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On the Internal Resonance Modes of Time Domain Surface Integral Equations for Acoustic Transmission Problems

The internal resonance problem pertinent to time domain surface integral equations (SIEs) for analyzing transient acoustic scattering from penetrable objects is investigated. The first equation considered here is constructed by combining SIE representations of the internal and external problems via the continuity of the velocity potential and its normal derivative. Just like its frequency-domain counterpart, this equation suffers from the internal resonance problem. But it is demonstrated in this work that, unlike the frequency-domain solution, by increasing the accuracy of the discretization, the amplitude of these spurious modes can be suppressed to a level that does not significantly affect the solution. The second equation considered here is obtained by linearly combining the first equation with its normal derivative and its solution is completely free from spurious internal resonance modes.