Voir la notice de l'article provenant de la source Math-Net.Ru
@article{SJVM_1999_2_4_a5, author = {Yu. M. Laevsky and A. M. Matsokin}, title = {Decomposition methods for the solution to elliptic and parabolic boundary value problems}, journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki}, pages = {361--372}, publisher = {mathdoc}, volume = {2}, number = {4}, year = {1999}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/SJVM_1999_2_4_a5/} }
TY - JOUR AU - Yu. M. Laevsky AU - A. M. Matsokin TI - Decomposition methods for the solution to elliptic and parabolic boundary value problems JO - Sibirskij žurnal vyčislitelʹnoj matematiki PY - 1999 SP - 361 EP - 372 VL - 2 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/SJVM_1999_2_4_a5/ LA - ru ID - SJVM_1999_2_4_a5 ER -
%0 Journal Article %A Yu. M. Laevsky %A A. M. Matsokin %T Decomposition methods for the solution to elliptic and parabolic boundary value problems %J Sibirskij žurnal vyčislitelʹnoj matematiki %D 1999 %P 361-372 %V 2 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/item/SJVM_1999_2_4_a5/ %G ru %F SJVM_1999_2_4_a5
Yu. M. Laevsky; A. M. Matsokin. Decomposition methods for the solution to elliptic and parabolic boundary value problems. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 2 (1999) no. 4, pp. 361-372. http://geodesic.mathdoc.fr/item/SJVM_1999_2_4_a5/
[1] Schwarz H. A., “Uber einige Abbildungsaufgaben”, Ges. Math. Abh., 2, Springer, Berlin, 1890, 133–143
[2] Sobolev S. L., “Algoritm Shvartsa v teorii uprugosti”, Dokl. AN SSSR, 4:6 (1936), 235–238
[3] Aleksidze M. A., “O tselesoobraznosti primeneniya alterniruyuschego metoda Shvartsa na elektronnykh tsifrovykh mashinakh”, Dokl. AN SSSR, 120:2 (1958), 231–234 | MR | Zbl
[4] Miller K., “Numerical analogs to the Schwarz alternating procedure”, Numer. Math., 7 (1965), 91–103 | DOI | MR | Zbl
[5] Dyakonov E. G., Raznostnye metody resheniya kraevykh zadach. Vyp. I (statsionarnye zadachi), Izd-vo MGU, M., 1971
[6] Romanova S. E., Priblizhennye metody resheniya raznostnykh uravnenii Laplasa i Puassona na mnogougolnikakh asimptoticheski za dva slozheniya na tochku, Dis. $\dots$ kand. fiz.-mat. nauk: 01.01.07, M., 1983
[7] Matsokin A. M., “Metod fiktivnykh komponent i modifitsirovannyi raznostnyi analog metoda Shvartsa”, Vychislitelnye metody lineinoi algebry, AN SSSR. Sib. otd-nie. VTs, Novosibirsk, 1980, 66–77 ; Sov. J. of Numer. Anal. and Math. Modell., 4:6 (1989), 471–477 | MR | DOI | MR
[8] Sander S. A., Modifikatsiya algoritma Shvartsa dlya resheniya setochnykh kraevykh zadach v oblastyakh, sostavlennykh iz pryamougolnikov i parallelepipedov, Preprint / AN SSSR. Sib. otd-nie. VTs; 83, Novosibirsk, 1981 | MR
[9] Matsokin A. M., Nepomnyaschikh S. V., “Primenenie okaimleniya pri reshenii sistem setochnykh uravnenii”, Vychislitelnye algoritmy v zadachakh matematicheskoi fiziki, AN SSSR. Sib. otd-nie. VTs, Novosibirsk, 1983, 99–109; Sov. J. of Numer. Anal. and Math. Modell., 4:6 (1989), 487–492 | DOI | MR
[10] Matsokin A. M., Nepomnyaschikh S. V., “Metod alternirovaniya Shvartsa v podprostranstve”, Izv. Vyssh. uchebnykh zavedenii. Matematika, 1985, no. 10, 61–66 | MR | Zbl
[11] Matsokin A.M., “Kriterii skhodimosti metoda Shvartsa v gilbertovom prostranstve”, Vychislitelnye protsessy i sistemy, 6, Nauka, M., 1988, 221–224 | MR
[12] Matsokin A. M., Reshenie setochnykh uravnenii na neregulyarnykh setkakh, Preprint / AN SSSR. Sib. otd-nie. VTs; 738, Novosibirsk, 1987 | MR | Zbl
[13] Nepomnyaschikh S. V., O primenenii metoda okaimleniya k smeshannoi kraevoi zadache dlya ellipticheskikh uravnenii i osetochnykh normakh v $W_2^{1/2}(S)$, Preprint / AN SSSR. Sib. otd-nie. VTs; 106, Novosibirsk, 1984 ; Sov. J. of Numer. Anal. and Math. Modell., 4:6 (1989), 493–506 | Zbl | DOI | MR
[14] Katsnelson V. E., Menshikov V. V., “Ob odnom algoritme alterniruyuschego metoda Shvartsa”, Teoriya funktsii, funktsionalnyi analiz i ikh prilozheniya, 17, Kharkov, 1973
[15] Mateeva E. I., Paltsev B. V., “O razdelenii oblasti pri reshenii kraevykh zadach dlya uravneniya Puassona v oblastyakh slozhnoi formy”, Zhurn. vychisl. matem. i mat. fiz., 13:6 (1973), 1441–1458 | MR | Zbl
[16] Smelov V. V., “Printsip iterirovaniya po podoblastyam v zadachakh s uravneniem perenosa”, Metody resheniya variatsionno-raznostnykh uravnenii, AN SSSR. Sib. otd-nie. VTs, Novosibirsk, 1979, 139–158 ; Sov. J. of Numer. Anal. and Math. Modell., 4:6 (1989), 523–533 | MR | DOI | MR
[17] Lebedev V. I., Agoshkov V. I., Obobschennyi algoritm Shvartsa s peremennymi parametrami, Preprint / AN SSSR. OVM; 19, M., 1981 | MR
[18] Tsvik L. B., “Obobschenie algoritma Shvartsa na sluchai oblastei sopryazhennykh bez naleganiya”, Dokl. AN SSSR, 224:2 (1975), 309–312 | MR | Zbl
[19] Lebedev V. I., Agoshkov V. I., Variatsionnye algoritmy metoda razdeleniya oblasti, Preprint / AN SSSR. OVM; 54, M., 1983
[20] Dryja M., Substructuring methods for parabolic problems, Technical Report / N.-Y. University. Computer Sci. Depart.; 529, N.-Y., 1990 | MR
[21] Cai X.-C., “Additive Schwartz algorithms for parabolic convection-diffusion equations”, Numer. Math., 60 (1991), 41–61 | DOI | MR
[22] Kuznetsov Yu.A., Novye algoritmy priblizhennoi realizatsii neyavnykh raznostnykh skhem, Preprint / AN SSSR. OVM; 142, M., 1987 ; Sov. J. of Numer. Anal. and Math. Modell., 3:2 (1988), 99–114 | MR | DOI | Zbl
[23] Laevskii Yu. M., “Metody razbieniya oblasti pri reshenii dvumernykh parabolicheskikh uravnenii”, Variatsionno-raznostnye metody v zadachakh chislennogo analiza, AN SSSR. Sib. otd-nie VTs, Novosibirsk, 1987, 112–128 | MR
[24] Vabischevich P. N., “Raznostnye skhemy dekompozitsii raschetnoi oblasti pri reshenii nestatsionarnykh zadach”, Zhurn. vychisl. matem. i mat. fiz., 29:12 (1989), 1822–1829
[25] Laevskii Yu. M., Pryamoi metod dekompozitsii oblasti resheniya parabolicheskikh uravnenii, Preprint / AN SSSR. Sib. otd-nie VTs; 946, Novosibirsk, 1992 ; “On the domain decomposition method for parabolic problems”, Bull. NCC, Numer. Anal., 2 (1993), 41–62 | MR
[26] Laevsky Yu. M., “On the explicit-implicit domain decomposition method for parabolic problems”, Bull. NCC, Numer. Anal., 2 (1993), 79–90
[27] Rannacher R., The Summer Conference on DD in Lambrecht, 1991
[28] Dawson C. N., Du O., “A domain decomposition method for parabolic equations based on finite elements”, 4-th Intern. Conf. on DDM for PDE, SIAM, Philadelphia, 1991, 255–263 | MR
[29] Mathew T., Russo G., Wang J., Abstr. for 7-th Intern. Conf. on DDM in Sci. and Eng. (Perm. State Univ., 1993)
[30] Vabischevich P. N., “Regionalno-additivnye raznostnye skhemy stabiliziruyuschei popravki dlya parabolicheskikh zadach”, Zhurn. vychisl. matem. i mat. fiz., 34:12 (1994), 1832–1842 | MR
[31] Samarskii A. A., Vabischevich P. N., “Vektornye additivnye skhemy dekompozitsii oblasti dlya parabolicheskikh zadach”, Diff. uravn., 31:9 (1995), 1563–1569 | MR
[32] Laevskii Yu. M., “O dekompozitsii oblasti dlya parabolicheskikh zadach s razryvnymi resheniyami i metode shtrafa”, Zhurn. vychisl. matem. i mat. fiz., 34:5 (1994), 702–719 | MR
[33] Laevskii Yu. M., Gololobov S. V., “Yavno-neyavnye metody dekompozitsii oblasti resheniya parabolicheskikh uravnenii”, Sib. matem. zhurn., 36:3 (1995), 590–601 | MR
[34] Gololobov S. V., Laevsky Yu. M., “On one domain decomposition method with nonmatching grids for solving parabolic equations”, Bull. NCC, Numer. Anal., 7 (1996), 35–49
[35] Laevsky Yu. M., “Preconditioning operators for grid parabolic problems”, Rus. J. of Numer. Anal. and Math. Modell., 11:6 (1996), 497–515 | DOI | MR | Zbl
[36] Laevsky Yu. M., “On domain decomposition method for grid parabolic problems”, Rus. J. of Numer. Anal. and Math. Modell., 13:5 (1998), 389–403 | DOI | MR | Zbl
[37] Laevskii Yu. M., Ob odnom klasse trekhsloinykh raznostnykh skhem i metode fiktivnykh oblastei, Preprint / RAN. Sib. otd-nie. IVMiMG; 1117, Novosibirsk, 1998; Сиб. матем. журн., 40:5 (1999) (в печати) | MR