On capacity computation for symmetric polygonal condensers

Sergei Bezrodnykh; Andrei Bogatyrëv; Sergei Goreinov; Oleg Grigor'ev; Harri Hakula; Matti Vuorinen

doi:10.1016/j.cam.2019.03.030

On capacity computation for symmetric polygonal condensers

Sergei Bezrodnykh
, Andrei Bogatyrëv^*
, Sergei Goreinov
, Oleg Grigor'ev
, Harri Hakula
, Matti Vuorinen

^*Corresponding author for this work

Research output: Contribution to journal › Article › Scientific › peer-review

14 Citations (Scopus)

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 (Bezrodnykh and Vlasov, 2002; Bezrodnykh, 2016 [64,65]) and Riemann theta functions (Bogatyrëv, 2012; Grigoriev, 2013; Bogatyrëv and Grigor'ev, 2017; Bogatyrëv 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).

Original language	English
Pages (from-to)	271-282
Number of pages	12
Journal	Journal of Computational and Applied Mathematics
Volume	361
DOIs	https://doi.org/10.1016/j.cam.2019.03.030
Publication status	Published - 1 Dec 2019
MoE publication type	A1 Journal article-refereed

Funding

The work of AB, SG and OG was supported by RSCF grant 16-01-10349 , SB acknowledges the receipt of support from the RUDN University ’Program 5-100’ and RFBR grant 19-07-00750 . All authors are indebted to Professors Vladimir Vlasov and Antti Rasila who supported this research at all its stages.

Keywords

Boundary integral method
Capacity
Condenser
Finite element method
Lauricella function
Theta function

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10.1016/j.cam.2019.03.030

https://arxiv.org/abs/1804.01420

Cite this

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title = "On capacity computation for symmetric polygonal condensers",

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 (Bezrodnykh and Vlasov, 2002; Bezrodnykh, 2016 [64,65]) and Riemann theta functions (Bogatyr{\"e}v, 2012; Grigoriev, 2013; Bogatyr{\"e}v and Grigor'ev, 2017; Bogatyr{\"e}v 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).",

keywords = "Boundary integral method, Capacity, Condenser, Finite element method, Lauricella function, Theta function",

author = "Sergei Bezrodnykh and Andrei Bogatyr{\"e}v and Sergei Goreinov and Oleg Grigor'ev and Harri Hakula and Matti Vuorinen",

year = "2019",

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day = "1",

doi = "10.1016/j.cam.2019.03.030",

language = "English",

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journal = "Journal of Computational and Applied Mathematics",

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TY - JOUR

T1 - On capacity computation for symmetric polygonal condensers

AU - Bezrodnykh, Sergei

AU - Bogatyrëv, Andrei

AU - Goreinov, Sergei

AU - Grigor'ev, Oleg

AU - Hakula, Harri

AU - Vuorinen, Matti

PY - 2019/12/1

Y1 - 2019/12/1

N2 - 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 (Bogatyrëv, 2012; Grigoriev, 2013; Bogatyrëv and Grigor'ev, 2017; Bogatyrëv 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).

AB - 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 (Bogatyrëv, 2012; Grigoriev, 2013; Bogatyrëv and Grigor'ev, 2017; Bogatyrëv 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).

KW - Boundary integral method

KW - Capacity

KW - Condenser

KW - Finite element method

KW - Lauricella function

KW - Theta function

UR - https://www.scopus.com/pages/publications/85065450576

U2 - 10.1016/j.cam.2019.03.030

DO - 10.1016/j.cam.2019.03.030

M3 - Article

AN - SCOPUS:85065450576

SN - 0377-0427

VL - 361

SP - 271

EP - 282

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

ER -

On capacity computation for symmetric polygonal condensers

Abstract

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Keywords

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