On the Spurious Interior Resonance Modes of Time Domain Integral Equations for Analyzing Acoustic Scattering from Penetrable Objects

The interior resonance problem of time domain integral equations (TDIEs) formulated to analyze acoustic field interactions on penetrable objects is investigated. Two types of TDIEs are considered: The first equation, which is termed the time domain potential integral equation (TDPIE) (in unknowns velocity potential and its normal derivative), suffers from the interior resonance problem, i.e., its solution is replete with spurious modes that are excited at the resonance frequencies of the acoustic cavity in the shape of the scatterer. Numerical experiments demonstrate that, unlike the frequency-domain integral equations, the amplitude of these modes in the time domain could be suppressed to a level that does not significantly affect the solution. The second equation is obtained by linearly combining TDPIE with its normal derivative. Weights of the combination are carefully selected to enable the numerical computation of the singular integrals. The solution of this equation, which is termed the time domain combined potential integral equation (TDCPIE), does not involve any spurious interior resonance modes.