Author(s)

H. Abraham, P. Lazi´c & H. ˇ Stefanˇci´c

Abstract

We introduce a novel numerical method of solving electrostatic problems based on a nonlocal charge transfer, named the Robin Hood method. Some of the many advantages of this method such as small memory requirements, stability, absence of Critical Slowing Down and fast and global convergence will be emphasized and demonstrated. Due to very broad applicability, a variety of examples will be presented. Some are of purely theoretical character, but are interesting for error and stability analysis. Others are the analyses of realistic experimental instruments, namely a particle accelerator and a spark plug. Others, such as medical instruments, onboard electronics and particle detectors, could be considered as many others as well. Keywords: boundary element, electrostatics, Robin Hood, nonlocal charge transfer, equipotentiality, Critical Slowing Down, numerical methods. 1 Introduction In this article we give a brief theoretical introduction and demonstrate some of the most interesting results obtained using rather different approach for solving electrostatic problems named the Robin Hood (RH) method. First of all, the RH method as implemented to electrostatic problems here is somewhat similar to Boundary Elements methods. However using only the boundaries of the objects is more property of the electrostatics in general than the main idea of the RH method. The method can also be applied to different problems where it looks more like Finite Differences method. Anyway, in electrostatic problems as we have implemented it, objects which are analyzed are defined by their surfaces which are then divided into a finite number of elements. Because of the technical reasons these elements are the rectangular triangles, as will be explained later.

Keywords

boundary element, electrostatics, Robin Hood, nonlocal charge transfer, equipotentiality, Critical Slowing Down, numerical methods