Isogeometric analysis of acoustic scattering using infinite elements

Abstract

Isogeometric analysis (IGA) has proven to be an improvement on the classical finite element method (FEM) in several fields, including structural mechanics and fluid dynamics. In this paper, the performance of IGA coupled with the infinite element method (IEM) for some acoustic scattering problems is investigated. In particular, the simple problem of acoustic scattering by a rigid sphere, and the scattering of acoustic waves by an elastic spherical shell with fluid domains both inside and outside, representing a full acoustic-structure interaction (ASI) problem. Finally, a mock shell and a simplified submarine benchmark are investigated.The numerical examples include comparisons between IGA and the FEM. Our main finding is that the usage of IGA significantly increases the accuracy compared to the usage of C 0 FEM due to increased inter-element continuity of the spline basis functions.

ADITU: A mesh-free formulation for the solution of Helmholtz equation in bounded and unbounded domains

“…The advantage is that the techniques of FEM can be applied (variational formulation, basis functions, numerical integration, etc.). Recently, Isogeometric Analysis has been coupled to IEM [14], and IEM still remains a field of research. IEM methods do have the capacity of dealing with systems with objects of different mass properties; but, whenever a new object is added, it must be included using a 3D finite mesh, increasing significantly the number of degrees of freedom of the global system to be solved.…”

An efficient scaled boundary finite element method for transient vibro-acoustic analysis of plates and shells

“…Unfortunately, the classical BEM suffers from densely populated system matrices and various acceleration techniques have to be adopted to improve its efficiency [29]. Another way of simulating the exterior acoustic field is to divide the whole region by an artificial boundary into a finite interior domain and an infinite residual domain, where the former is modeled using the conventional approaches such as FEM [30], IGA [31] and SFEM [23] and the latter by some specific methods including infinite elements [32] and Dirichlet-to-Neumann (DtN) map [33]. However, the infinite element schemes tend to become ill-conditioned for sufficiently high radial orders unless proper shape functions are selected [34], whilst the global property of the DtN boundary condition makes its numerical implementation unfeasible for large-scale problems over long time intervals.…”

An automatic approach for the acoustic analysis of three-dimensional bounded and unbounded domains by scaled boundary finite element method

“…As a result, this will inevitably increase the computational costs for acoustic-structure interaction analyses. Therefore, various open boundaries, such as the infinite elements [2,3,14,53,54], perfectly matched layers [8,13,26,29], and high-order open boundaries [15,6,27,21,4,55,64] are developed to represent the unbounded domain by satisfying the radiation condition at infinity. For detailed reviews of open boundaries, readers are referred to [20,28,21].…”