An efficient procedure for solving potential field problems: the Conformal Boundary Differences Method

TL;DR

This paper introduces a novel conformal boundary differences method based on Schwarz-Christoffel transformation, enabling fast, accurate solutions for potential field problems in complex domains, surpassing traditional numerical methods like FEA.

Contribution

The paper presents a new conformal boundary differences method that improves efficiency and applicability for potential field problems in complex, inhomogeneous, and multiply connected domains.

Findings

Method achieves high accuracy in complex domains

Results outperform traditional FEA in speed and precision

Applicable to practical engineering problems

Abstract

A novel method rooted in the classical Schwarz-Christoffel transformation from the disk is introduced, which allows for fast and accurate solution of potential field problems in possibly inhomogeneous and multiply connected domains: this is for sure its most outstanding feature, circumventing the barriers that have increasingly restricted the scope of conformal mappings in applications since the advent of computers and purely numerical methods. An example problem, derived from a case of practical interest, is analyzed and results are compared with those obtained from FEA.