A numerical experimental study of inverse preconditioning for the parallel iterative solution to 3D finite element flow equations

Journal of Computational and Applied Mathematics

Volumn 210, Issue 1-2, 2007, Pages 64-70

  Bergamaschi, L ^a   Gambolati, G ^a   Pini, G ^a  

^a UNIVERSITY OF PADOVA   (Italy)

Author keywords

Approximate inverse; Finite elements; Iterative method; Parallel preconditioning

Indexed keywords

CONJUGATE GRADIENT METHOD; FINITE DIFFERENCE METHOD; FINITE ELEMENT METHOD; ITERATIVE METHODS; LINEAR EQUATIONS; PROBLEM SOLVING;

APPROXIMATE INVERSE; FACTORIZED SPARSE APPROXIMATE INVERSE; PARALLEL PRECONDITIONING; PRECONDITIONED CONJUGATE GRADIENTS (PCG);

INVERSE PROBLEMS;

EID: 34848814418     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2006.10.056     Document Type: Article

References (25)

1. Axelsson O. Iterative Solution Methods (1994), Cambridge University Press, Cambridge
2. Benzi M. Preconditioning techniques for large linear systems: a survey. J. Comput. Phys. 182 2 (2002) 418-477
3. L. Bergamaschi, A. Martínez, Parallel acceleration of Krylov solvers by factorized approximate inverse preconditioners, in: M. Daydè, et al. (Eds.), VECPAR 2004, Lecture Notes in Computer Science, vol. 3402, Springer, Heidelberg, 2005, pp. 623-636.
4. Bergamaschi L., Pini G., and Sartoretto F. Computational experience with sequential and parallel preconditioned Jacobi Davidson for large sparse symmetric matrices. J. Comput. Phys. 188 1 (2003) 318-331
5. L. Bergamaschi, G. Pini, F. Sartoretto, Parallel solution of sparse linear systems arising in flow and transport problems, in: Euro-par 2005, Parallel Processing, 11th International Euro-Par Conference, Lisbon, Portugal. Lecture Notes in Computer Science, vol. 3648, Springer, Berlin, 2005, pp. 804-814.
6. L. Bergamaschi, M. Putti, Efficient parallelization of preconditioned conjugate gradient schemes for matrices arising from discretizations of diffusion equations, in: Proceedings of the Ninth SIAM Conference on Parallel Processing for Scientific Computing, March, 1999 (CD-ROM).
7. J. Crank, P. Nicolson, A practical method for numerical evaluation of solutions of partial differential equations of the heat conduction type, in: Proceedings of Cambridge Philosophical Society, vol. 40, 1947, pp. 50-67.
8. Gambolati G., Pini G., and Tucciarelli T. A 3-D finite element conjugate gradient model of subsurface flow with automatic mesh generation. Adv. Water Resour. 3 (1986) 34-41
9. Geus R., and Röllin S. Towards a fast parallel sparse matrix-vector multiplication. In: D'Hollander E.H., et al. (Ed). Parallel Computing: Fundamentals and Applications (2000), Imperial College Press, London 308-315
10. Gravvanis G.A. Generalized approximate inverse finite element matrix techniques. Neural Parallel Sci. Comput. 7 4 (1999) 487-500
11. G.A. Gravvanis, K.M. Giannoutakis, Parallel approximate finite element inverse preconditioning on distributed systems, in: ISPDC/HeteroPar, 2004, pp. 277-283.
12. Gravvanis G.A., Giannoutakis K.M., and Missirlis N.M. A distributed normalized explicit preconditioned conjugate gradient method. Parallel Algorithms Appl. 19 2-3 (2004) 163-174
13. Grote M.J., and Huckle T. Parallel preconditioning with sparse approximate inverses. SIAM J. Sci. Comput. 18 3 (1997) 838-853
14. Huckle T.K. Efficient computation of sparse approximate inverses. Numer. Linear Algebra Appl. 5 1 (1998) 57-71
15. Huckle T.K. Approximate sparsity patterns for the inverse of a matrix and preconditioning. Appl. Numer. Math. 30 2-3 (1999) 291-303 (iterative methods and preconditioners, Berlin, 1997)
16. Kershaw D.S. The incomplete Cholesky-conjugate gradient method for the iterative solution of systems of linear equations. J. Comput. Phys. 26 (1978) 43-65
17. Kolotilina L.Yu., Nikishin A.A., and Yeremin A.Yu. Factorized sparse approximate inverse preconditionings IV. Simple approaches to rising efficiency. Numer. Linear Algebra Appl. 6 (1999) 515-531
18. Kolotilina L.Yu., and Yeremin A.Yu. Factorized sparse approximate inverse preconditionings I. Theory. SIAM J. Matrix Anal. 14 (1993) 45-58
19. Li Z., Saad Y., and Sosonkina M. pARMS: a parallel version of the algebraic recursive multilevel solver. Numer. Linear Algebra Appl. 10 5-6 (2003) 485-509 (preconditioning, 2001, Tahoe City, CA)
20. Meijerink J.A., and van der Vorst H.A. An iterative solution method for linear systems of which the coefficient matrix is a symmetric M-matrix. Math. Comput. 31 (1977) 148-162
21. Pini G., and Gambolati G. Is a simple diagonal scaling the best preconditioner for conjugate gradients on supercomputers?. Adv. Water Resour. 13 3 (1990) 147-153
22. Y. Saad, SPARSKIT: a basic tool kit for sparse matrix computation, Technical Report 1029, University of Illinois, CSRD, Urbana, 1990.
23. Saad Y. ILUT: a dual threshold incomplete ILU factorization. Numer. Linear Algebra Appl. 1 (1994) 387-402
24. Sauter S. The ILU method for finite-element discretizations. J. Comput. Appl. Math. 36 1 (1991) 91-106
25. Smolarski D.C. Diagonally-striped matrices and approximate inverse preconditioners. J. Comput. Appl. Math. 186 2 (2006) 416-431