https://doi.org/10.26089/NumMet.v27r325

Parallel version of the spectral preconditioner for solving the Poisson equation

Authors

  • Aleksei A. Manaev
  • Vadim V. Lisitsa

Keywords:

Poisson equation
preconditioner
spectral decomposition
domain decomposition

Abstract

This paper presents a parallel version of the spectral preconditioner for the numerical solution of the Poisson equation in heterogeneous media. The action of the spectral preconditioner is based on the eigendecomposition of operators approximating derivatives and the corresponding boundary conditions along one spatial direction, followed by the solution of a series of independent one-dimensional problems along another spatial direction. The parallel version is based on the domain decomposition method using a polynomial approximation of the inverse matrix and a block-diagonal matrix, where each block is analogous in its action to the spectral preconditioner. It is shown that the proposed approach for constructing the preconditioner can significantly accelerate computations compared to standard preconditioning methods.


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Published

2026-07-15

Issue

Vol. 27 (2026): Issue 3.

Section

Methods and algorithms of computational mathematics and their applications

Authors

Aleksei A. Manaev

Sobolev Institute of Mathematics of SB RAS

• Engineer

Vadim V. Lisitsa

Sobolev Institute of Mathematics of SB RAS

• Head of Laboratory

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