Enhanced perfectly matched layer formulation for near- and far-field pressures of exterior acoustic and vibroacoustic problems

Abstract

This paper develops a frequency-independent surrogate of perfectly matched layer unbounded absorption function for the frequency-domain finite element analysis of exterior acoustic and fully-coupled structural-acoustic problems. It does not require a very large computational domain or a relatively thick enclosed layer, even in the low-frequency range, which saves computational resources. The introduction of fillets for the cylindrical and Cartesian geometry cases is proposed to simplify the computation of the Jacobian matrix in the absorbing layer. In addition, in order to take advantage of symmetry when solving large-scale sparse linear systems, the scalar velocity potential instead of the sound pressure is used as the fundamental unknown to describe the fluid part of vibro-acoustic interaction models. Due to the frequency-independent property of the resulting system matrices, an adaptive projection-based model order reduction technique can be directly utilized to ease the associated computational expense of frequency sweeps. After the solution inside the truncated domain is obtained, the acoustic pressure distribution in the far field, i.e. outside the finite element domain, is evaluated via the Kirchhoff surface integral formula. Three-dimensional acoustic problems with different boundary conditions and vibro-acoustic coupling problems with different artificial layer geometries, considering both infinite and semi-infinite fluid domains, are investigated to demonstrate the simplicity, versatility, and efficiency of the developed frequency-independent perfectly matched layer technique and model order reduction approach.