Transient responses impose additional restrictions concerning model order reduction of acoustic finite element systems. Time-stable model order reduction methods achieve model compaction while guaranteeing frequency domain models transform in a physically meaningful way. Efficiency and stability are of course of little consequence if the model is rendered inaccurate. Krylov subspaces inherently include system input and/or output behavior in the reduction basis making them ideal reduction bases for investigating system behavior outside of steady state. Realistic boundary conditions are demanded and must be preserved in the reduction basis. Frequency dependent impedance boundary conditions help in this regard but complicate both model reduction and time-integration strategies. Multiplications to enforce system damping in the frequency domain become time-domain convolutions. Recursively calculated minimal memory convolution formulations have long proven useful in lowering the associated computational burden. Complex frequency-dependent damping matrices create a challenge for Krylov subspace based model reduction due to the way the reduction basis is constructed. Arnoldi iterations implicitly match the moments of the system transfer function to span a Krylov subspace. This paper demonstrates how to maintain compatibility with such algorithms while including frequency dependent damping. This work proposes combining projection based model order reduction with an efficient time domain-impedance boundary condition formulation. An important benefit of working in the time domain is the ability to directly output binaural audio signals. To this end, discrepancies are discussed in the perceptual context of audibility. A reduction of system degrees of freedom from $\mathrm{NDOF}=13125$ to $\mathrm{RDOF}=63$ and the inclusion of time-domain impedance boundary conditions are shown to enable computational speedups by a factor of 11–36 without introducing audible differences.

瞬态响应对声学有限元系统的模型阶数降低施加了额外的限制。时间稳定模型降阶方法实现模型压缩，同时保证频域模型以物理上有意义的方式转换。如果模型变得不准确，效率和稳定性当然不会有什么影响。克雷洛夫子空间固有地将系统输入和/或输出行为包含在归约基础中，使其成为研究稳态以外系统行为的理想归约基础。需要现实的边界条件，并且必须在减少基础中保留。频率相关阻抗边界条件在这方面有所帮助，但会使模型简化和时间积分策略复杂化。在频域中强制执行系统阻尼的乘法成为时域卷积. 递归计算的最小记忆卷积公式长期以来被证明有助于降低相关的计算负担。由于缩减基础的构建方式，复杂的频率相关阻尼矩阵对基于 Krylov 子空间的模型缩减提出了挑战。Arnoldi 迭代隐式匹配系统传递函数的矩以跨越 Krylov 子空间。本文演示了如何在包含频率相关阻尼的同时保持与此类算法的兼容性。这项工作建议将基于投影的模型阶数减少与有效的时域阻抗边界条件公式相结合。在时域中工作的一个重要好处是能够直接输出双声道音频信号。为此，在可听性的感知环境中讨论了差异。系统自由度的减少$\mathrm{NDOF}=13125$ 到 $\mathrm{RDOF}=63$ 并且显示包含时域阻抗边界条件可以使计算速度提高 11-36 倍，而不会引入听觉差异。