Applications of a new and efficient composite BIE formulation for 3-D acoustic problems are studied in this paper, based on an improved weakly-singular form of the hypersingular boundary integral equation (HBIE). This new form of the HBIE involves only tangential derivatives of the density function and thus its discretization using the boundary element method (BEM) is easier to perform. C conti...

The numerical construction of a Green’s function for multiple interacting planar cracks in an anisotropic elastic space is considered. The numerical Green’s function can be used to obtain a special boundary integral method for an important class of two-dimensional elastostatic problems involving planar cracks in an anisotropic body.

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

We consider time-harmonic scattering by penetrable polygonal obstacles in 2D. We present a boundary element method (BEM) based on a hybrid numerical-asymptotic (HNA) approximation space built from oscillatory basis functions. The basis functions are carefully chosen to capture the leading order terms in the highfrequency asymptotic behaviour of the boundary solution. Numerical experiments sugge...

The present work summarises a numerical procedure aimed to the residual strength assessment of a cracked butt joint, based on R-curve analysis and plastic collapse prediction. In a linear elastic fracture analysis, the SIF’s (Stress Intensity Factors) evaluation is based on the use of the Dual Boundary Element Method, as implemented in the BEASY code. A two -dimensional approximation (plane str...

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...

Electrophysiological modeling of Magnetoand Electro-encephalography (MEG and EEG) rely on accurate forward solvers that relate source activities to sensor measurements. In comparing a Boundary Element (BEM) and a Finite Element Method (FEM) for forward electroencephalography, in our early numerical experiments, we found the FEM to have a better accuracy than the BEM. This triggered a quest to i...

The analysis of adhesively bonded joints started in 1938 with the closed-form model of Volkersen. The equilibrium equation of a single lap joint led to a simple governing differential equation with a simple algebraic equation. However, if there is yielding of the adhesive and/or the adherends and substantial peeling is present, a more complex model is necessary. The more complete is an analysis...

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...