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

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...

analysis of the stresses, displacements, and horizontal strains of the ground subsidence due to underground excavation in rocks can be accomplished by means of a hybridized higher order indirect boundary element/finite difference (be/fd) formulation. a semi-infinite displacement discontinuity field is discretized (numerically) using the cubic displacement discontinuity elements (i.e. each highe...