray (num_faces_of_cell, num_faces_of_cell)
Local mass Hdiv matrix.