the asymmetric problem of rocking rotation of a circular rigid disk embedded in a finite depth of a transversely isotropic half-space is analytically addressed. the rigid disk is assumed to be in frictionless contact with the elastic half-space. by virtue of appropriate green's functions, the mixed boundary value problem is written as a dual integral equation. employing further mathematica...

We study a boundary integral equation method for solving Laplace s equation u with nonlinear boundary conditions This nonlinear boundary value problem is reformulated as a nonlinear boundary in tegral equation with u on the boundary as the solution being sought The integral equation is solved numerically by using the collocation method with piecewise quadratic functions used as approximations t...

in this paper, shielding effectiveness (se) of a perforated enclosure with imperfectly conducting walls is evaluated. to this end, first, an accurate numerical technique based on method of moments (mom) ispresented. in this method, lossy metallic walls of the enclosure are replaced by equivalent electric surfacecurrent sources. then, the impedance boundary condition on the imperfectly conductin...

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 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 provide a new method to study the classical Dirichlet problem for Laplace's equation on a convex polyhedron. This new approach was motivated by Fokas' unified method for boundary value problems. The central object in this approach is the global relation: an integral equation which couples the known boundary data and the unknown boundary values. This integral equation depends holomorphically ...

In the direct boundary integral equation method, boundary-value problems are reduced to integral equations by an application of Green’s theorem to the unknown function and a fundamental solution (Green’s function). Discretization of the integral equation then leads to a boundary element method. This approach was pioneered by Jaswon and his students in the early 1960s. Jaswon’s work is reviewed ...

The paper studies boundary integral operators of the bi{Laplacian on piecewise smooth curves with corners and describes their mapping properties in the trace spaces of variational solutions of the biharmonic equation. We formulate a direct integral equation method for solving mixed boundary value problems for the biharmonic equation on a nonsmooth plane domain, analyse the solvability of the co...

The third problem for the Stokes system is studied on a bounded domain in R with Ljapunov connected boundary. We construct a solution of this problem in the form of appropriate potentials and determine unknown source densities via integral equation systems on the boundary of the domain. The solution is given explicitly in the form of a series. Then we study the integral equation which we obtain...