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Highly accurate acoustic scattering: isogeometric analysis coupled with local high order Farfield Expansion ABC. (English) Zbl 1441.76063
Summary: This work is concerned with a unique combination of high order local absorbing boundary conditions (ABC) with a general curvilinear Finite Element Method (FEM) and its implementation in Isogeometric Analysis (IGA) for time-harmonic acoustic waves. The ABC employed were recently devised by V. Villamizar et al. [J. Comput. Phys. 333, 331–351 (2017; Zbl 1375.35290)]. They are derived from exact Farfield Expansions representations of the outgoing waves in the exterior of the regions enclosed by the artificial boundary. As a consequence, the error due to the ABC on the artificial boundary can be reduced conveniently such that the dominant error comes from the volume discretization method used in the interior of the computational domain. Reciprocally, the error in the interior can be made as small as the error at the artificial boundary by appropriate implementation of $$p$$- and $$h$$-refinement. We apply this novel method to cylindrical, spherical and arbitrary shape scatterers including a prototype submarine. Our numerical results exhibit spectral-like approximation and high order convergence rate. Additionally, they show that the proposed method can reduce both the pollution and artificial boundary errors to negligible levels even in very low- and high-frequency regimes with rather coarse discretization densities in the IGA. As a result, we have developed a highly accurate computational platform to numerically solve time-harmonic acoustic wave scattering in two- and three-dimensions.

##### MSC:
 76M10 Finite element methods applied to problems in fluid mechanics 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 65D07 Numerical computation using splines 76Q05 Hydro- and aero-acoustics
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