An Efficient Trefftz-Based Method for Three-Dimensional Helmholtz Problems in Unbounded Domains
Bart Bergen; Bert Van Genechten, Dirk Vandepitte and Wim Desmet

Source CMES: Computer Modeling in Engineering & Sciences, Vol. 61, No. 2, pp. 155-176, 2010
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Keywords Trefftz, Wave Based Method, mid-frequency, numerical acoustics, scattering
Abstract The Wave Based Method (WBM) is a numerical prediction technique for Helmholtz problems. It is an indirect Trefftz method using wave functions, which satisfy the Helmholtz equation, for the description of the dynamic variables. In this way, it avoids both the large systems and the pollution errors that jeopardize accurate element-based predictions in the mid-frequency range. The enhanced computational efficiency of the WBM as compared to the element-based methods has been proven for the analysis of both three-dimensional bounded and two-dimensional unbounded problems. This paper presents an extension of the WBM to the application of three-dimensional acoustic scattering and radiation problems. To this end, an appropriate function set is proposed which satisfies both the governing Helmholtz equation and the Sommerfeld radiation condition. Also, appropriate source formulations are discussed for relevant sources in scattering problems. The accuracy and efficiency of the resulting method are evaluated in some numerical examples, including the 3D cat's eye scattering problem.
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