Algebraic-Geometric Multigrid Methods of Domain Decomposition

Some iterative processes in Krylov subspaces are considered for solving systems of linear algebraic equations (SLAE) with high-order sparse matrices that arise in grid approximations of multidimensional boundary value problems. The SLAE are preconditioned by a uniform combined method that includes d...

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Published inNumerical analysis and applications Vol. 18; no. 2; pp. 148 - 156
Main Author Il’in, V. P.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.06.2025
Springer Nature B.V
Subjects
Algebra
Algorithms
Approximation
Boundary value problems
Decomposition
Domain decomposition methods
Linear algebra
Mathematics
Mathematics and Statistics
Methods
Multigrid methods
Numerical Analysis
Sparse matrices
Subspaces
multidimensional problems
domain decomposition
multigrid approaches
preconditioned Krylov methods
diagonal compensation
incomplete factorization
parallelization of algorithms
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ISSN1995-4239
1995-4247
DOI10.1134/S1995423925020041

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Summary:Some iterative processes in Krylov subspaces are considered for solving systems of linear algebraic equations (SLAE) with high-order sparse matrices that arise in grid approximations of multidimensional boundary value problems. The SLAE are preconditioned by a uniform combined method that includes domain decomposition and recursive application of a two-grid algorithm, which are implemented by forming block-tridiagonal algebraic and grid structures inverted by using incomplete factorization and diagonal compensation. Stability and convergence of iterations are studied for some Stieltjes systems. Parallelization and generalization of the methods to wider classes of relevant practical problems are discussed.
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ISSN:1995-4239
1995-4247
DOI:10.1134/S1995423925020041