A fast Fourier transform based direct solver for the Helmholtz problem
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
Published inNumerical Linear Algebra with Applications
© 2020 John Wiley & Sons, Ltd.
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.
PublisherJohn Wiley & Sons
Publication in research information system
MetadataShow full item record
Related funder(s)Academy of Finland
Funding program(s)Academy Project, AoF
Additional information about fundingThe authors gratefully acknowledge the financial support by the Academy of Finland under the grant 295897.
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