Numerical solution of boundary integral equations of the plane theory of elasticity in curvilinear polygons
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2015), pp. 57-61 Cet article a éte moissonné depuis la source Math-Net.Ru

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A numerical method for solving boundary integral equations of the plane theory of elasticity in domains with piecewise analytic boundaries and a finite number of corner points is proposed. This method is based on the application of a family of composite quadrature formulas on condensing grids. It is proved that the proposed method is exponentially convergent with respect to the number of quadrature nodes in use.
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I. O. Arushanyan. Numerical solution of boundary integral equations of the plane theory of elasticity in curvilinear polygons. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2015), pp. 57-61. http://geodesic.mathdoc.fr/item/VMUMM_2015_4_a10/

[1] Babušhka I., Guo B.Q., Stephan E.P., “On the exponential convergence of the $h$–$p$ version for boundary element Galerkin methods on polygons”, Math. Methods Appl. Sci., 12:5 (1990), 413–427 | DOI | MR | Zbl

[2] Bremer J., Rokhlin V., “Efficient discretization of Laplace boundary integral equations on polygonal domains”, J. Comput. Phys., 229:7 (2010), 2507–2525 | DOI | MR | Zbl

[3] Chandler G.A., “Superconvergent approximations to the solution of a boundary integral equation on polygonal domains”, SIAM J. Numer. Anal., 23:6 (1986), 1214–1229 | DOI | MR | Zbl

[4] Kress R., “A Nyström method for boundary integral equations in domains with corners”, Numer. Math., 58:1 (1990), 145–161 | DOI | MR | Zbl

[5] Kress R., Linear integral equations, Springer, Heidelberg, 1999 | Zbl

[6] Arushanyan I.O., “O chislennom reshenii granichnykh integralnykh uravnenii vtorogo roda v oblastyakh s uglovymi tochkami”, Zhurn. vychisl. matem. i matem. fiz., 36:6 (1996), 101–113 | MR | Zbl

[7] Arushanyan I.O., “Primenenie metoda kvadratur dlya resheniya granichnykh integralnykh uravnenii ploskoi teorii uprugosti na mnogougolnikakh”, Vychisl. metody i programmir., 4 (2003), 142–154

[8] Arushanyan I.O., “Semeistvo kvadraturnykh formul dlya chislennogo resheniya granichnykh integralnykh uravnenii”, Vychisl. metody i programmir., 14 (2013), 461–467

[9] Arushanyan I.O., “Chislennoe reshenie granichnykh integralnykh uravnenii na krivolineinykh mnogougolnikakh”, Vestn. Mosk. un-ta. Matem. Mekhan., 2014, no. 4, 55–57 | MR | Zbl

[10] Arushanyan I.O., “Eksponentsialno skhodyaschiisya metod resheniya granichnykh integralnykh uravnenii na mnogougolnikakh”, Vychisl. metody i programmir., 15 (2014), 417–426

[11] Mazya V.G., “Granichnye integralnye uravneniya”, Itogi nauki i tekhniki, 27, VINITI, M., 1988, 131–228