Exponential finite volume schemes for solving of evolutional equations on irregular grids
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 149 (2007) no. 4, pp. 121-131
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A numerical solution of evolutionary equations on irregular grids is considered. The conservative weakly monotone finite volume schemes on both triangular and tetrahedral grids for convection-diffusion type equations are proposed. The conditions of stability and convergence of these schemes are formulated. The proposed numerical approach are illustrated for one vacuum microelectronics problem connected with computations of electron emission from edge surface of silicon microcathode.
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S. V. Polyakov. Exponential finite volume schemes for solving of evolutional equations on irregular grids. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 149 (2007) no. 4, pp. 121-131. http://geodesic.mathdoc.fr/item/UZKU_2007_149_4_a9/

[1] Chung T. J., Computational fluid dynamics, Cambridge Univ. Press, Cambridge, 2002, 1022 pp. | MR

[2] Li R., Chen Zh., Wu W., Generalized difference methods for differential equations. Numerical analysis of finite volume methods, M. Dekker Inc., 2000, 459 pp. | MR

[3] Samarskii A. A., Teoriya raznostnykh skhem, Nauka, M., 1983, 616 pp. | MR

[4] Goland E. I., “O sopryazhennykh semeistvakh raznostnykh skhem dlya uravnenii parabolicheskogo tipa s mladshimi chlenami”, Zhurn. vychisl. matem. i matem. fiz., 18:5 (1978), 1162–1169 | MR

[5] Karetkina N. V., “Bezuslovno ustoichivaya raznostnaya skhema dlya parabolicheskikh uravnenii, soderzhaschikh pervye proizvodnye”, Zhurn. vychisl. matem. i matem. fiz., 20:7 (1980), 236–240 | MR | Zbl

[6] Dulan E., Miller Dzh., Shilders U., Ravnomernye chislennye metody resheniya zadach s pogranichnym sloem, Mir, M., 1983, 198 pp. | MR

[7] Polyakov S. V., Sablikov V. A., “Lateralnyi perenos fotoindutsirovannykh nositelei zaryada v geterostrukturakh s dvumernym elektronnym gazom”, Matem. modelirovanie, 9:12 (1997), 76–86 | Zbl

[8] Karamzin Yu. N., Popov I. V., Polyakov S. V., “Raznostnye metody resheniya zadach mekhaniki sploshnoi sredy na nestrukturirovannykh treugolnykh i tetraedralnykh setkakh”, Matem. modelirovanie, 15:11 (2003), 3–12 | MR | Zbl

[9] Kalinichenko M. I., Polyakov S. V., “Chislennye metody dlya dvumernoi modeli rasprostraneniya lazernogo izlucheniya v khimicheski aktivnom gaze v sluchae razvitoi termodiffuzii”, Zhurn. vychisl. matem. i matem. fiz., 37:3 (1997), 334–347 | MR | Zbl

[10] Fedirko V. A., Polyakov S. V., “Modelirovanie na MVS ustroistv vakuumnoi mikroelektroniki”, Fundamentalnye fiziko-matematicheskie problemy i modelirovanie tekhniko-tekhnologicheskikh sistem, vyp. 7, ed. L. A. Uvarova, Yanus-K, ITs MGTU “Stankin”, M., 2004, 138–147

[11] Dyuzhev N. A., Makhiboroda M. A., Fedirko V. A., “Issledovanie razlichnykh rezhimov avtoelektronnoi emissii kremnievogo kantilevera”, XIV nauch.-tekhn. konf. s uchastiem zarubezhnykh spetsialistov “Vakuumnaya nauka i tekhnika”, materialy konf., ed. D. V. Bykov, MIEM, M., 2007, 248–251