Geodesic
On the construction of two-dimensional local-modified quasistructured grids and solving on them two-dimensional boundary value problem in the domains with curvilinear boundary
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ Vyčislitelʹnaâ matematika i informatika, Tome 6 (2017) no. 2, pp. 5-21 Cet article a éte moissonné depuis la source Math-Net.Ru

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New approaches to local modification quasistructured grids, which allow to track the inhomogeneous boundary value problems in the computational domain and adaptable to curved boundaries, as well as easy to use and does not require the storage of large amounts of data as required in unstructured grids are developed. Such grids are proposed to use for the efficient simulation of a wide class of electro physical devices. It is experimentally shown the need for a local modification of the rectangular grid in calculations in domains with curvilinear boundary. The two-step algorithms for local modifications of considered quasistructured grids are developed. On the first step modification of the near boundary nodes is carried out by the its shift along the normal to boundary and on the second step the transformation of the grid elements that do not meet the quality criteria in a quality grid elements is carried out. Special algorithms for such transformations, which do not violate the structuring subgrids in subdomains are developed. Recommendations for the construction of grids on the interface of subdomains that contain the uncoordinated grids have been done. Algorithms local modification of grids on the interface between the subdomains, one of which contains a segment of the computational domain boundaries, have been developed. The series of numerical experiments on solving a model problem are carried out. The results of numerical experiments showed the validity of the proposed approaches.
Keywords: quasistructured grids, problems of high current electronics.
Mots-clés : local modification, domain decomposition method 
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A. N. Kozyrev; V. M. Sveshnikov. On the construction of two-dimensional local-modified quasistructured grids and solving on them two-dimensional boundary value problem in the domains with curvilinear boundary. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ Vyčislitelʹnaâ matematika i informatika, Tome 6 (2017) no. 2, pp. 5-21. http://geodesic.mathdoc.fr/item/VYURV_2017_6_2_a0/

[1] V. M. Sveshnikov, D. O. Belyaev, “Construction of Quasi-Structured Locally Modified Grids for Solving Problems of High Current Electronics”, Bulletin of South Ural State University. Series: Computational Mathematics and Software Engineering, 2012, no. 40(299), 130–140

[2] V. A. Syrovoj, Introduction to the Theory of Intense Charged Particle Beams, Energoatomizdat, Moscow, 2004, 522 pp.

[3] V. D. Liseikin, Grid generation methods, Springer-Verlag, Berlin, 1999, 363 pp.

[4] Yu. I. Shokin, N. T. Danaev, G. S. Hakimzyanov, N. Yu. Shokina, Lectures on the Difference Scheme on Moving Grids, Part 2, Kazakh National University, Almaty, 2008, 184 pp.

[5] A. F. Sidorov, “An Algorithm for Calculating the Optimal Difference Grids”, Proceedings of the Mathematical Steklov Institute, 74 (1966), 147–151

[6] O. V. Ushakova, “An Algorithm for Constructing Two-dimensional Optimal Adaptive Grids”, Mathematical modeling, 9:2 (1997), 88–90

[7] A. I. Anuchina, N. A. Artemova, T. N. Bronina, V. A. Gordeychuk, O. V. Ushakova, “On the development of the algorithm for constructing grids in the constructions formed by volumes of rotation, including when their deformation”, Abstracts of the VIII All–Russian conference dedicated to the memory of A.F. Sidorov and Russian youth school–conference (Abrau–Durso, 5–10 September 2016), Publishing House of the Krasovsky Institute of Mathematics and Mechanics. UB RAS, Ekaterinburg, 2016, 7–9

[8] A. M. Matsokin, “Automation triangulation of domains with smooth boundary for solving elliptic equations”, Preprint, v. 15, Computing Center of USSR Academy of Sciences, Novosibirsk, 1975, 15 pp.

[9] V. P. Ilin, E. A. Itskovich, G. Y. Kuklina, I. A. Sander, S. A. Sander, V. M. Sveshnikov, “Calculation of Electrostatic Fields on Locally Modified Grids”, Computational methods and technology solutions of problems of mathematical physics, 1993, 63–72

[10] V. M. Sveshnikov, “The numerical calculation of charged particle beams on locally modified grids”, Preprint, v. 1109, Computing Center of Russian Academy of Sciences, Novosibirsk, 1997, 28 pp.

[11] I. A. Sander, “The program of Delaunay triangulation construction for the domain with the piecewise smooth boundary”, Bulletin of the Novosibirsk Computing Center. Series: Numerical Analysis, 1998, 71–79

[12] V. P. Ilin, V. M. Sveshnikov, V. S. Synakh, “On Grid Technologies for Two-Dimensional Boundary Value Problems”, Journal of Applied and Industrial Mathematics, 3:1 (2000), 124–136

[13] V. M. Sveshnikov, “Construction of Direct and Iterative Methods of Decomposition”, Journal of Applied and Industrial Mathematics, 12:3(39) (2009), 99–109

[14] V. P. Ilin, Methods and Technologies of Finite Elements, ICM SBRAS, Novosibirsk, 2007, 37 pp.

[15] A. V. Skvortcov, “Overview of Algorithms for Constructiong Delanau Triangulation”, Numerical Methods and Programming, 3:1 (2002), 18–43

[16] D. O. Belyaev, A. N. Kozyrev, V. M. Sveshnikov, “Program Package ERA-DD for Solving Two-Dimensional Boundary Value problems on Quasi-Structured Grids”, Novosibirsk State University Journal of Information Technologies, 8:1 (2010), 3–11

[17] A. A. Samarskiy, The Theory of Difference Schemes, Nauka, Moscow, 1977, 656 pp.

[18] G. I. Marchuk, Methods of Computational Mathematics, Nauka, Moscow, 1977, 456 pp.