Parallel incomplete factorizations with pseudo-overlapped subdomains

Parallel Computing

Volumn 27, Issue 8, 2001, Pages 989-1008

  Magolu Monga Made, Mardochée ^a   Van Der Vorst, Henk A ^b  

^a UNIVERSITÉ LIBRE DE BRUXELLES   (Belgium)

^b UTRECHT UNIVERSITY   (Netherlands)

Author keywords

Domain decomposition; Incomplete factorizations; Large sparse linear systems; Multiprocessor computers; Preconditioned conjugate gradient

Indexed keywords

COMPUTATIONAL COMPLEXITY; LINEAR CONTROL SYSTEMS; PROBLEM SOLVING;

LARGE SPARSE LINEAR SYSTEMS; PRECONDITIONED CONJUGATE GRADIENTS;

PARALLEL PROCESSING SYSTEMS;

EID: 0035400544     PISSN: 01678191     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-8191(01)00082-5     Document Type: Article

References (49)

1. C.C. Ashcraft, R.G. Grimes, On vectorizing incomplete factorization and SSOR preconditioners, SIAM J. Sci. Stat. Comput. 9 (1988) 122-151.
2. O. Axelsson, V. Eijkhout, Vectorizable preconditioners for elliptic difference equations in three space dimensions, J. Comput. Appl. Math. 27 (1989) 299-321.
3. O. Axelsson, G. Carey, G. Lindskog, On a class of preconditioned iterative methods on parallel computers, Int. J. Numer. Meth. Eng. 27 (1989) 637-654.
4. O. Axelsson, G. Lindskog, On the eigenvalue distribution of a class of preconditioning methods, Numer. Math. 48 (1986) 479-498.
5. R.F. Barret, M. Berry, T.F. Chan, J. Demmel, J. Donato, J.J. Dongarra, V. Eijkhout, R. Pozo, C. Romine, H. van der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods, SIAM, Philadelphia, 1994.
6. R. Beauwens, Modified incomplete factorization strategies, in: O. Axelsson, L. Kolotilina (Eds.), in: Preconditioned Conjugate Gradient Methods, Lectures Notes in Mathematics No. 1457, Springer, Berlin, 1990, pp. 1-16.
7. 3), World Scientific, Singapore, 1994, pp. 26-34.
8. E. Brakkee, C. Vuik, P. Wesseling, An investigation of Schwarz domain decomposition using accurate and inaccurate solution of subdomains, Report 95-18, Faculty of Technical Mathematics and Informatics, Delft University of Technology, 1995.
9. G. Radicati di Brozolo, Y. Robert, Parallel conjugate gradient like algorithms for solving sparse nonsymmetric linear systems on a vector multiprocessor, Parallel Comput. 11 (1989) 223-239.
10. E.M. Daoudi, P. Manneback, Implementation of ICCG algorithm on distributed memory architecture, in: R. Beauwens, P. de Groen (Eds.), in: Iterative Methods in Linear Algebra, North-Holland, Amsterdam, 1992, pp. 339-347.
11. S. Doi, A. Lichnewsky, A graph-theory approach for analyzing the effects of ordering on ILU preconditioning. INRIA report 1452, INRIA-Rocquencourt, France, 1991.
12. S. Doi, T. Washio, Ordering strategies and related techniques to overcome the trade-off between parallelism and convergence in incomplete factorizations, Parallel Comput. 25 (1999) 1995-2014.
13. J.J. Dongarra, I.S. Duff, D.C. Sorensen, H.A. van der Vorst, in: Numerical Linear Algebra for High-Performance Computers, SIAM, Philadelphia, PA, 1998.
14. I.S. Duff, Direct methods, Technical Report RAL-TR-1998-054, Rutherford Appleton Laboratory, Chilton, Didcot, OX11 0QX, UK, 1998.
15. I.S. Duff, G.A. Meurant, The effect of ordering on preconditioned conjugate gradients, BIT 29 (1989) 635-657.
16. I.S. Duff, H.A. van der Vorst, Developments and trends in the parallel solution of linear systems, Parallel Comput. 25 (1999) 1931-1970.
17. T. Dupont, R.P. Kendall, H.H. Rachford, An approximate factorization procedure for solving self-adjoint elliptic difference equations, SIAM J. Numer. Anal. 5 (1968) 559-573.
18. V. Eijkhout, Beware of unperturbed modified incomplete factorizations, in Iterative Methods, in: R. Beauwens, P. de Groen (Eds.), in: Iterative Methods in Linear Algebra, North-Holland, Amsterdam, 1992, pp. 583-591.
19. H. Elman, E. Agrón, Ordering techniques for the preconditioned conjugate gradient method on parallel computers, Comput. Phys. Commun. 53 (1989) 253-269.
20. S. Fujino, S. Doi, Optimizing multicolor ICCG methods on some vectorcomputers, in: R. Beauwens, P. de Groen (Eds.), in: Iterative Methods in Linear Algebra, North-Holland, Amsterdam, 1992, pp. 349-358.
21. M.B. van Gijzen, An analysis of element-by-element preconditioners for nonsymmetric problems, Comput. Methods Appl. Mech. Eng. 105 (1993) 23-40.
22. G.H. Golub, C.F. van Loan, in: Matrix Computations, third ed., The John Hopkins University Press, Baltimore, Maryland, 1996.
23. I. Gustafsson, A class of first order factorization methods, BIT 18 (1978) 142-156.
24. G. Haase, Parallel incomplete Cholesky preconditioners based on the nonoverlapping data distribution, Parallel Comput. 24 (1998) 1685-1703.
25. D. Hysom, A. Pothen, A scalable parallel algorithm for incomplete factor preconditioning, SIAM J. Sci. Comput. (To appear).
26. M. Magolu monga Made, Ordering strategies for modified block incomplete factorizations, SIAM J. Sci. Comput. 16 (1995) 378-399.
27. M. Magolu monga Made, Implementation of parallel block preconditionings on a transputer-based multiprocessor, Future Generation Comput. Syst. 11 (1995) 167-173.
28. M. Magolu monga Made, Taking advantage of the potentialities of dynamically modified block incomplete factorizations, SIAM J. Sci. Comput. 19 (1998) 1083-1108.
29. M. Magolu monga Made, R. Beauwens, G. Warzee, Preconditioning of discrete Helmholtz operators perturbed by a diagonal complex matrix, Commun. Numer. Meth. Eng. 16 (2000) 801-817.
30. M. Magolu monga Made, B. Polman, Efficient planewise like preconditioners to cope with 3D problems, Numer. Linear Algebra Appl. 6 (1999) 379-406.
31. J.A. Meijerink, H.A. van der Vorst, An iterative solution method for linear systems of which the coefficient matrix is a symmetric M-matrix, Math. Comput. 31 (1977) 148-162.
32. J.A. Meijerink, H.A. van der Vorst, Guidelines for the usage of incomplete decompositions in solving sets of linear equations as they occur in practical problems, J. Comput. Phys. 44 (1981) 134-155.
33. N. Munksgaard, Solving sparse symmetric sets of linear equations by preconditioned conjugate gradient method, ACM Trans. Math. Software 6 (1980) 206-219.
34. S. Nakamura, in: Computational Methods in Engineering and Science, Wiley, New York, 1977.
35. Y. Notay, DRIC: A dynamic version of the RIC method, Numer. Linear Algebra Appl. 1 (1994) 511-532.
36. Y. Notay, An efficient parallel discrete PDE solver, Parallel Comput. 21 (1995) 1725-1748.
37. Y. Notay, A. Van de Velde, Coarse grid acceleration of parallel incomplete preconditioners, in: S. Margenov, P. Vassilevski, (Eds.), Iterative Methods in Linear Algebra II, IMACS series in Computational and Applied Mathematics, vol. 3, 1996, pp. 106-130.
38. T. Oppe, W. Joubert, Improved SSOR and incomplete Cholesky solution of linear equations on shared and distributed memory parallel computers, Numer. Linear Algebra Appl. 1 (1994) 287-311.
39. Y. Saad, in: Iterative Methods for Sparse Linear Systems, PWS Publishing, Co., Boston, MA, 1996.
40. B.F. Smith, P.E. Björstad, D. Gropp, in: Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations, Cambridge University Press, Cambridge, 1996.
41. E. de Sturler, Incomplete block LU preconditioners on slightly overlapping subdomains for a massively parallel computer, Technical Report CSCS-TR-94-03, Swiss Scientific Computing Center, ETH, Zurich, 1994.
42. K.H. Tan, J. Groeneweg, M.J.A. Borsboom, Locally optimized block preconditioners based on domain decomposition, Preprint 880, Department of Mathematics, Utrecht University, 1994.
43. R.S. Varga, in: Matrix Iterative Analysis, Prentice- Hall, Englewood Cliffs, NJ, 1962.
44. H.A. van der Vorst, A vectorizable variant of some ICCG methods, SIAM J. Sci. Stat. Comput. 3 (1982) 350-356.
45. H.A. van der Vorst, Large tridiagonal and block tridiagonal linear systems on vector and parallel computers, Parallel Comput. 5 (1987) 54.
46. H.A. van der Vorst, High performance preconditioning, SIAM J. Sci. Stat. Comput. 10 (1989) 1174-1185.
47. H.A. van der Vorst, ICCG and related methods for 3D problems on vector computers, Comput. Phys. Commun. 53 (1989) 223-235.
48. T. Washio, K. Hayami, Parallel block preconditioning based on SSOR and MILU, Numer. Linear Algebra Appl. 1 (1994) 533-553.
49. Y.G. Zhong, X.Y. Kong, G.M. Xu, G.H. Kuang, Multiple sequential staging of tasks: A new approach to parallel computations, Commun. Numer. Meth. Eng. 15 (1999) 367-373.