The present work is aimed at the development of a numerical procedure, based on the usage of the Boundary Element Method (BEM) as implemented in the software LMS Virtual.Lab, for the vibro-acoustics analysis of an exhaust manifold. The manifold vibrations are induced by two different ways: engine vibrations (transmitted to the manifold surfaces) and turbulences generated by the air flow in the ...

In this note we prove in the case of a Lipschitz interface the stability of the coupling of finite and boundary element methods when the direct boundary integral equation with single and double layer potentials is used only. In particular we prove an ellipticity estimate of the coupled bilinear form. Hence we can use standard arguments to derive stability and error estimates for the Galerkin di...

Many boundary integral equations for exterior boundary value problems for the Helmholtz equation suffer from a notorious instability for wave numbers related to interior resonances. The so-called combined field integral equations are not affected. However, if the boundary is not smooth, the traditional combined field integral equations for the exterior Dirichlet problem do not give rise to an L...

The need for numerical methods in studying electromagnetic scattering from rough surfaces is well established. The most commonly used numerical method is the surface integral equation method and its solution by the method of moments (MoM). Conventional implementation of MoM requires O(N^3) operations, where N is the number of surface unknowns. When N is large, as frequently encountered in study...

We analyze the boundary element Galerkin method for weakly singular and hypersingular integral equations of the rst kind on open surfaces. We show that the hp-version of the Galerkin method with geometrically reened meshes converges exponentially fast for both integral equations. The proof of this fast convergence is based on the special structure of the solutions of the integral equations whic...

Applications of three-dimensional Galerkin boundary element methods require the numerical evaluation of many four-dimensional integrals. In this paper we explore the possibility of using extrapolation quadrature. To do so, one needs appropriate error functional expansions. The treatment here is limited to integration over a region T1×T2, where T1 and T2 are planar triangular elements in a hangi...

on Γ := {(x1, 0) : x1 ∈ R}, where k > 0 (the wavenumber) is some arbitrary positive constant. This boundary value problem can arise when modelling the acoustic scattering of an incident wave by a planar surface with spatially varying acoustical properties [1]. The total acoustic field u ∈ C(U)∩C(U) satisfies (1)– (2) where the wavenumber k = 2πμ/c, with μ being the frequency of the incident wav...

In this paper, the natural boundary element method (NBEM) for an anisotropic hyperbolic problem in an exterior elliptic domain is investigated. By the theory of the natural boundary reduction (NBR), the natural integral equation (NIE) and the Poisson integral formula of the problem considered are obtained, and the numerical method of the NIE is given. Finally, some numerical examples are presen...

An analytical method for evaluating pole-residues in spectral method of moments (MoM) formulations is presented. Spectral integral formulations for periodic structures involve the inverse of the MoM matrix, which exhibits a periodic set of pole singularities, corresponding to the zeros of the matrix’s determinant. So far, these singularities have not been extracted and the corresponding pole-re...

H-Matrix LU-decomposition based preconditioners for BEM