Fast Parallel Direct Solvers for Coarse Grid Problems

Journal of Parallel and Distributed Computing

Volumn 61, Issue 2, 2001, Pages 151-177

  Tufo, H M ^a   Fischer, P F ^b  

^a THE UNIVERSITY OF CHICAGO   (United States)

^b ARGONNE NATIONAL LABORATORY   (United States)

Author keywords

Direct solver; sparse factorization; nested dissection; parallel computing; coarse grid problems

Indexed keywords

EID: 0006606983     PISSN: 07437315     EISSN: None     Source Type: Journal    
DOI: 10.1006/jpdc.2000.1676     Document Type: Article

References (22)

1. Alvarado F., Pothen A., Schreiber R. Univ. Waterloo Research Report. 1992.
2. Benzi M., Marin J., Tuma M. A two-level parallel preconditioner based on sparse approximate inverses. Kincaid D. R. Iterative Methods in Scientific Computation IV. IMACS. 1999;167-177.
3. Benzi M., Meyer C. D., Tuma M. A sparse approximate inverse preconditioner for the conjugate gradient method. SIAM J. Sci. Comput. 17:1995;1135-1149.
4. Cai X.-C. The use of pointwise interpolation in domain decomposition with non-nested meshes. SIAM J. Sci. Comput. 14:1995;250-256.
5. Chan T., Shao J. P. Parallel complexity of domain decomposition methods and optimal coarse grid size. Parallel Computing. 21:1995;1033-1049.
6. Dryja M., Widlund O. Towards a unified theory of domain decomposition algorithms for elliptic problems. Glowinski R., Periaux J., Widlund O. Proceedings of the Third International Symposium on Domain Decomposition Methods for Partial Differential Equations. 1990;3-18 SIAM, Philadelphia.
7. Farhat C., Chen P. S. Tailoring domain decomposition methods for efficient parallel coarse grid solution and for systems with many right hand sides. Contemp. Math. 180:1994;401-406.
8. Fischer P. F., Miller N. I., Tufo H. M. An overlapping Schwarz method for spectral element simulation of three-dimensional incompressible flows. Bjørstad P., Luskin M. Parallel Solution of Partial Differential Equations. 2000;159-181 Springer-Verlag, Berlin/New York.
9. Fischer P. F. Parallel multi-level solvers for spectral element methods. Scott R. Proceedings of Intl. Conf. on Spectral and High-Order Methods '95, Houston, TX. 1996;595-604 Houston J. Math.
10. Fischer P. F. Parallel domain decomposition for incompressible fluid dynamics. Contemp. Math. 157:1994;313-322.
11. Fox L., Huskey H. D., Wilkinson J. H. Notes on the solution of algebraic linear simultaneous equations. Quart. J. Mech. Appl. Math. 1:1948;149-173.
12. George J. A. Nested dissection of a regular finite element mesh. SIAM J. Numer. Anal. 15:1978;1053-1069.
13. Gropp W. D. Parallel computing and domain decomposition. Chan T. F., Keyes D. E., Meurant G. A., Scroggs J. S., Voigt R. G. Fifth Conference on Domain Decomposition Methods for Partial Differential Equations. 1992;349-362 SIAM, Philadelphia.
14. Gropp W. D., Keyes D. E. Domain decomposition with local mesh refinement. SIAM J. Sci. Statist. Comput. 15:1992;967-993.
15. Keyes D. E., Saad Y., Truhlar D. G. Domain-Based Parallelism and Problem Decomposition Methods in Computational Science and Engineering. 1995;SIAM, Philadelphia.
16. Gustafson J. L., Montry G. R., Benner R. E. Development of parallel methods for a 1024-processor hypercube. SIAM J. Sci. Statist. Comput. 9:1988;609-621.
17. Kolotilina L. Yu., Yeremin A. Yu. Factorized sparse approximate inverse preconditionings I: Theory. SIAM J. Matrix Anal. Appl. 14:1993;45-58.
18. Pothen A., Simon H. D., Liou K. P. Partitioning sparse matrices with eigenvectors of graphs. SIAM J. Matrix Anal. Appl. 11:1990;430-452.
19. Smith B., Bjørstad P., Gropp W. Domain Decomposition. 1996;Cambridge Univ. Press, MA.
20. Tufo H. M., Fischer P. F. Terascale Spectral Element Algorithms and Implementations. 1999.
21. van de Geijn R. On global combine operations. J. Parallel Distrib. Comput. 22:1994;324-328.
22. Widlund O. B. Iterative substructuring methods: Algorithms and theory for elliptic problems in the plane. Glowinski R., Golub G. H., Meurant G. A., Periaux J. Proceedings of the First International Symposium on Domain Decomposition Methods for Partial Differential Equations. 1988;SIAM, Philadelphia.