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

^*Tämän työn vastaava kirjoittaja

Tutkimustuotos: Lehtiartikkeli › Article › Scientific › vertaisarvioitu

14 Sitaatiot (Scopus)

Abstrakti

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).

Alkuperäiskieli	Englanti
Sivut	271-282
Sivumäärä	12
Julkaisu	Journal of Computational and Applied Mathematics
Vuosikerta	361
DOI - pysyväislinkit	https://doi.org/10.1016/j.cam.2019.03.030
Tila	Julkaistu - 1 jouluk. 2019
OKM-julkaisutyyppi	A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä

Rahoitus

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.

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10.1016/j.cam.2019.03.030

https://arxiv.org/abs/1804.01420

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@article{c85da0350c974b02a17aafca6ae29948,

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 Mathematics",

issn = "0377-0427",

publisher = "Elsevier",

}

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

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