Geodesic
Conformal mapping of a strip onto a circular numerable polygon of strip type
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2024), pp. 34-44 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider a simply connected domain of strip type with the symmetry of transfer. The boundary of the domain consists of circular arcs (circular numerable polygon). We write the Schwarz derivative of the mapping of a strip onto a circular numerable polygon in terms of elliptic functions. We obtain a generalization of the Schwarz–Christoffel formula for mapping of a strip onto a numerable polygon with the boundary consisting of straight line segments. One special case of a numerable polygon with additional symmetry with respect to a vertical line is considered.
Keywords: conformal mapping, strip, circular numerable polygon, symmetry of transfer, Schwarz–Christoffel formula. 
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I. A. Kolesnikov; Yu. A. Loboda; A. Kh. Sharofov. Conformal mapping of a strip onto a circular numerable polygon of strip type. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 9 (2024), pp. 34-44. http://geodesic.mathdoc.fr/item/IVM_2024_9_a3/

[1] Aleksandrov I.A., Teoriya funktsii kompleksnogo peremennogo, TGU, Tomsk, 2002

[2] Hussenpflug W.S., “Elliptic integrals and the Schwarz-Christoffel transformation”, Comput. Math. Appl., 33:12 (1997), 15–114 | DOI | MR

[3] Aleksandrov I.A., “Konformnye otobrazheniya poluploskosti na oblasti s simmetriei perenosa”, Izv. vuzov. Matem., 1999, no. 6, 15–18

[4] Kolesnikov I.A., “Otobrazhenie na krugovoi schetnougolnik s simmetriei perenosa”, Vestn. Tomsk. gos. un-ta. Ser. Matem. Mekhan., 2013, no. 2(22), 33–43

[5] Fujimori S., Weber M., “Triply periodic minimal surfaces bounded by vertical symmetry planes”, Manuscripta mathem., 2009, no. 129, 29-53 | DOI | MR | Zbl

[6] Driscoll T.A., Trefethen L.N., Schwarz–Christoffel mapping, Cambridge Monographs Appl. Comput. Math., 8, Cambridge Univ. Press, 2002 | MR | Zbl

[7] Floryan J.M., “Conformal-mapping-based coordinate generation method for flows in periodic configurations”, J. Comput. Phys., 62:1 (1986), 221–247 | DOI | MR | Zbl

[8] Kolesnikov I.A., Kopaneva L.S., “Konformnoe otobrazhenie na schetnougolnik s dvoinoi simmetriei”, Izv. vuzov. Matem., 2014, no. 12, 37–47 | Zbl

[9] Kolesnikov I.A., “Opredelenie aktsessornykh parametrov dlya otobrazheniya na schetnougolnik”, Vestn. Tomsk. gos. un-ta. Ser. Matem. Mekhan., 2014, no. 2(28), 18–28

[10] Kolesnikov I.A., “Opredelenie aktsessornykh parametrov konformnykh otobrazhenii iz verkhnei poluploskosti na pryamolineinye schetnougolniki s dvoinoi simmetriei i krugovye schetnougolniki”, Vestn. Tomsk. gos. un-ta. Ser. Matem. Mekhan., 2019, no. 60, 42–60 | Zbl

[11] Kolesnikov I.A., “Konformnoe otobrazhenie poluploskosti na schetnougolnik tipa poluploskosti”, Vestn. Tomsk. gos. un-ta. Ser. Matem. Mekhan., 2022, no. 77, 5–16 | Zbl

[12] Floryan J.M., “Conformal-mapping-based coordinate generation method for channel flows”, J. Comput. Phys., 58:2 (1985), 229–245 | DOI | MR | Zbl

[13] Baddoo P.J., Crowdy D.G., “Periodic Schwarz-Christoffel mappings with multiple boundaries per period”, Proc. Math. Phys. Engin. Sci., 475:2228 (2019), 1–20 | MR

[14] Hale N., Tee T.W., “Conformal maps to multiply slit domains and applications”, SIAM J. Sci. Comput., 31:4 (2009), 3195–3215 | DOI | MR | Zbl

[15] Gysen B.L.J., Lomonova E.A., Paulides J.J.H., Vandenput A.J.A., “Analytical and numerical techniques for solving Laplace and Poisson equations in a tubular permanent magnet actuator: Part II. Schwarz-Christoffel mapping”, IEEE Trans. Magnetics, 44:7 (2008), 1761–1767 | DOI

[16] Baddoo P.J., Ayton L.J., “A calculus for flows in periodic domains”, Theor. Comput. Fluid Dynam., 35 (2021), 145–168 | DOI | MR

[17] Fyrillas M.M., “Shape factor and shape optimization for a periodic array of isothermal pipes”, Internat. J. Heat Mass Transf., 53:5-6 (2010), 982–989 | DOI | Zbl

[18] Leontiou T., Ikram M., Beketayev K., Fyrillas M.M., “Heat transfer enhancement of a periodic array of isothermal pipes”, Internat. J. Therm. Sci., 104:9 (2016), 480–488 | DOI

[19] Lavrentev M.A., Shabat B.V., Metody teorii funktsii kompleksnogo peremennogo, Lan, M., 2002 | MR

[20] Akhiezer N.I., Elementy teorii ellipticheskikh funktsii, Nauka, M., 1970 | MR

[21] Nasyrov S.R., Geometricheskie problemy teorii razvetvlennykh nakrytii rimanovykh poverkhnostei, Magarif, Kazan, 2008