A fast Fourier transform based direct solver for the Helmholtz problem. Issue 3 (29th January 2020)

• Record Type: Journal Article
• Authors: Toivanen, Jari; Wolfmayr*, Monika
• Is Part Of: Numerical linear algebra with applications. Volume 27:Issue 3(2020)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2020-01-29
• Subjects: absorbing boundary conditions -- fast direct solver -- finite‐element discretization -- Fourier transform -- Helmholtz equation; Algebras, Linear -- Periodicals; 512.5
• DOI: 10.1002/nla.2283
• Languages: English
• ISSNs: 1070-5325

Abstract

Summary: 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.