During the last two-three decades the importance of computer simulations based on numerical full-wave solutions of Maxwell’s has continuously increased in electrical engineering. Software products based on integral equation methods have an unquestionable importance in the frequency domain electromagnetic analysis and design of open-region problems. This paper deals with the surface and volume i...

We construct and analyze a family of well-conditioned boundary integral equations for the Krylov iterative solution of three-dimensional elastic scattering problems by a bounded rigid obstacle. We develop a new potential theory using a rewriting of the Somigliana integral representation formula. From these results, we generalize to linear elasticity the well-known Brakhage-Werner and Combined F...

We present cubature methods approximating the surface integrals arising by Galerkin discretization of boundary integral equations on surfaces in R 3. This numerical integrator does not depend on the explicit form of the kernel function, the trial and test space, or the surface parametrization. Thus, it is possible to generate the system matrix for a broad class of integral equations just by rep...

In this paper, the possibilities of finding out surface plasmons in negative-permittivity metamaterial scatterers, using surface integral equations, are discussed. Electrostatic resonances manifest themselves as very high values of the polarizability for a certain (negative) value of the permittivity. Another way to locate the position of the resonances is to calculate the eigenvalues of the so...

where p and q are points on S, G is the free-space Green’s function, ∂/∂nq denotes normal differentiation at q, and uinc is the incident field. The Helmholtz integral equations are familiar boundary integral equations, for which there is a complete theoretical framework (Kleinman and Roach, 1974; Colton and Kress, 1983). Many examples of their numerical treatment, usually using boundary element...

‎‎In this paper, Solvability nonlinear Volterra integral equations with general vanishing delays is stated. So far sinc methods for approximating the solutions of Volterra integral equations have received considerable attention mainly due to their high accuracy. These approximations converge rapidly to the exact solutions as number sinc points increases. Here the numerical solution of nonlinear...

The dielectric withstand capabilities of insulating materials is related to their surface electric field and potential distributions. These distributions, in the presence of polluting layers, are quite different from these encountered in classical electrostatics. This work is concerned with the application of boundary integral equations method to the calculation of electric fields and potential...

In this paper we apply the technique of measures of noncompactness to the theory of infinite system of integral equations in the Fr´echet spaces. Our aim is to provide a few generalization of Tychonoff fixed point theorem and prove the existence of solutions for infinite systems of nonlinear integral equations with help of the technique of measures of noncompactness and a generalization of Tych...

In this paper, a reliable iterative approach, for solving a wide range of linear and nonlinear Volterra-Fredholm integral equations is established. First the approach considers a discretized form of the integral terms where considering some conditions on the kernel of the integral equation it is proved that solution of the discretized form converges to the exact solution of the problem. Then th...

Algebraic integral equations is a special category of Volterra integral equations system,  that has many applications in physics and engineering. The principal aim of this paper is to serve the numerical solution of an integral algebraic equation by using the Taylor expansion method. In this method, using the Taylor expansion of the unknown function, the algebraic integral equation system becom...