Geodesic
Finete superelement method and its application for solving science and technology problems
Matematičeskoe modelirovanie, Tome 25 (2013) no. 6, pp. 32-40.

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The algorithm for construction and study of Fedorenko finite superelements method (FSEM) is described. Different variants of Fedorenko FSEM for simulation of media with small inclusions are presented. The algorithms are implemented and software complex for numerical solution of boundary value problems with singularities is developed. The theoretical substantiation of different variants of method for elliptic equations on the example of the Laplace equation is realized. The results of numerical solution for several tasks are presented.
Keywords: Fedorenko finite superelements method, boundary value problems with singularities
Mots-clés : Laplace equation. 
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M. P. Galanin; S. A. Lazareva. Finete superelement method and its application for solving science and technology problems. Matematičeskoe modelirovanie, Tome 25 (2013) no. 6, pp. 32-40. http://geodesic.mathdoc.fr/item/MM_2013_25_6_a2/

[1] Strakhovskaya L. G., Fedorenko R. P., “Ob odnom variante metoda konechnykh elementov”, ZhVM i MF, 19:4 (1979), 950–960 | MR | Zbl

[2] Strakhovskaya L. G., Fedorenko R. P., Raschet diffuzii v mnogosvyaznoi oblasti metodom konechnykh superelementov, preprint No 171, IPM im. M. V. Keldysha AN SSSR, M., 1987, 26 pp. | MR

[3] Strakhovskaya L. G., Fedorenko R. P., Raschet napryazhenii v kompozitnom tele metodom konechnykh superelementov, preprint No 97, IPM im. M. V. Keldysha RAN, 1994, 26 pp.

[4] Fedorenko R. P., Vvedenie v vychislitelnuyu fiziku, Izdatelstvo MFTI, M., 1994, 528 pp.

[5] Galanin M., Savenkov E., “Fedorenko finite superelement method as special Galerkin approximation”, Mathematical Modelling and Analysis, 7:1 (2002), 41–50 | MR | Zbl

[6] Galanin M. P., Savenkov E. B., “K obosnovaniyu metoda konechnykh superelementov Fedorenko”, ZhVM i MF, 43:5 (2003), 713–729 | MR | Zbl

[7] Galanin M. P., Lazareva S. A., Savenkov E. B., Chislennoe issledovanie metoda konechnykh superelementov na primere resheniya zadachi o skvazhine dlya uravneniya Laplasa, preprint No 79, IPM im. M. V. Keldysha RAN, M., 2005, 30 pp.

[8] Galanin M., Savenkov E., “Metod konechnykh superelementov dlya zadachi o skorostnom skin-sloe”, Trudy mezhdunarodnoi konferentsii po vychislitelnoi matematike MKVM-2004 (21–25 iyunya 2004 g., Novosibirsk, Akademgorodok, Rossiya), 455–460

[9] Galanin M., Savenkov E., Temis J., “Finite Superelements Method for Elasticity Problems”, Mathematical Modelling and Analysis, 10:3 (2005), 237–246 | MR | Zbl

[10] Galanin M., Lazareva S., Savenkov E., “Numerical investigation of the Finite Superelement Method for the 3D elasticity problems”, Mathematical Modelling and Analysis, 12:1 (2007), 39–50 | DOI | MR | Zbl

[11] Galanin M., Lazareva S., “Local regularity and asymptotic behavior of Fedorenko finite superelement method solution”, Int. J. Computing Science and Mathematics, 2:3 (2009), 201–221 | DOI | MR | Zbl

[12] Lazareva S. A., “Analiz tochnosti priblizhenii metoda konechnykh superelementov Fedorenko”, Vestnik MGTU im. N. E. Baumana, ser. Estestvennye nauki, 2009, no. 2, 3–27

[13] Lazareva S. A., “Approksimatsionnye svoistva metoda konechnykh superelementov Fedorenko”, Vychislitelnye tekhnologii, 13:8, spets. vyp. (2008), 75–81 | Zbl

[14] Galanin M., Lazareva S., Savenkov E., “Fedorenko Finite Superelement Method and its Applications”, Computational Methods in Applied Mathematics, 7:1 (2007), 3–24 | MR | Zbl

[15] Galanin M. P., Savenkov E. B., “Sovmestnoe ispolzovanie metoda konechnykh elementov i metoda konechnykh superelementov”, ZhVM i MF, 46:2 (2006), 270–283 | MR | Zbl

[16] Syarle F., Metod konechnykh elementov dlya ellipticheskikh zadach, Mir, M., 1980, 512 pp. | MR

[17] Agoshkov V. I., Lebedev V. I., “Operatory Puankare–Steklova i metody razdeleniya oblasti v variatsionnykh zadachakh”, Vychislitelnye protsessy i sistemy, 2 (1985), 173–227 | MR | Zbl

[18] Oben Zh.-P., Priblizhennoe reshenie ellipticheskikh kraevykh zadach, Mir, M., 1977, 384 pp. | MR

[19] Andreev V. B., “Setochnye approksimatsii negladkikh reshenii differentsialnykh uravnenii”, Differentsialnye uravneniya, 16:7 (1980), 1172–1184 | MR | Zbl

[20] Galanin M. P., Popov Yu. P., Kvazistatsionarnye elektromagnitnye polya v neodnorodnykh sredakh. Matematicheskoe modelirovanie, Nauka, Fizmatlit, M., 1995, 320 pp. | MR | Zbl