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

Department of Mathematics and Systems Analysis

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

5 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

Keywords

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

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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",

month = dec,

day = "1",

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

language = "English",

volume = "361",

pages = "271--282",

journal = "Journal of Computational and Applied Mechanics",

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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

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DO - 10.1016/j.cam.2019.03.030

M3 - Article

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JO - Journal of Computational and Applied Mechanics

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SN - 0377-0427

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