A fast Fourier transform based direct solver for the Helmholtz problem
Numerical Analysis
2019-10-24 v3 Numerical Analysis
Abstract
This paper is devoted to the efficient numerical solution of the Helmholtz equation in a two- or three-dimensional 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 two- and three-dimensional problems are presented confirming the efficiency of the method discussed.
Cite
@article{arxiv.1809.03808,
title = {A fast Fourier transform based direct solver for the Helmholtz problem},
author = {Jari Toivanen and Monika Wolfmayr},
journal= {arXiv preprint arXiv:1809.03808},
year = {2019}
}