The Application Of The Robin Hood Method In
Electrostatic Problems
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
Related Book
Other papers in this volume
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