An efficient method for fast frequency sweeps in exterior acoustics using frequency-independent perfectly matched layers

Abstract

Modeling wave propagation in unbounded domains requires efficient truncation techniques such as perfectly matched layers (PMLs). While frequency-dependent PMLs provide excellent absorption, they hinder the application of standard model order reduction (MOR) techniques for fast frequency sweeps. Existing frequency-independent formulations suffer from accuracy limitations, particularly across wide frequency ranges. We propose a novel computational methodology for fast frequency sweeps that integrates frequency-independent PML formulations, p-adaptive finite elements, and MOR. Our frequency-independent PML formulation introduces two fundamental innovations: the replacement of the constant wavenumber in the PML coordinate stretching with a spatially-varying frequency-independent function, and an optimization strategy that minimizes the discrete projection error of the decay field in the PML region. Through symbolic regression, we identify a simple two-parameter exponential function for this spatially-varying term that delivers excellent accuracy while maintaining physical interpretability. We use adaptive finite elements and develop a specialized a priori error indicator for automatic polynomial order selection in frequency-independent PML regions. Numerical experiments confirm that our formulation significantly outperforms existing approaches, maintaining excellent absorption for large frequency ratios. Furthermore, we integrate our formulation with frequency-adaptive discretization for Krylov-based MOR, enabling efficient frequency sweeps while maintaining a single computational mesh. This combination substantially reduces the offline computational cost while preserving solution accuracy, making it particularly valuable for industrial acoustic simulations.

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ORCID for S. van Ophem: orcid.org/0000-0003-1050-7318

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