Stochastic iterative refinement with preconditioning for solving Helmholtz equation via boundary integral equation

Sabelfeld Karl K. () and Prokopiev Alexander ()
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Sabelfeld Karl K.: Institute of Computational Mathematics and Mathematical Geophysics, Russian Academy of Sciences; and Sobolev Institute of Mathematics, Russian Academy of Sciences, Novosibirsk, Russia
Prokopiev Alexander: Institute of Computational Mathematics and Mathematical Geophysics, Russian Academy of Sciences, Novosibirsk, Russia

Monte Carlo Methods and Applications, 2025, vol. 31, issue 4, 329-342

Abstract: This work suggests different Monte Carlo algorithms for solving large systems of linear algebraic equations arising from the numerical solution of the Dirichlet problem for the Helmholtz equation. Approach based on boundary integral representations, vector randomization algorithm, method of fundamental solutions, stochastic projection algorithm, and randomized singular value decomposition are applied. It is shown that the use of stochastic iterative refinement and preconditioning can significantly improve the accuracy and stability of the computations. Simulation results are presented, demonstrating the effectiveness of the proposed methods.

Keywords: Boundary integral equations; vector randomized algorithm; large system of linear equations; iterative refinement; Helmholtz equation; randomized SVD; stochastic projection methods (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:bpj:mcmeap:v:31:y:2025:i:4:p:329-342:n:1007

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DOI: 10.1515/mcma-2025-2022

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