In this study, the Fredholm hypersingular integral equation of first kind with a singular right-hand function on interval − 1 , is solved. The discontinuous solution domain id="M2"> approximated by piecewise polynomial, and collocation method introd...

In this article, we consider the radiation characteristics of a THz antenna made circular dielectric rod decorated with conformal graphene strip and illuminated by field line magnetic current. The has arbitrary angular size location its surface impedance is characterized Kubo theory. Our mathematically accurate analysis uses dedicated hypersingular integral equation for current induced on strip...

We consider an integral equation obtained by the “direct method” for the Neumann problem on a polygonal domain which may contain slits, i.e., interior angles of 2π. By using a Galerkin method with piecewise linear functions on a suitable graded mesh one can obtain the optimal convergence rate h3/2. Using a Gauss solver for the arising linear system would require C h−3 operations. We show that a...

1.1 INTRODUCTION This paper gives a survey on additive Schwarz methods applied to the h and p versions of the boundary element method. We consider weakly singular and hypersingular integral equations, namely the single layer potential operator and the normal derivative of the double layer potential operator. That means we have to consider weak formulations of the form

We establish a mortar boundary element scheme for hypersingular boundary integral equations representing elliptic boundary value problems in three dimensions. We prove almost quasi-optimal convergence of the scheme in broken Sobolev norms of order 1/2. Sub-domain decompositions can be geometrically non-conforming and meshes must be quasi-uniform only on sub-domains. Numerical results confirm th...

The approach we follow consists in transforming the numerical evaluation of hypersingular integrals into the calculation of a nearly singular integral whose mass is distributed according to a positive parameter ε. To evaluate the latter we apply a Gauss quadrature formula associated with a nearly singular weight function. It is estimated the error in terms of ε. Some numerical results are prese...

For hypersingular integral equations in 2D and 3D, we analyze easy-to-implement error estimators like (h − h/2)-based estimators, two-level estimators, and averaging on large patches and prove their equivalence. Moreover, we introduce some ZZ-type error estimators. All of these a posteriori error estimators are analyzed within the framework of localization techniques for the energy norm.

Two-dimensional integral equations of the first kind over a circular disc are considered. The kernels involve the distance between two points on the disc raised to an arbitrary power. A review is given, comparing several published exact solutions for weakly-singular equations: these solutions are complicated, but three of them are shown to be equivalent. Some extensions to hypersingular equatio...