Recent Advances in Acoustic Boundary Element Methods

Abstract

The modern scope of boundary element methods (BEM) for acoustics is reviewed in this paper. Over the last decades the BEM has gained popularity despite suffering from shortcomings, such as fictitious eigenfrequencies and poor scalability due to its dense and frequency-dependent coefficient matrices. Recent research activities have been focused on alleviating these drawbacks to enhance BEM usability across industry and academia. This paper reviews what is commonly known as direct BEM for linear time-harmonic acoustics. After introducing the boundary integral formulation of the Helmholtz equation for interior and exterior acoustic problems, recommendations are given regarding the boundary meshing and treatment of the non-uniqueness problem. It is shown how frequency sweeps and modal analyses can be carried out with BEM. Further extensions for efficient modeling of large-scale problems, including fast BEM and solutions methods, are surveyed. Additionally, this review paper discusses new application areas for modern BEM, such as viscothermal wave propagation, surface contribution analyses, and simulation of periodically arranged structures as found in acoustic metamaterials.

Design sensitivity analysis of modal frequencies of elastic structures submerged in an infinite fluid domain

“…Such fictitious eigenvalues are consistent with the eigenvalues of the related interior Dirichlet problem. 20,21 In the numerical simulation of acoustic radiation or scattering, they act as resonant frequencies and make the numerical solutions erroneous in their vicinities. The problem arising from them is thus called the non-unique solution difficulty.…”

“…The Burton-Miller (BM) method 38 has been confirmed as an effective approach to conquer the non-unique solution difficulty in the BEM simulation of acoustic radiation and scattering. 20,21 The idea of the BM method is to use the following combined formula instead of the KHIE:…”

“…For the infinite fluid domain, the boundary element method (BEM) is more favorable since it can solve unbounded-domain acoustic problems accurately and rigorously without any truncation or approximation of the problem domain. 20,21 As a result the coupled finite element and boundary element (FE-BE) methods are usually preferred for the numerical simulation of fluid-structure interaction systems. 22,23 In spite of the advantages of solving the vibro-acoustic problems in unbounded fluid domain, the acoustic BEM makes the system of equations of the coupled FE-BE method have frequency-dependent coefficient matrices, which results in a typical nonlinear eigenvalue problem (NEP) in the modal analysis of submerged elastic structures.…”

“…37 Furthermore, a small GEP is formulated to calculate the gradients of repeated eigenvalues. As is widely known, the BEM based on the Kirchhoff-Helmholtz integral equation suffers from the fictitious eigenfrequency problem for exterior wave propagation problems, 20,21 and the coupled FE-BE method inherits this problem. 22,23 In the response analysis, this problem is also referred to as the non-uniqueness difficulty as the numerical solutions are erroneous at the vicinities of fictitious eigenfrequencies.…”

Multi‐fidelity Gaussian processes for an efficient approximation of frequency sweeps in acoustic problems

“…For instance, a greedy reduced basis [1][2][3] or parametric model order reduction methods [4][5][6][7] have been developed. The interested reader is referred to [8] for a thorough review in this area. These existing techniques, however, do not account for uncertainties eventually occurring in the design process.…”