Implementation of the Spectral Preconditioner to Solve Poisson Equation

Implementation of the Spectral Preconditioner to Solve Poisson Equation Full article

Conference

Computational Science and Its Applications
30 Jun - 3 Jul 2025 , Istanbul

Source

Computational Science and Its Applications (ICCSA 2025 Workshops) : Proceedings
Compilation, Springer Cham. Switzerland.2026. 462 c. ISBN 978-3-031-97596-7.

Journal

Lecture Notes in Computer Science
ISSN: 0302-9743 , E-ISSN: 1611-3349

Output data

Year: 2025, Volume: 15888, Pages: 388-401 Pages count : 14 DOI: 10.1007/978-3-031-97596-7_26

Funding (1)

Russian Science Foundation

19-77-20004-П

In this paper, we present an original preconditioner to solve Poisson equation for strongly heterogeneous media. We suggest using the Conjugate Gradient method with the preconditioner based on the solution of the Poisson equation for homogeneous media. Corresponding operator is easy to invert by spectral method, where spectral decomposition is applied in two spatial directions and the Gauss elimination method is applied to solve a series of 1D problems. We illustrate that use of such precondtioner strongly decreases the number of iterations to solve the original Poisson equation, moreover the number of iterations weakly depends on the problem size. Implementation of the suggested approach using modern GPUs allows solving problems of up to the size of 10003 voxels.

Lisitsa V. , Manaev A. , Solovyev S.
Implementation of the Spectral Preconditioner to Solve Poisson Equation
In compilation Computational Science and Its Applications (ICCSA 2025 Workshops) : Proceedings. – Springer Cham., 2025. – Т.Part III. – C.388-401. – ISBN 978-3-031-97596-7. DOI: 10.1007/978-3-031-97596-7_26 Scopus OpenAlex

Published print:	May 28, 2025
Published online:	May 28, 2025

Scopus:	2-s2.0-105010820478
OpenAlex:	W4412059006

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