A1 Journal article (refereed)
A fast Fourier transform based direct solver for the Helmholtz problem (2020)

Toivanen, J., & Wolfmayr, M. (2020). A fast Fourier transform based direct solver for the Helmholtz problem. Numerical Linear Algebra with Applications, 27(3), Article e2283. https://doi.org/10.1002/nla.2283

JYU authors or editors

Publication details

All authors or editors: Toivanen, Jari; Wolfmayr, Monika

Journal or series: Numerical Linear Algebra with Applications

ISSN: 1070-5325

eISSN: 1099-1506

Publication year: 2020

Volume: 27

Issue number: 3

Article number: e2283

Publisher: John Wiley & Sons

Publication country: United Kingdom

Publication language: English

DOI: https://doi.org/10.1002/nla.2283

Publication open access: Not open

Publication channel open access:

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/67645

Publication is parallel published: https://arxiv.org/abs/1809.03808


This article is devoted to the efficient numerical solution of the Helmholtz equation in a two‐ or three‐dimensional (2D or 3D) rectangular domain with an absorbing boundary condition (ABC). The Helmholtz problem is discretized by standard bilinear and trilinear finite elements on an orthogonal mesh yielding a separable system of linear equations. The main key to high performance is to employ the fast Fourier transform (FFT) within a fast direct solver to solve the large separable systems. The computational complexity of the proposed FFT‐based direct solver is O(N log N) operations. Numerical results for both 2D and 3D problems are presented confirming the efficiency of the method discussed.

Keywords: numerical analysis; numerical methods; partial differential equations; Fourier series

Free keywords: absorbing boundary conditions; fast direct solver; finite‐element discretization; Fourier transform; Helmholtz equation

Contributing organizations

Related projects

Ministry reporting: Yes

Reporting Year: 2020

JUFO rating: 1

Last updated on 2021-07-07 at 21:31