A Galerkin Implementation Of The MultipoleExpansion Approach For Accurate And FastSolution Of First And Second Kind FredholmEquations

In 1983 Rohklin [9] introduced the notion of multipole expansion for the rapid solution of first and second kind Fredholm equations arising from potential theory. Recently, these ideas have been extended to 3D by the work of White, Korsmeyer [7], and others interested in rapid parameter extraction for characterization of electrical circuits. At the same time, the Galerkin formulation of the boundary element method has recently received renewed attention. The Galerkin BEM approach can substantially increase accuracy near corner singularities, while at the same time introduce desirable convergence properties as demonstrated by Hsiao [6], and Wendland and Arnold [2]. To date the multipole expansion alternative has only been implemented and tested for collocation boundary elements. This work will discuss a Galerkin formulation of multipole expansion for two dimensional problems in electrostatics, and contrast the accuracy and computational costs of classical collocation, Galerkin BEM, collocation multipole expansion, and a Galerkin-multipole formulation. Introduction The solution of open field boundary value problems in electrostatics is of great interest to engineers in the field of power and high voltage engineering. Information regarding the electric field structure on and near conducting and dielectric boundaries is very useful in the design and evaluation of new devices. There are currently several methods of solving these problems, including: the finite element method, the charge simulation method, and the boundary element method. In our previous work, we have used the boundary element approach in which we model all conductor surfaces and dielectric interfaces by unknown charge distributions and enforce DirichTransactions on Modelling and Simulation vol 1, © 1993 WIT Press, www.witpress.com, ISSN 1743-355X