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Extended isogeometric boundary element method (XIBEM) for three-dimensional medium-wave acoustic scattering problems. (English) Zbl 1425.65202
Summary: A boundary element method (BEM), based on non-uniform rational B-splines (NURBS), is used to find solutions to three-dimensional wave scattering problems governed by the Helmholtz equation. The method is extended in a partition-of-unity sense, multiplying the NURBS functions by families of plane waves; this method is called the eXtended Isogeometric Boundary Element Method (XIBEM).{
}In this paper, the collocation XIBEM formulation is described and numerical results are given. The numerical results are compared against closed-form or converged solutions. Comparisons are made against the conventional boundary element method and the non-enriched isogeometric BEM (IGABEM).{
}When compared to non-enriched boundary element simulations, using XIBEM significantly reduces the number of degrees of freedom required to obtain a solution of a given error; thus, with a fixed computational resource, problems of a shorter wavelength can be solved.

MSC:
 65N38 Boundary element methods for boundary value problems involving PDEs 65D17 Computer-aided design (modeling of curves and surfaces) 74S15 Boundary element methods applied to problems in solid mechanics 76Q05 Hydro- and aero-acoustics
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