pyamg.classical#

Classical AMG.

pyamg.classical.air_solver(A, strength=('classical', {'norm': 'min', 'theta': 0.3}), CF=('RS', {'second_pass': True}), interpolation='one_point', restrict=('air', {'degree': 2, 'theta': 0.05}), presmoother=None, postsmoother=('fc_jacobi', {'c_iterations': 1, 'f_iterations': 2, 'iterations': 1, 'omega': 1.0, 'withrho': False}), filter_operator=None, max_levels=20, max_coarse=20, keep=False, **kwargs)[source]#

Create a multilevel solver using approximate ideal restriction (AIR) AMG.

Parameters:

Acsr_matrix: Square (non)symmetric matrix in CSR format
strength[‘symmetric’, ‘classical’, ‘evolution’, ‘distance’,: ‘algebraic_distance’,’affinity’, ‘energy_based’, None]

Method used to determine the strength of connection between unknowns of the linear system. Method-specific parameters may be passed in using a tuple, e.g. strength=(‘symmetric’,{‘theta’ : 0.25 }). If strength=None, all nonzero entries of the matrix are considered strong.
CF{string}default ‘RS’ with second pass: Method used for coarse grid selection (C/F splitting) Supported methods are RS, PMIS, PMISc, CLJP, CLJPc, and CR.
interpolation{string}default ‘one_point’: Options include ‘direct’, ‘classical’, ‘inject’ and ‘one-point’.
restrict{string}default distance-2 AIR, with theta = 0.05.: Option is ‘air’ for local approximate ideal restriction (lAIR), with inner options specifying degree, strength tolerance, etc.
presmoother{string or dict}default None: Method used for presmoothing at each level. Method-specific parameters may be passed in using a tuple.
postsmoother{string or dict}: Postsmoothing method with the same usage as presmoother. postsmoother=(‘fc_jacobi’, … ) with 2 F-sweeps, 1 C-sweep is default.
filter_operator(bool, tol)default None: Remove small entries in operators on each level if True. Entries are considered “small” if |a_ij| < tol |a_ii|.
max_levels: {integer}default 20: Maximum number of levels to be used in the multilevel solver.
max_coarse: {integer}default 20: Maximum number of variables permitted on the coarse grid.
keep: {bool}default False: Flag to indicate keeping strength of connection matrix (C) in hierarchy.

Returns:

mlmultilevel_solver: Multigrid hierarchy of matrices and prolongation operators

See also

aggregation.smoothed_aggregation_solver, multilevel_solver
aggregation.rootnode_solver, ruge_stuben_solver

Notes

“coarse_solver” is an optional argument and is the solver used at the coarsest grid. The default is a pseudo-inverse. Most simply, coarse_solver can be one of [‘splu’, ‘lu’, ‘cholesky, ‘pinv’, ‘gauss_seidel’, … ]. Additionally, coarse_solver may be a tuple (fn, args), where fn is a string such as [‘splu’, ‘lu’, …] or a callable function, and args is a dictionary of arguments to be passed to fn. See [2001TrOoSc] for additional details.

References

[1] Manteuffel, T. A., Münzenmaier, S., Ruge, J., & Southworth, B. S. (2019). Nonsymmetric reduction-based algebraic multigrid. SIAM Journal on Scientific Computing, 41(5), S242-S268.

[2] Manteuffel, T. A., Ruge, J., & Southworth, B. S. (2018). Nonsymmetric algebraic multigrid based on local approximate ideal restriction (lAIR). SIAM Journal on Scientific Computing, 40(6), A4105-A4130.

Examples

>>> from pyamg.gallery import poisson
>>> from pyamg import air_solver
>>> A = poisson((10,),format='csr')
>>> ml = air_solver(A,max_coarse=3)

pyamg.classical.ruge_stuben_solver(A, strength=('classical', {'theta': 0.25}), CF=('RS', {'second_pass': False}), interpolation='classical', presmoother=('gauss_seidel', {'sweep': 'symmetric'}), postsmoother=('gauss_seidel', {'sweep': 'symmetric'}), max_levels=30, max_coarse=10, keep=False, **kwargs)[source]#

Create a multilevel solver using Classical AMG (Ruge-Stuben AMG).

Parameters:

Acsr_matrix: Square matrix in CSR format
strengthstr: Valid strings are [‘symmetric’, ‘classical’, ‘evolution’, ‘distance’, ‘algebraic_distance’,’affinity’, ‘energy_based’, None]. Method used to determine the strength of connection between unknowns of the linear system. Method-specific parameters may be passed in using a tuple, e.g. strength=(‘symmetric’,{‘theta’: 0.25 }). If strength=None, all nonzero entries of the matrix are considered strong.
CFstr or tuple, default ‘RS’: Method used for coarse grid selection (C/F splitting) Supported methods are RS, PMIS, PMISc, CLJP, CLJPc, and CR.
interpolationstr, default ‘classical’: Method for interpolation. Options include ‘direct’, ‘classical’.
presmootherstr or dict: Method used for presmoothing at each level. Method-specific parameters may be passed in using a tuple, e.g. presmoother=(‘gauss_seidel’,{‘sweep’:’symmetric}), the default.
postsmootherstr or dict: Postsmoothing method with the same usage as presmoother
max_levelsint, default 30: Maximum number of levels to be used in the multilevel solver.
max_coarseint, default 20: Maximum number of variables permitted on the coarse grid.
keepbool, default False: Flag to indicate keeping strength of connection (C) in the hierarchy for diagnostics.

Returns:

mlMultilevelSolver: Multigrid hierarchy of matrices and prolongation operators