On capacity computation for symmetric polygonal condensers

: Bezrodnykh S, Bogatyrev A, Goreinov S, Grigor'ev O, Hakula H, Vuorinen M

Publisher: ELSEVIER SCIENCE BV

: 2019

: Journal of Computational and Applied Mathematics

: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

: J COMPUT APPL MATH

: 361

: 271

: 282

: 12

: 0377-0427

: 1879-1778

DOI: https://doi.org/10.1016/j.cam.2019.03.030

: https://arxiv.org/abs/1804.01420

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 (Bezrodnykh and Vlasov, 2002; Bezrodnykh, 2016 [64,65]) and Riemann theta functions (Bogatyrev, 2012; Grigoriev, 2013; Bogatyrev and Grigor'ev, 2017; Bogatyrev and Grigor'ev, 2018). We apply these results to benchmark the performance of numerical algorithms, which are based on adaptive hp-finite element method (Hakula et al. 2011, 2013, 2018) and boundary integral method (Tsuji, 1959; Jaswon and Symm, 1977; Albrecht and Collatz, 1980). (C) 2019 Elsevier B.V. All rights reserved.