Efficient methods for stiff multidimensional multiparametric problems
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N. S. Bakhvalov. Efficient methods for stiff multidimensional multiparametric problems. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 39 (1999) no. 12, pp. 2019-2049. http://geodesic.mathdoc.fr/item/ZVMMF_1999_39_12_a5/

[1] Saulev V. K., “O reshenii nekotorykh kraevykh zadach na bystrodeistvuyuschikh vychislitelnykh mashinakh metodom fiktivnykh oblastei”, Sibirskii matem. zh., 4:4 (1963), 912–925 | MR

[2] Kaporin I. E., “Modifitsirovannyi marshevyi algoritm dlya resheniya raznostnoi zadachi Dirikhle dlya uravneniya Puassona v pryamougolnike”, Raznostnye metody matem. fiz., Izd-vo MGU, M., 1980, 11–21

[3] Lebedev V. I., “Raznostnye analogi ortogonalnykh razlozhenii osnovnykh differentsialnykh operatorov i nekotorykh kraevykh zadach matematicheskoi fiziki. I”, Zh. vychisl. matem. i matem. fiz., 4:3 (1964), 449–465 ; II:4, 649–659 | MR | Zbl

[4] Bogachev K. Yu., “Obosnovanie metoda fiktivnykh oblastei resheniya smeshannykh kraevykh zadach dlya kvazilineinykh ellipticheskikh uravnenii”, Vestn. MGU. Ser. 1: Matem., Mekhan., 1996, no. 3, 16–23 | MR | Zbl

[5] Dyakonov E. G., “O nekotorykh pryamykh i iteratsionnykh metodakh, osnovannykh na okaimlenii matrits”, Chisl. metody v matem. fiz., 4, VTs SO AN SSSR, Novosibirsk, 1979, 45–68

[6] D'yakonov E. G., “On triangulation in the finite element method and Efficient iterative methods”, Topics in Numeric. Analys, v. III, Acad. Press, 1979, 103–123 | MR

[7] Bakhvalov H. C., Panasenko G. P., Osrednenie protsessov v periodicheskikh sredakh. Matematicheskie zadachi mekhaniki kompozitsionnykh materialov, Nauka, M., 1984 ; Homogehization. Averaging processes in periodic media. Mathematical problems in mechanics of composite materials, Kluwer Acad. Publ., Dordrecht etc., 1989 | MR | Zbl | MR | Zbl

[8] Kobelkov G. M., “Fictitious domain method and the solution of elliptic equations with highly varying coefficients”, Sovet. J. Numer. Analys. and Math. Modelling, 2:6 (1987), 407–418 | DOI | MR

[9] Lebedev V. I., “O KR-metode uskoreniya skhodimosti iteratsii pri reshenii kineticheskogo uravneniya”, Chisl. metody resheniya zadach matem. fiz., 6, no. 4, Nauka, M., 1966, 154–176 | MR

[10] Marchuk G. I., Kuznetsov Yu. A., “Ob optimalnykh iteratsionnykh protsessakh”, Dokl. AN SSSR, 186:2 (1968), 1331–1334

[11] Kuznetsov Yu. A., “Vychislitelnye metody v podprostranstvakh”, Vychisl. protsessy i sistemy, 2, Nauka, M., 1984, 265–350

[12] Bakhvalov N. S., Kobelkov G. M., Chizhonkov E. V., Iteratsionnyi metod resheniya ellipticheskikh zadach so skorostyu skhodimosti, ne zavisyaschei ot razbrosa koeffitsientov, Preprint No 190, OVM AN SSSR, M., 1988 | MR

[13] Bakhvalov N. S., Reshenie pervoi kraevoi zadachi dlya sistemy uravnenii teorii uprugosti metodom fiktivnykh oblastei, Preprint No 191, OVM AN SSSR, M., 1988 | MR

[14] Bakhvalov N. S., Knyazev A. V., “Novyi iteratsionnyi algoritm resheniya zadach metoda fiktivnykh potokov dlya ellipticheskikh uravnenii”, Dokl. AN SSSR, 312:4 (1990), 783–786 | MR | Zbl

[15] Bakhvalov N. S., Knyazev A. V., “Effektivnoe vychislenie osrednennykh kharakteristik kompozitov periodicheskoi struktury iz suschestvenno raznorodnykh materialov”, Dokl. AN SSSR, 313:4 (1990), 777–781 | MR | Zbl

[16] Bakhvalov N. S., Knyazev A. V., “Metody effektivnogo vychisleniya osrednennykh kharakteristik kompozitov periodicheskoi struktury iz suschestvenno raznorodnykh materialov”, Vychisl. protsessy i sistemy, 8, Nauka, M., 1991, 52–94 ; “Fictitious domain method and computation of homogenized properties of composites with a periodic structure of essentially different components”, Numer. Methods and Applic., CRC, Boca Raton, 1994, 221–267 | MR | MR

[17] Bakhvalov N. S., “An iterative method for solving the diffusion equation with highly varying coefficients”, Rus. J. Numer. Analys. and Math. Modelling, 9:2 (1994), 91–97 | DOI | MR | Zbl

[18] Kobelkov G. M., “On the solution of the boundary value problem for the diffusion equation with highly varying coefficient”, Rus. J. Numer. Analys. and Math. Modelling, 11:6 (1996), 487–495 | DOI | MR | Zbl

[19] Bakhvalov N. S., Knyazev A. V., “Effektivnyi iteratsionnyi metod resheniya uravneniya Lame dlya pochti neszhimaemykh sred i uravneniya Stoksa”, Dokl. AN SSSR, 319:1 (1991), 13–17 | MR | Zbl

[20] Bakhvalov N. S., Bogachev K. Yu., Eglit M. E., “Vychislenie effektivnykh uprugikh modulei neszhimaemogo poristogo materiala”, Mekhan. kompozitsionnykh materialov, 32:5 (1996), 579–587

[21] Astrakhantsev G. P., “Metod fiktivnykh oblastei dlya ellipticheskogo uravneniya vtorogo poryadka s estestvennymi granichnymi usloviyami”, Zh. vychisl. matem. i matem. fiz., 18:1 (1978), 118–125 | MR | Zbl

[22] Matsokin A. M., “Metod fiktivnykh komponent i modifitsirovannyi raznostnyi analog metoda Shvartsa”, Vychisl. metody lineinoi algebry, VTs SO AN SSSR, Novosibirsk, 1980, 66–77 | MR

[23] Kaporin I. E., Nikolaev E. S., “Metod fiktivnykh neizvestnykh dlya resheniya raznostnykh ellipticheskikh kraevykh zadach v neregulyarnykh oblastyakh”, Differents. ur-niya, 16:7 (1980), 1211–1225 | MR | Zbl

[24] Abramov N. N., Kucherenko V. V., “Algoritm chislennogo resheniya zadachi Dirikhle”, Dokl. AN SSSR, 305:3 (1989), 521–525 | MR

[25] Bogachev K. Yu., “Iteratsionnyi metod resheniya smeshannoi zadachi dlya kvazilineinykh ellipticheskikh uravnenii v oblastyakh slozhnoi formy”, Dokl. RAN, 340:6 (1995), 727–730 | MR | Zbl

[26] Bogachev K. Yu., “Iterative method for solving quasilinear elliptic equations with widely varying coefficients singularly depending on to parameters”, Rus. J. Numer. Analys. and Math. Modelling, 10:1 (1995), 9–32 | DOI | MR | Zbl

[27] Agranovich M. C., Vishik M. I., “Ellipticheskie zadachi s parametrom i parabolicheskie zadachi obschego vida”, Uspekhi matem. nauk, 20:3 (1964), 53–161

[28] Besov O. V., “Prodolzhenie funktsii za predely oblasti s sokhraneniem differentsialno-raznostnykh svoistv v $L_p$”, Matem. sb., 66:1 (1965), 80–90 | MR

[29] Vishik M. M., “Metod ortogonalnykh i pryamykh razlozhenii v teorii ellipticheskikh differentsialnykh uravnenii”, Matem. sb., 25(67) (1949), 189–234 | Zbl

[30] Bakhvalov N. S., “Solution of the Stokes' nonstationary problem by the fictitious domain method”, Rus. J. Numer. Analys. and Math. Modelling, 10:1 (1995), 163–172 | DOI | MR | Zbl

[31] Dyakonov E. G., Minimizatsiya vychislitelnoi raboty, Nauka, M., 1989 | MR

[32] Bakhvalov N. S., Zhidkov N. P., Kobelkov G. M., Chislennye metody, Nauka, M., 1987 | MR | Zbl

[33] Ryabinin O. V., “Iteratsionnyi metod resheniya variatsionno-raznostnykh analogov ellipticheskikh zadach s bolshim razbrosom koeffitsientov”, Dokl. RAN, 339:4 (1994), 454–457 | MR | Zbl

[34] Bakhvalov N. S., Bogachev K. Yu., Metr Zh. F., “Effektivnyi algoritm resheniya zhestkikh ellipticheskikh zadach s prilozheniyami k metodu fiktivnykh oblastei”, Zh. vychisl. matem. i matem. fiz., 39:6 (1999), 919–931 | MR | Zbl

[35] Nepomnyaschikh S. V., Metod dekompozitsii oblastei dlya razryvnykh koeffitsientov, Tekhn. otchet No 891, VTs SO AN SSSR, Novosibirsk, 1990

[36] Nepomnayaschikh S. V., “Domain decomposition method for elliptuc problems with discontinuous coefficients”, Proc. 4-th Conf. Domain Decomposition Methods for Partial Differential Equations, SIAM, Philadelphia, PA, 1991, 242–251

[37] Kuznetsov Yu. A., “Multigrid domain decomposition method for elliptuc problems”, Proc. 8-th Internat. Conf. Comput. Meth. for Appl. Sci. and Engng., v. 2, 1987, 605–616

[38] Zang X., “Multilevel Schwarz methods”, Numer. Math., 63 (1992), 521–539 | DOI | MR

[39] D'yakonov E. G., Optimization in solving elliptic problems, CRC, Boca Raton, 1996 | MR

[40] Fedorenko P. P., “O skorosti skhodimosti odnogo iteratsionnogo metoda”, Zh. vychisl. matem. i matem. fiz., 4:3 (1964), 559–564 | MR | Zbl

[41] Bakhvalov N. S., “O skhodimosti odnogo relaksatsionnogo metoda pri estestvennykh ogranicheniyakh na ellipticheskii operator”, Zh. vychisl. matem. i matem. fiz., 6:5 (1966), 861–883 | Zbl

[42] Agoshkov V. I., Lebedev V. I., Operatory Puankare–Steklova i ikh prilozheniya v analize, AN SSSR, OVM, M., 1983 | MR | Zbl

[43] Bakhvalov N. S., Knyazev A. V., Kobelkov G. M., “Iterative methodsTor solving equations with highly varying coefficients”, Domain Decomposition Methods Partial Differential Equations, SIAM, Philadelphia, 1991, 197–205 | MR

[44] Bakhvalov N. S., Orekhov M. Yu., “O bystrykh sposobakh resheniya uravneniya Puassona”, Zh. vychisl. matem. i matem. fiz., 22:6 (1982), 1386–1392 | MR | Zbl