Acoustic modelling by BEM–FEM coupling procedures taking into account explicit and implicit multi‐domain decomposition techniques

Abstract

SUMMARYThe numerical modelling of interacting acoustic media by boundary element method-finite element method (BEM-FEM) coupling procedures is discussed here, taking into account time-domain approaches. In this study, the global model is divided into different sub-domains and each sub-domain is analysed independently (considering BEM or FEM discretizations): the interaction between the different subdomains of the global model is accomplished by interface procedures. Numerical formulations based on FEM explicit and implicit time-marching schemes are discussed, resulting in direct and optimized iterative BEM-FEM coupling techniques. A multi-level time-step algorithm is considered in order to improve the flexibility, accuracy and stability (especially when conditionally stable time-marching procedures are employed) of the coupled analysis. At the end of the paper, numerical examples are presented, illustrating the potentialities and robustness of the proposed methodologies.

Frequency domain analysis of acoustic wave propagation in heterogeneous media considering iterative coupling procedures between the method of fundamental solutions and Kansa's method

“…In [13], a FEM-BEM iterative coupling algorithm was first considered to analyse dynamics models. Later on, the formulation was extended and solid [14,15], fluid-solid [16][17][18], acoustic [18,19] and electromagnetic [20] coupled models were considered, taking into account time-domain FEM-BEM and BEM-BEM iterative coupling procedures (nontransient iterative coupling analyses have also been presented, mostly considering potential and elastostatic problems [21][22][23]). In frequency domain analysis, iterative procedures have been reported in the literature, directly [24] or not directly related to the coupling technique itself [25][26][27].…”

Perfectly Matched Layer for Galbrun׳s aeroacoustic equation in a cylindrical coordinates system with an axial and a swirling steady mean flow

“…Integrating by parts and applying boundary conditions (Eqs. (4) and (5)) yields the following variational problem:…”

“…Numerical methods need efficient and easy to implement techniques to truncate the computational domain without disturbing the solution of the original problem. Several efficient methods have been developed in the literature to cope with unbounded domain problem: the Non-Reflecting Boundary Condition (NRBC) methods [1][2][3] using the operator commonly called Dirichlet-to-Neumann (DtN) based on an analytical representation of the external field and needing particular geometries; the Boundary Element Methods (BEM) [4] which is another exact non-reflecting and non-local boundary condition whose main drawbacks are the singularity and the non-uniqueness of the solutions at some characteristic frequencies; and the Infinite Element Methods (IEM) [5] whose efficiency depends on the choice of the multipole expansion functions in the radial direction and on the truncation of the radial order.…”

Recent Advances and Emerging Applications of the Boundary Element Method

“…While the FEM is the preferred tool in the field of structural vibrations, using the BEM for the unbounded linear domain has the additional benefit that the Sommerfeld radia tion condition for exterior domains is inherently fulfilled. Advanced applications have been presented by Chen et al [448], Czygan and von Estorff [449], Gaul and Wenzel [450], Langer and Antes [451], Fischer and Gaul [425], and Soares [452].…”