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Convergent iterative schemes for time parallelization
Author(s):
Izaskun
Garrido;
Barry
Lee;
Gunnar
E.
Fladmark;
Magne
S.
Espedal.
Journal:
Math. Comp.
75
(2006),
1403-1428.
MSC (2000):
Primary 65N55, 65Y05;
Secondary 65M55, 65M60
Posted:
February 24, 2006
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Abstract:
Parallel methods are usually not applied to the time domain because of the inherit sequentialness of time evolution. But for many evolutionary problems, computer simulation can benefit substantially from time parallelization methods. In this paper, we present several such algorithms that actually exploit the sequential nature of time evolution through a predictor-corrector procedure. This sequentialness ensures convergence of a parallel predictor-corrector scheme within a fixed number of iterations. The performance of these novel algorithms, which are derived from the classical alternating Schwarz method, are illustrated through several numerical examples using the reservoir simulator Athena.
References:
-
- 1.
- L.Baffico, S.Bernard, Y.Maday, G.Turinici, G.Zérah, Parallel in time molecular dynamics simulations, 2002.
- 2.
- G.Bal, Y.Maday, A parareal time discretization for non-linear PDE's with application to the pricing of an American put, Lect. Notes Comput. Sci. Eng., vol. 23, Springer, Berlin, 2002. MR1962689
- 3.
- S.Bellavia, B.Morini, A globally convergent Newton-GMRES subspace method for systems of nonlinear equations, SIAM J. Sci. Comput., 23, No. 3, SIAM, 2001, pp. 940-960. MR 1860971 (2002h:65077)
- 4.
- P. N. Brown, Y. Saad, Hybrid Krylov Methods for nonlinear systems of equations, SIAM J. Sci. Stat. Comput., 11, No. 3, SIAM, 1990, pp. 450-481. MR 1047206 (91e:65069)
- 5.
- G. E. Fladmark, Secondary Oil Migration. Mathematical and numerical modelling in SOM simulator, In Norsk Hydro (eds.), Research centre Bergen, R-077857, 1997.
- 6.
- M.J. Gander, H. Zhao, Overlapping Schwarz Waveform Relaxation for the Heat Equation in n-Dimensions, BIT, 42, 2002, pp. 779-795. MR 1944537 (2003m:65170)
- 7.
- I. Garrido, E. Øian, M. Chaib, G. Fladmark, M. Espedal, Implicit treatment of compositional flow, Comput. Geosci., 8, No. 3, Kluwer, 2004, pp. 1-19. MR 2057524
- 8.
- J. L.Lions, Y.Maday, GabrielTurinici, Rèsolution d'EDP par un schéma en temps pararéel, C. R. Acad. Sci. Paris, 332, No. 1, pp. 1-6, 2001. MR 1842465 (2002c:65140)
- 9.
- G. Å. Øye, H. Reme, Parallelization of a Compositional Simulator with a Galerkin Coarse/Fine Method, P. Amestoy and others (eds.), 1685, pp. 586-594. Euro-Par'99, Springer-Verlag, Berlin, 1999.
- 10.
- G. Qin, H. Wang, R. E. Ewing and M. S. Espedal, Numerical simulation of compositional fluid flow in porous media, Z.-C. Shi Z. Chen, R. E. Ewing (eds.), Numerical treatement of multiphase flows in porous media, 552, pp. 232-243. Springer-Verlag, Berlin, 2000.MR 1876022
- 11.
- H. Reme, G.Å. Øye, Use of local grid refinement and a Galerkin technique to study secondary migration in fractured and faulted regions, Computing and Visualisation in Science, 2, pp. 153-162, Springer-Verlag, Berlin, 1999.
- 12.
- S. Schaffer, A semicoarsening multigrid method for elliptic partial differential equations with highly discontinuous and anisotropic coefficients SIAM J. Sci. Comput, 20, No. 1, pp. 228-242, 1998. MR 1639126 (99d:65355)
- 13.
- U. Trottenberg, C.W.Oosterlee and A.Schuller, Multigrid, Academic Press, 2001. MR 1807961 (2002b:65002)
- 14.
- S. Vandewalle, and G.Horton, A space-time multigrid method for parabolic partial differential equations, SIAM J. Sci. Comput, 16, No. 4, pp. 848-864, 1995.MR 1335894 (96d:65158)
- 15.
- P.Wesseling, An Introduction to Multigrid Methods, John Wiley, 1992.MR 1156079 (93g:65006)
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Additional Information:
Izaskun
Garrido
Affiliation:
Department of Mathematics, University of Bergen, Johs. Brunsgt. 12, N-5008 Bergen, Norway
Email:
izaskun@mi.uib.no
Barry
Lee
Affiliation:
CASC, Lawrence Livermore National Laboratory, Livermore, California 94551
Gunnar
E.
Fladmark
Affiliation:
Department of Mathematics, University of Bergen, Johs. Brunsgt. 12, N-5008 Bergen, Norway
Magne
S.
Espedal
Affiliation:
Department of Mathematics, University of Bergen, Johs. Brunsgt. 12, N-5008 Bergen, Norway
DOI:
10.1090/S0025-5718-06-01832-1
PII:
S 0025-5718(06)01832-1
Keywords:
Alternating Schwarz,
time parallelization,
reservoir simulator,
multilevel,
full approximation storage
Received by editor(s):
May 29, 2003
Received by editor(s) in revised form:
April 20, 2005
Posted:
February 24, 2006
Copyright of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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