Work

Preconditioning of a pollution-free discretization of the Helmholtz equation

Year: 2026

Type: article

Abstract: We present a pollution-free first order system least squares (FOSLS) formulation for the Helmholtz equation, solved iteratively using a block preconditioner. This preconditioner consists of two components: one for the Schur complement, which corresponds to a preconditioner on $L_2(Ω)$, and another defined on the test space, which we ensure remains Hermitian positive definite using subspace correction techniques. The proposed method is easy to implement and is directly applicable to general domains, including scattering problems. Numerical experiments demonstrate a linear dependence of the number of MINRES iterations on the wave number $κ$. We also introduce an approach to estimate algebraic errors which prevents unnecessary iterations.

Source: Applied Numerical Mathematics

DOI: 10.1016/j.apnum.2026.04.012

Author: Harald Monsuur

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,000

Funder: Nederlandse Organisatie voor Wetenschappelijk Onderzoek

Award: Simultaneous space-time solvers for parabolic data-assimilation problems