Boundary value problems of the third kind are converted into boundary integral equations of the second kind with periodic logarithmic kernels by using Green’s formulas. For solving the induced boundary integral equations, a Nyström scheme and its extrapolation method are derived for periodic Fredholm integral equations of the second kind with logarithmic singularity. Asymptotic expansions for t...

In this paper,wepresent a parallel higher-order boundary integralmethod to solve the linear Poisson–Boltzmann (PB) equation. In our method, a well-posed boundary integral formulation is used to ensure the fast convergence of Krylov subspace linear solver such as GMRES. The molecular surfaces are first discretized with flat triangles and then converted to curved triangleswith the assistance of n...

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 ...

An efficient method to solve time harmonic Maxwell’s equations in exterior domain for high frequencies is obtained by using the integral formulation of Després combined with a coupling method (MLFMD) based on the Microlocal Discretization method (MD) and the Multi-Level Fast Multipole Method (MLFMM) [1]. In this paper, we consider curved finite elements of higher order in the MLFMD method. More...

A weak solution of the Neumann problem for the Stokes system in Sobolev space is studied in a bounded Lipschitz domain with connected boundary. A solution is looked for in the form of a hydrodynamical single layer potential. It leads to an integral equation on the boundary of the domain. Necessary and sufficient conditions for the solvability are given. Moreover, it is shown that we can obtain ...

In this paper, we derive a new integral equation method for direct electromagnetic scattering in homogeneous media and present a numerical confirmation of the new method via a computer simulation. The new integral equation method is based on a paper written by DeSanto [1], originally for scattering from an infinite rough surface separating homogeneous dielectric half-spaces. Here, it is applied...

The numerical treatment of boundary integral equations in the form of boundary element methods has became very popular and powerful tool for engineering computations of boundary value problems, in addition to finite difference and finite element methods. Here, we present some of the most important analytical and numerical aspects of the boundary integral equation. The concept of the principle s...

In this paper we propose a new a posteriori error estimator for a weakly singular integral equation concerned with a direct boundary element ap proach for a Dirichlet problem with a second order elliptic partial di er ential operator The method is based on an approximate solution of a second kind Fredholm integral equation by a Neumann series to estimate the error of a previous computed solutio...

This paper compares the hybrid FEM-BEM and FEM-DBCI methods for the solution of openboundary electrostatic field problems. Both methods couple a differential equation for the interior problem with an integral equation for the exterior one. The comparison shows that FEM-BEM is more accurate than FEM-DBCI but requires more computing time. PACS. 41.20.Cv Electrostatics; Poisson and Laplace equatio...