porepy.numerics.vem.mass_matrix module
Mass matrix classes for a discretization of a L2-mass bilinear form with constant test and trial functions for mixed methods (e.g. RT0, MVEM).
The discretization takes into account cell volumes and the mass_weight given in the parameters (the mass weight can again incorporate porosity, time step, apertures etc), so that the mass matrix (shape (sd.num_faces + sd.num_cells)^2) has the following diagonal for the cell_dof:
sd.cell_volumes * mass_weight
The right hand side is null. There is also a class for the inverse of the mass matrix.
Note that the matrix equals the discretization operator in this case, and so is stored directly in the data as self._key() + “mixed_mass” or self._key() + “inv_mixed_mass”. The corresponding (null) rhs vectors are stored as self._key() + “bound_mixed_mass” or self._key() + “bound_inv_mixed_mass”, respectively.
- class MixedInvMassMatrix(keyword='flow')[source]
Bases:
objectClass that provides the discretization of an inverse L2-mass bilinear form with constant test and trial functions for mixed methods (e.g. RT0, MVEM).
- Parameters
keyword (str) –
- assemble_matrix(sd, data)[source]
Return the inverse of the matrix for a discretization of a L2-mass bilinear form with constant test and trial functions. Also discretize the necessary operators if the data dictionary does not contain a discrete inverse mass matrix.
- Parameters
g (
Grid) – Computational grid, with geometry fields computed.data (
dictionary) – With data stored.sd (Grid) –
- Returns
- System matrix of this
discretization.
- Return type
scipy.sparse.csr_matrix (self.ndof x self.ndof)
- assemble_matrix_rhs(sd, data)[source]
Return the inverse of the matrix and right-hand side (null) for a discretization of a L2-mass bilinear form with constant test and trial functions.
- assemble_rhs(sd, data)[source]
Return the (null) right-hand side for a discretization of the inverse of a L2-mass bilinear form with constant test and trial functions. Also discretize the necessary operators if the data dictionary does not contain a discretization of the boundary term.
- Parameters
g (
Grid) – Computational grid, with geometry fields computed.data (
dictionary) – With data stored.sd (Grid) –
- Returns
- Right hand side vector with representation of boundary
conditions: A null vector of length g.num_faces.
- Return type
np.ndarray
- discretize(sd, data)[source]
Discretize the inverse of a L2-mass bilinear form with constant test and trial functions.
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]
- parameter_dictionary contains the entries:
- mass_weight: (array, self.g.num_cells): Scalar values which may e.g.
represent the porosity or heat capacity. The discretization will multiply this weight with the cell volumes.
- matrix_dictionary will be updated with the following entries:
- mixed_mass: sps.dia_matrix (sparse dia, self.ndof x self.ndof): Mass matrix
obtained from the discretization.
bound_mass: all zero np.ndarray (self.ndof)
- Parameters
sd (
pp.Grid) – grid, or a subclass, with geometry fields computed.data (
dict) – dictionary to store the data.
- Return type
None
- class MixedMassMatrix(keyword='flow')[source]
Bases:
objectClass that provides the discretization of a L2-mass bilinear form with constant test and trial functions for mixed methods (e.g. RT0, MVEM).
- Parameters
keyword (str) –
- assemble_matrix(sd, data)[source]
Return the matrix for a discretization of a L2-mass bilinear form with constant test and trial functions.
- Parameters
sd (
pp.Grid) – Computational grid, with geometry fields computed.data (
dictionary) – With data stored.
- Returns
- System matrix of this
discretization.
- Return type
scipy.sparse.csr_matrix (self.ndof x self.ndof)
- assemble_matrix_rhs(sd, data)[source]
Return the matrix and right-hand side (null) for a discretization of a L2-mass bilinear form with constant test and trial functions. Also discretize the necessary operators if the data dictionary does not contain a mass matrix.
- Parameters
sd (
pp.Grid) – grid, or a subclass, with geometry fields computed.data (
dict) – dictionary to store the data.
- Returns
- Mass matrix obtained from the
discretization.
rhs (array, self.ndof): zero right-hand side.
- Return type
matrix (sparse dia, self.ndof x self.ndof)
The names of data in the input dictionary (data) are given in the documentation of discretize, see there.
- assemble_rhs(sd, data)[source]
Return the (null) right-hand side for a discretization of a L2-mass bilinear form with constant test and trial functions.
- Parameters
sd (
pp.Grid) – Computational grid, with geometry fields computed.data (
dictionary) – With data stored.
- Returns
- zero right hand side vector with representation of
boundary conditions.
- Return type
np.ndarray (self.ndof)
- discretize(sd, data)[source]
Discretize a L2-mass bilinear form with constant test and trial functions.
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]
- parameter_dictionary contains the entries:
- mass_weight: (array, self.g.num_cells): Scalar values which may e.g.
represent the porosity or heat capacity. The disrcetization will multiply this weight with the cell volumes.
- matrix_dictionary will be updated with the following entries:
- mixed_mass: sps.dia_matrix (sparse dia, self.ndof x self.ndof): Mass matrix
obtained from the discretization.
bound_mass: all zero np.ndarray (self.ndof)
- Parameters
sd (
pp.Grid) – A grid with geometry fields computed.data (
dict) – dictionary to store the data.
- Return type
None