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...

Based on acoustic radiation modes, the surface contribution method has been developed to predict the surface contributions to the radiated sound power from a vibrating structure. In this work, the surface contribution method is used to identify the sound field on a vibrating structure submerged in a heavy fluid. It was recently found that surface contribution method was not able to predict the ...

The purpose of this paper is to present an adaptive FEM-BEM coupling method that is valid for both twoand three-dimensional elasto-plastic analyses. The method takes care of the evolution of the elastic and plastic regions. It eliminates the cumbersome of a trial and error process in the identification of the FEM and BEM sub-domains in the standard FEM-BEM coupling approaches. The method estima...

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...

In this paper, a mortar element method is presented for coupling natural boundary element method and finite element method for the Dirichlet exterior problem. Optimal error estimate is obtained and some numerical results are reported.

H-Matrix LU-decomposition based preconditioners for BEM

The numerical solution of the Helmholtz equation with nonlocal radiation boundary conditions is considered. We model sound wave propagation in a multilayered piecewise homogeneous medium. A fourth-order accurate collocated, boundary element method is used, where the solution inside the domain is computed through a representation integral. The method is shown to have the expected fourth-order co...

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...