In this paper, we present a computational method for solving boundary integral equations with loga-rithmic singular kernels which occur as reformulations of a boundary value problem for the Laplacian equation. Themethod is based on the use of the Galerkin method with CAS wavelets constructed on the unit interval as basis.This approach utilizes the non-uniform Gauss-Legendre quadrature rule for ...

The elasticity mixed boundary values problems dealing with half-space contact are generally well resolved. A large number of these solutions are obtained by using the integral transformation method and methods based the integral equations. However, the problems of finite layer thicknesses are less investigated, despite their practical interests. This study resolves a quasi-stationary problem of...

The electrostatic problem of a hollow, conducting tube of finite length held at a fixed potential is solved using two methods. A twoterm Galerkin solution is constructed for the surface distribution of induced charge. The sum of a uniform component and a simple edgecondition term provides a variational solution to the dual integral equations that are the equations-of-motion for the mixed bounda...

This paper is concerned with optimal boundary control of an instationary reaction-diffusion system in three spatial dimensions. This problem involves a coupled nonlinear system of parabolic differential equations with bilateral as well as integral control constraints. The integral constraint is included in the cost by a penalty term whereas the bilateral control constraints are handled explicit...

A new single surface integral equation is derived for light scattering by circular dielectric cylinders. Without adopting the concept of equivalent electric or magnetic surface currents, our formulation is directly derived from coupled-surface integral equations by the property of commutative matrices of Green functions. Further development by such matrix equations leads to only one unknown fun...

A new boundary-integral formulation is proposed to analyze the heat transfer in zoned three-dimensional geometries. The proposed formulation couples the boundary formula, the gradient of the boundary formula, and the exterior formula. An advantage of this formulation over the traditional methods is that any linear condition at the interface between subdomains may be incorporated into the formul...

Richardson extrapolation is applied to improve the accuracy of the numerical solution of boundary integral equations. The boundary integral equations arise from a direct boundary integral method for solving a Laplace’s equation interior Dirichlet problem. Specifically, the Richardson extrapolation is used to improve the accuracy of collocation. Numerical justification is provided to support the...

in this paper, the optimal boundary control problem for distributed parabolic systems, involving second orderoperator with an infinite number of variables, in which constant lags appear in the integral form both in the state equations and in the boundary condition is considered. some specific properties of the optimal control arediscussed.

Boundary integral equations are a classical tool for the analysis of boundary value problems for partial differential equations. The term “ boundary element method” (BEM) denotes any method for the approximate numerical solution of these boundary integral equations. The approximate solution of the boundary value problem obtained by BEM has the distinguishing feature that it is an exact solution...