Numerical experiments with multilevel Subdomain decomposition method
Lobachevskii journal of mathematics, Tome 13 (2003), pp. 67-80.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper we present a new numerical approach to solve the continuous casting problem. The main tool is to use so-called IPEC method and DDM similar to [6] with multilevel domain decomposition. On the subdomains we use the multidecomposition of the subdomains. The IPEC is used both in the whole calculation domain and inside the subdomains. Calculation algorithm is presented and numerically tested. Several conclusions are made and discussed.
Keywords: Stefan problem, continuous casting process, finite element method, predictor-corrector scheme
Mots-clés : domain decomposition.
@article{LJM_2003_13_a7,
     author = {E. Laitinen and A. V. Lapin and J. Piesk\"a},
     title = {Numerical experiments with multilevel {Subdomain} decomposition method},
     journal = {Lobachevskii journal of mathematics},
     pages = {67--80},
     publisher = {mathdoc},
     volume = {13},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/LJM_2003_13_a7/}
}
TY  - JOUR
AU  - E. Laitinen
AU  - A. V. Lapin
AU  - J. Pieskä
TI  - Numerical experiments with multilevel Subdomain decomposition method
JO  - Lobachevskii journal of mathematics
PY  - 2003
SP  - 67
EP  - 80
VL  - 13
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/LJM_2003_13_a7/
LA  - en
ID  - LJM_2003_13_a7
ER  - 
%0 Journal Article
%A E. Laitinen
%A A. V. Lapin
%A J. Pieskä
%T Numerical experiments with multilevel Subdomain decomposition method
%J Lobachevskii journal of mathematics
%D 2003
%P 67-80
%V 13
%I mathdoc
%U http://geodesic.mathdoc.fr/item/LJM_2003_13_a7/
%G en
%F LJM_2003_13_a7
E. Laitinen; A. V. Lapin; J. Pieskä. Numerical experiments with multilevel Subdomain decomposition method. Lobachevskii journal of mathematics, Tome 13 (2003), pp. 67-80. http://geodesic.mathdoc.fr/item/LJM_2003_13_a7/

[1] Z. Chen, “Numerical solutions of a two-phase continuous casting problem”, Numerical Methods for Free Boundary Problem, International Series of Numerical Mathematics, 99, ed. P. Neittaanmäki, Birkhäuser, Basel, 1991, 103–121 | MR

[2] C. N. Dawson, Q. Du and T. F. Dupont, “A finite difference domain decomposition algorithm for numerical solution of the heat equation”, Mathematics of Computation, 57 (1991), 63–71 | DOI | MR | Zbl

[3] J. Jr. Douglas and T. F. Russel, “Numerical methods for convection-dominated diffusion problem based on combining the method of characteristic with finite element or finite difference procedures”, SIAM J. Numer. Anal., 19 (1982), 871–885 | DOI | MR | Zbl

[4] E. Laitinen and A. V. Lapin, Semi-Implicit Mesh Scheme and Splitting Iterative Methods for the Solution of Continuous Casting Problem, Preprint, University of Oulu, Finland, 1999, 19 pp.

[5] E. Laitinen, A. V. Lapin and J. Pieskä, “Splitting iterative methods and parallel solution of variational inequalities”, Lobachevskii Journal of Mathematics, 8 (2001), 167–184 | MR | Zbl

[6] A. V. Lapin and J. Pieskä, “On the parallel domain decomposition algorithms for time-dependent problems”, Lobachevskii Journal of Mathematics, 10 (2002), 27–44 | MR | Zbl

[7] A. V. Lapin and D. O. Solovyev, Splitting iterative methods for variational inequalities, Preprint No 783, Center of Calcul., Novosibirsk, 1988, 24 pp.

[8] J. M. Ortega and W. C. Rheinboldt, Iterative solution of nonlinear equations in several variables, Academic Press Inc., Orlando, Florida, 1970 | MR | Zbl

[9] W. Rivera, J. Zhu and D. Huddleston, “An efficient parallel algorithm with application to computational fluid dynamics”, Computers and Mathematics with Applications, 45:1–3 (2003), 165–188 | DOI | MR | Zbl

[10] W. Rivera and J. Zhu, “A scalable parallel domain decomposition algorithm for solving time dependent partial differential equations”, Proceedings of the International Conference on Parallel and Distributed Processing Technology and Applications, ed. H. R. Arabnia, CSREA Press, Athens GA, 1999, 240–246

[11] W. Rivera, J. Zhu and D. Huddleston, “An efficient parallel algorithm for solving unsteady nonlinear equations”, Proceedings of the International Conference on Parallel Processing Workshops, ed. T. M. Pinkston, IEEE Computer Society, Los Alamitos, California, 2001, 79–84

[12] J. F. Rodrigues and F. Yi, “On a two-phase continuous casting Stefan problem with nonlinear flux”, Euro J. App. Math., 1 (1990), 259–278 | MR | Zbl

[13] A. Quarteroni and A. Valli, Domain decomposition methods for partial differential equations, Clarendon Press, Oxford, New York, 1999 | MR | Zbl

[14] A. Samarskii, P. Vabischevich, Finite difference schemes with operator multipliers, Institute of Mathematics of Belorussia, Minsk, 1998, 442 pp.

[15] A. Samarskii, P. Vabischevich, “Factorized regional-additive schemes for convection-diffusion problems”, Reports of Rusian Acad. Sciences (Mathematics), 346 (1996), 742–745 (in Russian) | MR

[16] P. Vabischevich, “Parallel domain decomposition algorithms for time-dependent problems of mathematical physics”, Advances in Numerical Methods and applications, World scientific, Singapore, 1994, 293–299