Time integration for spherical acoustic finite–infinite element models

Abstract

SUMMARYIn this paper, we analyse the numerical time integration of models of exterior acoustics. The major challenge lies in the instabilities that may arise from the infinite elements. In this paper we consider the special case of spherical infinite elements formulations, which have shown their relevance for industrial applications. We propose a method that combines Crank-Nicholson's method with a filtering step by the backward Euler method. The paper is illustrated with an example relevant to industry.

Connection and comparison between frequency shift time integration and a spectral transformation preconditioner

“…With the infinite elements, the equations in the time domain may become instable [25], which makes time domain computations rather tricky. For spheroidal domains, the finite element-infinite element formulation leads to an index one stable system of differential algebraic equations [26].…”

“…Therefore, the linear systems that arise in implicit time integration methods are relatively easy to solve. When infinite elements are used, the matrices in (2) are non-symmetric, M can be singular, and there are cases where the equations are unstable [1,[23][24][25][26]. We have observed that infinite elements do not reduce the computational efficiency of the iterative linear systems solvers in the time domain.…”

Dimension Reduction of Large-Scale Systems

“…This is thus a differential algebraic equation. It is shown that it has index one [CMR03]. The input of the system is f , the output is the state vector x.…”

Ray‐tracing domain decomposition methods for real‐time simulation on multi‐core and multi‐processor systems

“…Numerical wave‐based methods, such as the boundary element method , the finite element method , the stabilized finite element , the infinite element method , and the coupling methods , provide very accurate solutions to various problems of wave physics. However, this accuracy requires a lot of computational power and memory, contrary to their geometrical counterparts, such as the image‐source method , the ray‐tracing method , and the beam‐tracing method .…”