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

Journal Monte Carlo Methods and Applications
ISSN: 0929-9629 , E-ISSN: 1569-3961
Output data Year: 2025, Volume: 31, Number: 4, Pages: 329-342 Pages count : 14 DOI: 10.1515/mcma-2025-2022
Tags Boundary integral equations; vector randomized algorithm; large system of linear equations; iterative refinement; Helmholtz equation; randomized SVD; stochastic projection methods
Authors Sabelfeld Karl K. 2 , Prokopiev Alexander 1
Affiliations
1 Institute of Computational Mathematics and Mathematical Geophysics , Russian Academy of Sciences
2 Sobolev Institute of Mathematics, Russian Academy of Sciences , Novosibirsk , Russia

Funding (1)

1 Russian Science Foundation 24-11-00107

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.
Cite: Sabelfeld K.K. , Prokopiev A.
Stochastic iterative refinement with preconditioning for solving Helmholtz equation via boundary integral equation
Monte Carlo Methods and Applications. 2025. V.31. N4. P.329-342. DOI: 10.1515/mcma-2025-2022 WOS Scopus OpenAlex
Dates:
Submitted: Jul 23, 2025
Accepted: Nov 15, 2025
Published online: Nov 16, 2025
Published print: Dec 1, 2025
Identifiers:
Web of science: WOS:001614544300001
Scopus: 2-s2.0-105021962375
OpenAlex: W7105754229
Citing: Пока нет цитирований
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