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The interior resonance problem of time domain integral equations (TDIEs)formulated to analyze acoustic field interactions on penetrable objects isinvestigated. Two types of TDIEs are considered: The first equation, which istermed the time domain potential integral equation (TDPIE) (in unknownsvelocity potential and its normal derivative), suffers from the interiorresonance problem, i.e., its solution is replete with spurious modes that areexcited at the resonance frequencies of the acoustic cavity in the shape of thescatterer. Numerical experiments demonstrate that, unlike the frequency-domainintegral equations, the amplitude of these modes in the time domain could besuppressed to a level that does not significantly affect the solution. Thesecond equation is obtained by linearly combining TDPIE with its normalderivative. Weights of the combination are carefully selected to enable thenumerical 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.

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