6533b7d6fe1ef96bd1265bda

RESEARCH PRODUCT

A fast Fourier transform based direct solver for the Helmholtz problem

Monika WolfmayrJari Toivanen

subject

finite‐element discretizationHelmholtz equationDiscretizationFast Fourier transform010103 numerical & computational mathematicsSystem of linear equationsabsorbing boundary conditions01 natural sciencessymbols.namesake35J05 42A38 65F05 65N22FOS: MathematicsFourier'n sarjatApplied mathematicsBoundary value problemMathematics - Numerical AnalysisHelmholtz equation0101 mathematicsMathematicsosittaisdifferentiaaliyhtälötAlgebra and Number Theorynumeeriset menetelmätApplied MathematicsNumerical Analysis (math.NA)SolverFinite element method010101 applied mathematicsFourier transformsymbolsFourier transformnumeerinen analyysifast direct solver

description

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

yearjournalcountryeditionlanguage
2018-09-11
http://urn.fi/URN:NBN:fi:jyu-202001311910