The stability of infinite element schemes for transient wave problems

The transformation of conjugated infinite elements from the frequency domain to the time domain is described. This procedure yields discrete numerical models for transient acoustics which are local in space and time. These can be integrated in time to solve unsteady problems of radiation or scattering in infinite domains provided that the discrete equations themselves are stable with time. The conditions under which this is true are investigated in this article. A numerical study is presented which shows that the stability of the numerical scheme depends critically upon the form of the inner surface of the infinite element domain. Solutions for test problems are presented to demonstrate that such criteria also apply when the equations are discretised in time, and that stable solutions can be obtained using implicit time integration schemes when simple criteria are correctly applied. Axisymmetric spherical and spheroidal formulations are considered.