Solving for Micro- and Macro- Scale Electrostatic Configurations Using the Robin Hood Algorithm

TL;DR

This paper introduces the Robin Hood algorithm, a highly efficient matrix-inversion method for solving complex electrostatic boundary element problems across micro and macro scales, including dielectrics and magnetic materials.

Contribution

The paper presents a novel, optimized boundary element method solver capable of handling large-scale electrostatic problems with high accuracy and expanded material modeling capabilities.

Findings

Successfully modeled a large volume beta-detector's electrostatic potential.

Analyzed field enhancement at nano-structured electrode surfaces.

Handled geometries with approximately 100,000 elements efficiently.

Abstract

We present a novel technique by which highly-segmented electrostatic configurations can be solved. The Robin Hood method is a matrix-inversion algorithm optimized for solving high density boundary element method (BEM) problems. We illustrate the capabilities of this solver by studying two distinct geometry scales: (a) the electrostatic potential of a large volume beta-detector and (b) the field enhancement present at surface of electrode nano-structures. Geometries with elements numbering in the O(10^5) are easily modeled and solved without loss of accuracy. The technique has recently been expanded so as to include dielectrics and magnetic materials.