A fast Fourier transform based direct solver for the Helmholtz problem
Year of publication
2020
Authors
Toivanen, Jari; Wolfmayr, Monika
Abstract
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.
Show moreOrganizations and authors
Publication type
Publication format
Article
Parent publication type
Journal
Article type
Original article
Audience
ScientificPeer-reviewed
Peer-ReviewedMINEDU's publication type classification code
A1 Journal article (refereed), original researchPublication channel information
Publisher
Volume
27
Issue
3
Article number
e2283
ISSN
Publication forum
Publication forum level
1
Open access
Open access in the publisher’s service
No
Self-archived
Yes
Other information
Fields of science
Mathematics
Keywords
[object Object],[object Object],[object Object],[object Object]
Publication country
United Kingdom
Internationality of the publisher
International
Language
English
International co-publication
No
Co-publication with a company
No
DOI
10.1002/nla.2283
The publication is included in the Ministry of Education and Culture’s Publication data collection
Yes