关于分析可穿透物体声散射的时域积分方程的虚假内部谐振模式
On the Spurious Interior Resonance Modes of Time Domain Integral Equations for Analyzing Acoustic Scattering from Penetrable Objects
AI总结：
针对可穿透声散射体TDIE的内部谐振问题，本文比较TDPIE与线性组合得到的TDCPIE，证明后者可消除虚假内部谐振模式。
摘要：
本文研究了为分析可穿透物体上声场相互作用而构建的时域积分方程（TDIE）的内部谐振问题。文中考虑了两类TDIE：第一类方程称为时域势积分方程（TDPIE）（以速度势及其法向导数为未知量），存在内部谐振问题，即其解中充满了在形状与散射体相同的声学腔体谐振频率处被激发的虚假模式。数值实验表明，与频域积分方程不同，这些模式在时域中的振幅可以被抑制到不会显著影响解的水平。第二类方程通过将TDPIE与其法向导数线性组合得到。组合权重经过仔细选择，以便能够对奇异积分进行数值计算。该方程称为时域组合势积分方程（TDCPIE），其解不包含任何虚假内部谐振模式。
英文摘要：
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.
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