Highly accurate acoustic scattering: Isogeometric Analysis coupled with local high order Farfield Expansion ABC

TL;DR

This paper introduces a highly accurate isogeometric analysis method combined with local high-order Farfield Expansion absorbing boundary conditions for solving time-harmonic acoustic wave scattering, achieving spectral-like convergence and reducing boundary errors.

Contribution

It develops a novel IGA-based approach with advanced ABCs that significantly improves accuracy and convergence in acoustic scattering simulations across various geometries.

Findings

Spectral-like approximation and high order convergence achieved.

Boundary and pollution errors reduced to negligible levels.

Effective for low- and high-frequency regimes with coarse discretization.

Abstract

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 Villamizar, Acosta and Dastrup [J. Comput. Phys. 333 (2017) 331] . 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 {\it p-} and {\it h}- refinement. We apply this novel method to cylindrical, spherical and arbitrary shape scatterers including a prototype submarine. Our numerical results exhibits 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.