On some Aitken-like acceleration of the Schwarz method

International Journal for Numerical Methods in Fluids

Volumn 40, Issue 12, 2002, Pages 1493-1513

  Garbey, M ^a,b   Tromeur Dervout, D ^b  

^a UNIVERSITÉ LYON 1   (France)

^b UNIVERSITY OF HOUSTON   (United States)

Author keywords

Distributed computing; Domain decomposition; Elliptic solver; Metacomputing

Indexed keywords

ALGORITHMS; BANDWIDTH; COMPUTER ARCHITECTURE; CONVERGENCE OF NUMERICAL METHODS; DIFFERENTIAL EQUATIONS; FINITE DIFFERENCE METHOD; LINEAR EQUATIONS; MATHEMATICAL OPERATORS; MICROPROCESSOR CHIPS; NONLINEAR EQUATIONS; PARALLEL PROCESSING SYSTEMS; POISSON EQUATION; PROBLEM SOLVING;

DOMAIN DECOMPOSITION;

ITERATIVE METHODS;

DISTRIBUTED NETWORK; MATHEMATICAL METHOD;

EID: 0037203271     PISSN: 02712091     EISSN: None     Source Type: Journal    
DOI: 10.1002/fld.407     Document Type: Article

References (20)

1. Garbey M, Vassilevsky Y. A parallel solver for unsteady incompressible 3D Navier-Stokes equation. Parallel Computing 2001; 27(4):363-389.
2. Schwarz HA. Gesammelte Mathematische Abhandlungen, vol. 2. Springer: Berlin, 1890; 133-143. (First published in Vierteljahrsschrift der Naturforschenden Gesellschaft in Zürich, vol. 15, 1870; 272-286.)
3. Lions P.-L. On the Schwarz alternating method. I. In First International Symposium on Domain Decomposition Methods for Partial Differential Equations, Glowinski R, Golub GH, Meurant GA, Périaux J (eds). SIAM: Philadelphia, PA, 1988; 1-42.
4. Kuznetsov YA. Overlapping domain decomposition methods for fe-problems with elliptic singular perturbed operators. In Fourth International Symposium on Domain Decomposition Methods for Partial Differential Equations, Glowinski R, Kuznetsov Y A, Meurant GA, Périaux J, Widlund O (eds). SIAM: Philadelphia, PA, 1991.
5. Garbey M. A schwarz alternating procedure for singular perturbation problems. SIAM Journal on Scientific Computing 1996; 17(5):1175-1201.
6. Garbey M, Tromeur-Dervout D. Aitken-Schwarz method on Cartesian grids. In Proceedings of the International Conference on Domain Decomposition Methods DD13, Debit N, Garbey M, Hoppe R, Périaux J, Keyes D, Kuznetsov Y (eds). CIMNE: Barcelona, 2002; 53-65 (Invited Lecture).
7. Loan CFV. Computational Frameworks for the Fast Fourier Transform, Frontiers in Applied Mathematics. SIAM: Philadelphia, PA, 1992.
8. Golub GH, Loan CFV. Matrix Computations (2nd edn). Johns Hopkins University Press: Baltimore, MD, 1989.
9. Garbey M, Tromeur-Dervout D. Two level domain decomposition for multi-cluster. In Proceedings of the International Conference on Domain Decomposition Methods DD12, Chan HKT, Kako T, Pironneau O (eds). CIMNE: Barcelona, 2001;325-340. (Invited lecture), http://applmath.tg.chiba-u.ac.jp/dd12/proceedings/Garbey.ps.gz.
10. Baranger J, Garbey M, Oudin-Dardun F. Recent development on Aitken-Schwarz method. In Proceedings of the International Conference on Domain Decomposition Methods DD13, Debit N, Garbey M, Hoppe R, Périaux J, Keyes D, Kuznetsov Y (eds). CIMNE: Barcelona, 2001; 287-294.
11. Garbey M, Tromeur-Dervout D. Operator splitting and domain decomposition for multicluster. In Proceedings of the International Conference on Parallel CFD99, Keyes D, Ecer A, Satofuka N, Fox P, Periaux J (eds). North-Holland: Williamsburg, 1999; 27-36. (Invited Lecture).
12. Henrici P. Elements of Numerical Analysis. Wiley: New York-London-Sydney, 1964.
13. Wieners C. A parallel newton multigrid method for high order finite elements and its application to numerical existence proofs for elliptic boundary value problem. Combustion Theory and Modelling 1996; 76(3):175-180.
14. Selberherr S. Analysis and Simulation of Semiconductor Devices. Springer: Wien, New York, 1984.
15. Baranger J. Personal communication. 2000.
16. Rossi T, Toivanen J. A nonstandard cyclic reduction method, its variants and stability. SIAM Journal on Matrix Analysis and Applications 1999; 20(3):628-645.
17. Rossi T, Toivanen J. A parallel fast direct solver for block tridiagonal systems with separable matrices of arbitrary dimension. SIAM Journal on Scientific Computing 1999; 20(5):1778-1796.
18. Vassilevski PS. Fast algorithm for solving a linear algebraic problem with separable variables. Comptes Rendus Academie Bulgare Sciences 1984; 37:305-308.
19. Kuznetsov YA, Matsokin M. On partial solution of systems of linear algebraic equations. Soviet Journal of Numerical Analysis and Mathematical Modelling 1989; 4(6):453-468.
20. Barberou N, Garbey M, Hess M, Resch M, Rossi T, Toivanen J, Tromeur-Dervout D. Scalable numerical algorithms and software tools for efficient metacomputing of elliptic equations. In Proceedings of the International Conference on Parallel CFD2001, Wilders P, Ecer A, Satofuka N, Fox P, Periaux J (eds). Elsevier/North-Holland: Amsterdam, 2002.