A hypersingular integral equation in two disjoint intervals is solved by using the solution of Cauchy type singular integral equation in disjoint intervals. Also a direct function theoretic method is used to determine the solution of the same hypersingular integral equation in two disjoint intervals. Solutions by both the methods are in good agreement with each other.

A novel iteration scheme, using boundary integral equations, is developed for error estimation in the boundary element method. The iteration scheme consists of using the boundary integral equation for solving the boundary value problem and iterating this solution with the hypersingular boundary integral equation to obtain a new solution. The hypersingular residual r is consistently defined as t...

We study the multiplicative Schwarz method for the p-version Galerkin boundary element method for a hypersingular and a weakly singular integral equation of the rst kind and for the h-version for a hypersingular integral equation of the rst kind. We prove that the rate of convergence of the multiplicative Schwarz operator is strictly less than 1 for the h-version for both two level and multilev...

A weakly singular form of the hypersingular boundary integral equation (BIE) (traction equation) for 3-D elastic wave problems is developed in this paper. All integrals involved are at most weakly singular and except for a stronger smoothness requirement on boundary elements, regular quadrature and collocation procedures used for conventional BIEs are sufficient for the discretization of the or...

In this article, computational results from boundary integral equations and their normal derivatives for the same test cases are compared. Both kinds of formulations are desingularized on their real boundary. The test cases are chosen as a uniform flow past a circular cylinder for both the Dirichlet and Neumann problems. The results indicate that the desingularized method for the standard bound...

A direct algorithm for evaluating hypersingular integrals arising in a three-dimensional Galerkin boundary integral analysis is presented. By integrating two of the four dimensions analytically, the coincident integration, deened as a limit to the boundary, is shown to be divergent. However, the divergent terms can be explicitly calculated and shown to cancel with corresponding singularities in...

This paper presents an easy numerical implementation of the Burton and Miller (BM) formulation, where the hypersingular Helmholtz integral is regularized by identities from the associated Laplace equation and thus needing only the evaluation of weakly singular integrals. The Helmholtz equation and its normal derivative are combined directly with combinations at edge or corner collocation nodes ...

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 exp...

A Legendre multiwavelet based method is developed in this paper to solve second kind hypersingular integral equation by converting it into a Cauchy singular integro-differential equation. Multiscale representation of the singular and differential operators is obtained by employing Legendre multiwavelet basis. An estimate of the error of the approximate solution of the integral equation is obtai...