An iterative solver for the 3D Helmholtz equation

Mikhail Belonosov, Maxim Dmitriev, Victor Kostin, Dmitry Neklyudov, Vladimir Tcheverda

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)


We develop a frequency–domain iterative solver for numerical simulation of acoustic waves in 3D heterogeneous media. It is based on the application of a unique preconditioner to the Helmholtz equation that ensures convergence for Krylov subspace iteration methods. Effective inversion of the preconditioner involves the Fast Fourier Transform (FFT) and numerical solution of a series of boundary value problems for ordinary differential equations. Matrix-by-vector multiplication for iterative inversion of the preconditioned matrix involves inversion of the preconditioner and pointwise multiplication of grid functions. Our solver has been verified by benchmarking against exact solutions and a time-domain solver.

Original languageEnglish
Pages (from-to)330-344
Number of pages15
JournalJournal of Computational Physics
Publication statusPublished - 15 Sep 2017
Externally publishedYes


  • Acoustics
  • Helmholtz equation
  • Iterative methods
  • Modeling
  • Preconditioning

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