Solutions of linear elliptic partial differential equations in unbounded domains can be represented by boundary potentials if they satisfy certain conditions at infinity. These radiation conditions depend on the fundamental solution chosen for the integral representation. We prove some basic results about radiation conditions in a rather general framework. Fundamental solutions G are considered...

This paper presents a boundary integral equation method for computing numerical conformal mapping of bounded multiply connected region onto an annulus with spiral slits region and its inverse. The method is an extension of the author’s method for computing the Annulus with circular slits map of bounded multiply connected regions (see [Sangawi, A. W. K., Murid, A. H. M., Nasser, M. M. S.: Annulu...

The recent progress of physiological measurement allows us to observe membrane potential behaviors of extensive regions with higher spatial and temporal resolutions. Accordingly, a new theory has been expected with which we can analyze the spatiotemporal dynamics of the membrane potential with the cell-shape and the spatial distributions of electrical parameters taken into consideration quantit...

In this paper we study boundary element methods for initialNeumann problems for the heat equation. Error estimates for some fully discrete methods are established. Numerical examples are presented.

In this paper we study boundary element methods for initialNeumann problems for the heat equation. Error estimates for some fully discrete methods are established. Numerical examples are presented.

Operator products occur naturally in a range of regularized boundary integral equation formulations. However, while a Galerkin discretisation only depends on the domain space and the test (or dual) space of the operator, products require a notion of the range. In the boundary element software package Bempp we have implemented a complete operator algebra that depends on knowledge of the domain, ...

We analyze the h-p version of the bem for mixed Dirichlet Neumann problems of the Laplacian in polyhedral domains. Based on a regularity analysis of the solution in count-ably normed spaces we show that the boundary element Galerkin solution of the h-p version converges exponentially fast on geometrically graded meshes.

We present new a priori error analyses of the coupling of the Raviart–Thomas (RT) method and BEM as well as of the coupling of the hybridizable discontinuous Galerkin (HDG) method with BEM. The novel features of the analysis of the RT-BEM coupling are the superconvergence estimates for the scalar approximation of the interior problem and new bounds in weak and strong norms for the boundary vari...