On capacity computation for symmetric polygonal condensers

TL;DR

This paper introduces two analytical-numerical methods for accurately computing the capacity of symmetric polygonal condensers, and uses these results to benchmark numerical algorithms like finite element and boundary integral methods.

Contribution

It presents novel analytical approaches based on Lauricella and Riemann theta functions for high-precision capacity computation of planar condensers.

Findings

Achieved highly accurate capacity values for a wide family of condensers.

Benchmarking shows the effectiveness of adaptive $hp$--finite element and boundary integral methods.

Provided reference solutions for future numerical method validations.

Abstract

Making use of two different analytical-numerical methods for capacity computation, we obtain matching to a very high precision numerical values for capacities of a wide family of planar condensers. These two methods are based respectively on the use of the Lauricella function and Riemann theta functions. We apply these results to benchmark the performance of numerical algorithms, which are based on adaptive $hp$--finite element method and boundary integral method.