Title of Paper:An accurate and efficient acoustic eigensolver based on a fast multipole BEM and a contour integral method

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Date of Publication:2016-01-15

Journal:JOURNAL OF COMPUTATIONAL PHYSICS

Included Journals:SCIE

Volume:305

Page Number:677-699

ISSN No.:0021-9991

Key Words:Acoustic eigenvalue analysis; Boundary element method; Wideband fast multipole method; Contour integral method; Fictitious eigenvalues; Coupling parameter

Abstract:An accurate numerical solver is developed in this paper for eigenproblems governed by the Helmholtz equation and formulated through the boundary element method. A contour integral method is used to convert the nonlinear eigenproblem into an ordinary eigenproblem, so that eigenvalues can be extracted accurately by solving a set of standard boundary element systems of equations. In order to accelerate the solution procedure, the parameters affecting the accuracy and efficiency of the method are studied and two contour paths are compared. Moreover, a wideband fast multipole method is implemented with a block IDR(s) solver to reduce the overall solution cost of the boundary element systems of equations with multiple right-hand sides. The Burton-Miller formulation is employed to identify the fictitious eigenfrequencies of the interior acoustic problems with multiply connected domains. The actual effect of the Burton-Miller formulation on tackling the fictitious eigenfrequency problem is investigated and the optimal choice of the coupling parameter as alpha = i/k is confirmed through exterior sphere examples. Furthermore, the numerical eigenvalues obtained by the developed method are compared with the results obtained by the finite element method to show the accuracy and efficiency of the developed method. (C) 2015 Elsevier Inc. All rights reserved.