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Sparse System Solution Methods for Complex Problems

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Parallel Computing Technologies (PaCT 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12942))

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Abstract

Sparse system solution methods (S\({}^3\)M) is a collection of interoperable linear solvers and preconditioners organized into a C++ header-only library. The current set of methods in the collection span both rather traditional Krylov space acceleration methods and smoothers as well as advanced incomplete factorization methods and rescaling and reordering methods. The methods can be integrated into algebraic multigrid and multi-stage fashion to construct solution strategies for complex linear systems that originate from coupled multi-physics problems. Several examples are considered in this work, that includes Constrained Pressure Residual (CPR) multi-stage strategy for oil & gas problem and Schur complement method for the system obtained with mimetic finite difference discretization for anisotropic diffusion problem.

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Acknowledgements

This work has been supported by Russian Science Foundation grant 21-71-20024.

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Authors and Affiliations

  1. Marchuk Institute of Numerical Mathematics, RAS, Moscow, 119333, Russia

    Igor Konshin & Kirill Terekhov

  2. Moscow Institute of Physics and Technology, Moscow, 141701, Russia

    Igor Konshin & Kirill Terekhov

  3. Dorodnicyn Computing Centre of FRC CSC, RAS, Moscow, 119333, Russia

    Igor Konshin

  4. Sechenov University, Moscow, 119991, Russia

    Igor Konshin

Authors
  1. Igor Konshin
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  2. Kirill Terekhov
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Correspondence to Igor Konshin .

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  1. Institute of Computational Mathematics and Mathematical Geophysics SB RAS, Novosibirsk, Russia

    Victor Malyshkin

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Konshin, I., Terekhov, K. (2021). Sparse System Solution Methods for Complex Problems. In: Malyshkin, V. (eds) Parallel Computing Technologies. PaCT 2021. Lecture Notes in Computer Science(), vol 12942. Springer, Cham. https://doi.org/10.1007/978-3-030-86359-3_5

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  • DOI: https://doi.org/10.1007/978-3-030-86359-3_5

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  • Online ISBN: 978-3-030-86359-3

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