A direct approach to calculating the hypersingular integral for a threedimensional Galerkin approximation is presented. The method does not employ either Stokes' Theorem or a regularization process to transform the integrand before the evaluation is carried out. Integrating two of the four dimensions analytically, the potentially divergent terms arising from the coincident and adjacent edge int...

This paper presents a posteriori error estimates for the hp{version of the boundary element method. We discuss two rst kind integral operator equations , namely Symm's integral equation and the integral equation with a hypersingular operator. The computable upper error bounds indicate an algorithm for the automatic hp{adaptive mesh{reenement. The eeciency of this method is shown by numerical ex...

In this paper we report on a non-overlapping and an overlapping domain decomposition method as preconditioners for the boundary element approximation of an indefinite hypersingular integral equation on a surface. The equation arises from an integral reformulation of the Neumann screen problem with the Helmholtz equation in the exterior of a screen in R. It is well-known that the linear algebrai...

Various problems involving the interaction of water waves with thin plates are reduced to hypersingular boundary integral equations. Examples include scattering by submerged curved plates and by surface-piercing plates, in two dimensions; trapping of waves by submerged plates; and scattering by submerged flat plates in three dimensions. Each integral equation is solved numerically, using an exp...

This paper deals with a general framework for a posteriori error estimates in boundary element methods which is specified for three examples, namely Symm's integral equation, an integral equation with a hypersingular operator, and a boundary integral equation for a transmission problem. Based on these estimates, an analog of Eriksson and Johnson's adaptive finite element method is proposed for ...

A numerical method is proposed and investigated for the hypersingular integral equations defined in Banach spaces. The hypersingular integral equations belong to a wider class of singular integral equations having much more stronger singularities. The proposed approximation method is an extension beyond the quadrature method. Moreover an error estimates theory is introduced for the hypersingula...

A direct algorithm for evaluating hypersingular integrals arising in a three-dimensional Galerkin boundary integral analysis is presented. The singular integrals are defined as limits to the boundary, and by integrating two of the four dimensions analytically, the coincident integral is shown to be divergent. However, the divergent terms can be explicitly calculated and shown to cancel with cor...

We analyze well-posedness of a scattering problem of time-harmonic electromagnetic waves by periodic structures with sign-changing coefficients. Transmission problems for Maxwell’s equations with sign-changing coefficients in bounded domains have been recently studied by Bonnet-Ben Dhia and co-workers in the so-called T -coercivity framework. In this article we generalize such framework for per...

Abstract A new numerical method is introduced and investigated for the hypersingular integral equations defined in Banach spaces. The hypersingular integral equations belong to a wider class of singular integral equations having much more stronger singularities.The proposed approximation method is an extension beyond the quadrature method. Beyond the above, an error estimates theory is proposed...

Kussmaul's (1969) formulation of acoustic scattering problems involves the superposition of a double-layer distribution and a simple-layer distribution on the boundary.This ensured the existence of a unique solution for all wave numbers of the incoming wave. However,the boundary integral equation involves a highly singular kernel which proves difficult to treat numerically. An alternative appro...