Parallel algorithm for spatially one-and two-dimensional initial-boundary-value problem for a parabolic equation
Kybernetika, Tome 37 (2001) no. 2, pp. 171-181 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

A generalization of the spatially one-dimensional parallel pipe-line algorithm for solution of the initial-boundary-value problem using explicit difference method to the two-dimensional case is presented. The suggested algorithm has been verified by implementation on a workstation-cluster running under PVM (Parallel Virtual Machine). Theoretical estimates of the speed-up are presented.
A generalization of the spatially one-dimensional parallel pipe-line algorithm for solution of the initial-boundary-value problem using explicit difference method to the two-dimensional case is presented. The suggested algorithm has been verified by implementation on a workstation-cluster running under PVM (Parallel Virtual Machine). Theoretical estimates of the speed-up are presented.
Classification : 65M06, 65Y05, 68W10
Keywords: initial-boundary-value problem; parallel virtual machine (PVM)
@article{KYB_2001_37_2_a5,
     author = {Purcz, Pavol},
     title = {Parallel algorithm for spatially one-and two-dimensional initial-boundary-value problem for a parabolic equation},
     journal = {Kybernetika},
     pages = {171--181},
     year = {2001},
     volume = {37},
     number = {2},
     mrnumber = {1839227},
     zbl = {1265.68355},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2001_37_2_a5/}
}
TY  - JOUR
AU  - Purcz, Pavol
TI  - Parallel algorithm for spatially one-and two-dimensional initial-boundary-value problem for a parabolic equation
JO  - Kybernetika
PY  - 2001
SP  - 171
EP  - 181
VL  - 37
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/KYB_2001_37_2_a5/
LA  - en
ID  - KYB_2001_37_2_a5
ER  - 
%0 Journal Article
%A Purcz, Pavol
%T Parallel algorithm for spatially one-and two-dimensional initial-boundary-value problem for a parabolic equation
%J Kybernetika
%D 2001
%P 171-181
%V 37
%N 2
%U http://geodesic.mathdoc.fr/item/KYB_2001_37_2_a5/
%G en
%F KYB_2001_37_2_a5
Purcz, Pavol. Parallel algorithm for spatially one-and two-dimensional initial-boundary-value problem for a parabolic equation. Kybernetika, Tome 37 (2001) no. 2, pp. 171-181. http://geodesic.mathdoc.fr/item/KYB_2001_37_2_a5/

[1] Burrage K.: Parallel methods for initial value problems. Appl. Numer. Math. 11 (1993), 5–25 | DOI | MR | Zbl

[2] Crank J., Nicolson P.: A practical method for numerical evaluation of solutions of PDEs of the heat-conduction type. Proc. Camb. Phil. Soc. 43 (1947), 60–67 | DOI | MR

[3] Freeman T. L., Phillips C.: Parallel Numerical Algorithms. Prentice Hall, Englewood Cliffs, N.J. 1992 | MR | Zbl

[4] Kogge P. M.: Parallel solution of recurrence problems. IBM J. Res. Develop. 2 (1974), 18, 138–148 | DOI | MR | Zbl

[5] Ortega J. M., Voigt R. G.: Solution of PDE on Vector and Parallel Computers. SIAM, Philadelphia, 1985 | MR

[6] Pavluš M.: Schwarz algorithm for solution of a quasiparabolic equation. Vestnik Moskov. Univ. 4 (1992), 15, 27–35 | MR

[7] Peaceman D. W., Rachford H. H.: The numerical solution of parabolic and elliptic differential equations. J. Soc. Indust. Appl. Math. 3 (1955), 28–41 | DOI | MR | Zbl

[8] Smith G. D.: Numerical Solution of PDE. Finite Difference Methods. Second edition. Clarendon Press, Oxford 1978 | MR

[9] Tyrtyshnikov E. E.: Parallelization of some numerical methods. In: Numerical Solution of Partial Differential Equation, Košice 1992

[10] Vajteršic M.: Algorithms for Elliptic Problems. Efficient Sequential and Parallel Solvers. VEDA, Bratislava 1988 | MR | Zbl