A fast Fourier transform based direct solver for the Helmholtz problem
| Autor: | Monika Wolfmayr, Jari Toivanen |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
finite‐element discretization
Helmholtz equation Discretization Fast Fourier transform 010103 numerical & computational mathematics System of linear equations absorbing boundary conditions 01 natural sciences symbols.namesake 35J05 42A38 65F05 65N22 FOS: Mathematics Fourier'n sarjat Applied mathematics Boundary value problem Mathematics - Numerical Analysis 0101 mathematics Mathematics osittaisdifferentiaaliyhtälöt Algebra and Number Theory numeeriset menetelmät Applied Mathematics Numerical Analysis (math.NA) Solver Finite element method 010101 applied mathematics Fourier transform symbols numeerinen analyysi fast direct solver |
| Popis: | 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. peerReviewed |
| Databáze: | OpenAIRE |
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