A numerical algorithm to damp instabilities of a retarded potential integral equation

This paper deals with a new systematic approach of the instability problem in acoustic boundary elements models. When a long enough marching-on-time (MOT) computation is carried out, an exponential growth of the pressure magnitude often appears. This unrealistic behaviour is a serious drawback for the method of retarded potential integral equations. In this paper, we show that the instability problem of this type of algorithm can be translated in terms of a polynomial eigenvector problem (PEVP). In the case of the hypersingular derivative Green method, examples are shown of suppressing all numerical instabilities related to open or closed diffracting objects using the PEVP. Among them, the vibroacoustic model of a test structure used by the CNES (Centre National dʹEtudes Spatiales) is successfully processed.