Geodesic
Improving the efficiency of variational methods for solving strongly nonsymmetric linear algebraic equation system received in convection-diffusion problems
Matematičeskoe modelirovanie, Tome 22 (2010) no. 10, pp. 56-68.

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

An effective algorithm for implementing the mathematical model of convective-diffusive transport with a dominant convection is proposed. Preconditioned Krylov subspace methods are used for the solution of a strongly nonsymmetric systems. A convergence analysis of product triangular preconditioners was made. Numerical experiments have confirmed the effectiveness of this technique.
Mots-clés : convection-diffusion equation, convergence.
Keywords: variational methods, triangular and product triangular preconditioners 
@article{MM_2010_22_10_a3,
     author = {L. A. Krukier and O. A. Pichugina and T. S. Martynova},
     title = {Improving the efficiency of variational methods for solving strongly nonsymmetric linear algebraic equation system received in convection-diffusion problems},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {56--68},
     publisher = {mathdoc},
     volume = {22},
     number = {10},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2010_22_10_a3/}
}
TY  - JOUR
AU  - L. A. Krukier
AU  - O. A. Pichugina
AU  - T. S. Martynova
TI  - Improving the efficiency of variational methods for solving strongly nonsymmetric linear algebraic equation system received in convection-diffusion problems
JO  - Matematičeskoe modelirovanie
PY  - 2010
SP  - 56
EP  - 68
VL  - 22
IS  - 10
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MM_2010_22_10_a3/
LA  - ru
ID  - MM_2010_22_10_a3
ER  - 
%0 Journal Article
%A L. A. Krukier
%A O. A. Pichugina
%A T. S. Martynova
%T Improving the efficiency of variational methods for solving strongly nonsymmetric linear algebraic equation system received in convection-diffusion problems
%J Matematičeskoe modelirovanie
%D 2010
%P 56-68
%V 22
%N 10
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MM_2010_22_10_a3/
%G ru
%F MM_2010_22_10_a3
L. A. Krukier; O. A. Pichugina; T. S. Martynova. Improving the efficiency of variational methods for solving strongly nonsymmetric linear algebraic equation system received in convection-diffusion problems. Matematičeskoe modelirovanie, Tome 22 (2010) no. 10, pp. 56-68. http://geodesic.mathdoc.fr/item/MM_2010_22_10_a3/

[1] Marchuk G. I., Metody vychislitelnoi matematiki, Nauka, M., 1989, 456 pp. | MR | Zbl

[2] Krukier L. A., “Neyavnye raznostnye skhemy i iteratsionnyi metod ikh resheniya dlya odnogo klassa sistem kvazilineinykh uravnenii”, Izv. VUZov. Mat., 1979, no. 7, 41–52 | MR | Zbl

[3] Samarskii A. A., Vabischevich P. N., Chislennye metody resheniya zadach konvektsii-diffuzii, Editorial URSS, M., 1999, 248 pp.

[4] Voevodin V. V., Kuznetsov Yu. A., Matritsy i vychisleniya, Nauka, M., 1984, 320 pp. | MR | Zbl

[5] Taussky O., “Positive-definite matrices and their role in the study of the characteristic roots of general matrices”, Adv. Math., 2 (1968), 175–186 | DOI | MR | Zbl

[6] Krukier L. A., “Reshenie silno nesimmetrichnykh sistem lineinykh algebraicheskikh uravnenii iteratsionnym metodom, osnovannym na kososimmetrichnoi chasti iskhodnoi polozhitelnoi matritsy”, Matematicheskoe modelirovanie, 13:3 (2002), 49–56 | MR | Zbl

[7] Saad Y., Schultz M. H., “GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems”, SIAM J. Scientific and Statistical Computing, 1986, 856–869 | MR | Zbl

[8] Tong C. H., Ye Q., Analysis of the finite precision biconjugate gradient algorithm for nonsymmetric linear systems, Report SCCM 95-11, Computer Science Dept., Stanford University, 1995

[9] Wang L., Bai Z.-Z., “Skew-Hermitian triangular splitting iteration methods for non-Hermitian positive definite linear systems of strong skew-Hermitian parts”, BIT Numer. Math., 44 (2004), 363–386 | DOI | MR | Zbl

[10] Saad Y., Iterative methods for Sparse Linear Systems, PWS Publishing Company, 1995, 447 pp.