Elimination of a non-oscillatory instability in a retarded potential integral equation

This paper deals with the unstable behaviour of an acoustic boundary element model. The model, based on a marching on time (MOT) algorithm, uses a hypersingular derivative Green method. It is able to cope with open or closed diffracting objects. These objects are rigid or can be deformed. When a long enough computation is carried out, the pressure magnitude shows an exponential growth, which is an unrealistic behaviour. In the paper we show that we are faced with a numerical instability of the static pressure in closed cavities. A simple processing method using the eigenelement decomposition of an ‘ad hoc’ matrix suffices to correct the problem without damage to other components of the result. The method is related to a more general method dedicated to instability problems.