TY - GEN

T1 - Multigrid Incomplete Factorization Methods in Krylov Subspaces on Unstructured Grids

AU - Batalov, Maxim

AU - Il’In, Valery

N1 - Conference code: 18

PY - 2024

Y1 - 2024

N2 - We consider multigrid methods for solving large systems of linear algebraic equations (SLAEs) with sparse matrices arising from approximations of multidimensional boundary-value problems on unstructured grids. The approaches we propose here are based on recursive data structures for variables defined on a sequence of embedded grids, and their implementation is carried out employing approximate matrix factorization, where the forward run and the backward run correspond to, respectively, the traditional reduction stage and to the prolongation of the solution. The constructed iterative processes, depending on matrix types, are preconditioned conjugate direction methods in Krylov subspaces. Multigrid algorithms are formulated according to a recursive application of two-grid algorithms. The paper investigates the application peculiarities of the discussed approaches to the solution of two- and three-dimensional problems, including the efficiency of parallel computations on distributed and hierarchical shared memory. The efficiency of the suggested mathematical tools and software is demonstrated by the results of computational experiments on a representative series of methodological examples.

AB - We consider multigrid methods for solving large systems of linear algebraic equations (SLAEs) with sparse matrices arising from approximations of multidimensional boundary-value problems on unstructured grids. The approaches we propose here are based on recursive data structures for variables defined on a sequence of embedded grids, and their implementation is carried out employing approximate matrix factorization, where the forward run and the backward run correspond to, respectively, the traditional reduction stage and to the prolongation of the solution. The constructed iterative processes, depending on matrix types, are preconditioned conjugate direction methods in Krylov subspaces. Multigrid algorithms are formulated according to a recursive application of two-grid algorithms. The paper investigates the application peculiarities of the discussed approaches to the solution of two- and three-dimensional problems, including the efficiency of parallel computations on distributed and hierarchical shared memory. The efficiency of the suggested mathematical tools and software is demonstrated by the results of computational experiments on a representative series of methodological examples.

KW - Algebraic multigrid method

KW - Incomplete factorization algorithm

KW - Krylov subspace

KW - Large sparse SLAE

KW - Parallelization of algorithms

KW - Recursive ordering

KW - Unstructured grid

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85215659082&origin=inward&txGid=2955a6fa87fbed598e8a71602314b559

UR - https://link.springer.com/chapter/10.1007/978-3-031-73372-7_12

UR - https://www.mendeley.com/catalogue/e71aff3f-6cf7-3bd0-925d-533d90ddd895/

U2 - 10.1007/978-3-031-73372-7_12

DO - 10.1007/978-3-031-73372-7_12

M3 - Conference contribution

SN - 9783031733741

T3 - Communications in Computer and Information Science

SP - 163

EP - 176

BT - Communications in Computer and Information Science

PB - Springer Science and Business Media Deutschland GmbH

T2 - 18th International Scientific Conference on Parallel Computational Technologies

Y2 - 2 April 2024 through 4 April 2024

ER -