Higher Order Finite and Infinite Acoustical Elements Based on Ultraspherical Polynomials

This paper deals with the simulation of interior as well as exterior acoustical phenomena in the mid to high frequency range using the finite/infinite element method. In terms of controlling the pollution effect it is relied on the p-FEM concept. Due to this modeling approach the resulting parameterized linear system of equation is sparse, complex valued, indefinite, and unsymmetrical. This usually renders challenging when Krylov subspace based iterative solvers are used for the solution step. That is why the focus of this paper is to change the basis of the polynomial finite element aproximation space in order to obtain a favourable spectrum of the system matrix at higher wave numbers and in turn to improve the rate of convergence. As a result a formulations based on ultraspherical polynomials has been developed and numerical test show that this indeed renders faster solver convergence and hence a computationally more efficient simulation.