Time-domain impedance boundary conditions for acoustic reduced order finite element simulations

Miller III, M., van Ophem, S., Deckers, E. and Desmet, W. (2021) Time-domain impedance boundary conditions for acoustic reduced order finite element simulations. Computer Methods in Applied Mechanics and Engineering, 387, [114173]. (doi:10.1016/j.cma.2021.114173).

Abstract

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 NDOF = 13125 to 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.

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Contributors

Author: S. van Ophem

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