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

Author

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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)

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.

Suggested Citation

  • Sabelfeld Karl K. & Prokopiev Alexander, 2025. "Stochastic iterative refinement with preconditioning for solving Helmholtz equation via boundary integral equation," Monte Carlo Methods and Applications, De Gruyter, vol. 31(4), pages 329-342.
    • Handle: RePEc:bpj:mcmeap:v:31:y:2025:i:4:p:329-342:n:1007
    DOI: 10.1515/mcma-2025-2022
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