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)

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

Parameters:

Acsr_array

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{str}default ‘RS’ with second pass

Method used for coarse grid selection (C/F splitting) Supported methods are RS, PMIS, PMISc, CLJP, CLJPc, and CR.

interpolationstr

Options include ‘direct’, ‘classical’, ‘inject’ and ‘one-point’.

restrictstr

Option is ‘air’ for local approximate ideal restriction (lAIR), with inner options specifying degree, strength tolerance, etc..

presmootherstr

Method used for presmoothing at each level. Method-specific parameters may be passed in using a tuple.

postsmootherstr

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.

keepbool

Flag to indicate keeping strength of connection matrix (C) in hierarchy.

**kwargsdict

Extra keywords passed to the Multilevel class.

Returns:

MultilevelSolver

Multigrid hierarchy of matrices and prolongation operators.

See also

pyamg.multilevel.MultilevelSolver

pyamg.aggregation.smoothed_aggregation_solver

pyamg.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’ or a callable function, and args is a dictionary of arguments to be passed to fn. See [3] 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.

[3]

Trottenberg, U.; Oosterlee, C. W. & Schüller, A. (2001), Multigrid, Vol. 33, Academic Press.

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)

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

Parameters:

Acsr_array

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.

**kwargsdict

Extra keywords passed to MultilevelSolver class.

Returns:

MultilevelSolver

Multigrid hierarchy of matrices and prolongation operators.

See also

aggregation.smoothed_aggregation_solver, MultilevelSolver

aggregation.rootnode_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 [1] for additional details.

References

[1]

Trottenberg, U.; Oosterlee, C. W. & Schüller, A. (2001), Multigrid, Vol. 33, Academic Press.

Examples

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