porepy.numerics.vem.mvem module
Module with implementation of the mixed virtual element method.
The main class is MVEM.
- class MVEM(keyword)[source]
Bases:
DualEllipticImplementation of the lowest order mixed virtual element method for scalar elliptic equations.
- Parameters
keyword (str) –
- static check_conservation(sd, u)[source]
Return the local conservation of mass in the cells. Parameters ———- sd: grid, or a subclass. u : array (sd.num_faces) velocity at each face.
- discretize(sd, data)[source]
Discretize a second order elliptic equation using a dual virtual element 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. Stored in the data dictionary.
- static massHdiv(K, inv_K, c_center, c_volume, f_centers, normals, sign, diam, weight=0.0)[source]
Compute the local mass Hdiv matrix using the mixed vem approach.
Parameters
- Kndarray (sd.dim, sd.dim)
Permeability of the cell.
- c_centerarray (sd.dim)
Cell center.
- c_volumescalar
Cell volume.
- f_centersndarray (sd.dim, num_faces_of_cell)
Center of the cell faces.
- normalsndarray (sd.dim, num_faces_of_cell)
Normal of the cell faces weighted by the face areas.
- signarray (num_faces_of_cell)
+1 or -1 if the normal is inward or outward to the cell.
- diamscalar
Diameter of the cell.
- weightscalar
weight for the stabilization term. Optional, default = 0.
Return
- out: ndarray (num_faces_of_cell, num_faces_of_cell)
Local mass Hdiv matrix.