Block constrained versus generalized Jacobi preconditioners for iterative solution of large-scale Biot's fem equations

Computers and Structures

Volumn 82, Issue 28 SPEC. ISS., 2004, Pages 2401-2411

  Phoon, K K ^a   Toh, K C ^a   Chen, X ^a  

^a NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

Author keywords

Biot's consolidation equations; Block constrained preconditioner Generalized Jacobi preconditioner; Symmetric quasi minimal residual (SQMR) method; Three dimensional finite element discretization

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL COMPLEXITY; CONSTRAINT THEORY; FINITE ELEMENT METHOD; ITERATIVE METHODS; MATRIX ALGEBRA; THREE DIMENSIONAL;

BIOT'S CONSOLIDATION EQUATIONS; BLOCK CONSTRAINED PRECONDITIONER; GENERALIZED JACOBI PRECONDITIONER; SYMMETRIC QUASI-MINIMAL RESIDUAL (SQMR) METHOD; THREE-DIMENSIONAL FINITE-ELEMENT DISCRETIZATION;

PROBLEM SOLVING;

EID: 4944255097     PISSN: 00457949     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compstruc.2004.04.012     Document Type: Conference Paper

References (17)

1. Phoon KK, Toh KC, Chan SH, Lee FH. An efficient diagonal preconditioner for finite element solution of Blot's consolidation equations. Int J Numer Methods Eng 2002;55(4):377-400.
2. Zienkiewicz OC, Vilotte JP, Toyoshima S, Nakazawa S. Iterative method for constrained and mixed approximation. An inexpensive improvement of FEM performance. Comput Methods Appl Mech Eng 1985;51:3-29.
3. Freund RW, Nachtigal NM. A new Krylov-subspace method for symmetric indefinite linear system. In: Proceedings of the 14th IMACS World Congress on Computational and Applied Mathematics, Atlanta, USA, 1994. p. 1253-6.
4. Phoon KK, Chan SH, Toh KC, Lee FH. Fast iterative solution of large undrained soil-structure interaction problems. Int J Numer Anal Methods Geomech 2003;27(3):159-81.
5. Murphy MF, Golub GH, Wathen AJ. A note on preconditioning for indefinite linear systems. SIAM J Sci Comput 2000;21(6):1969-72.
6. Huckle T. Approximate sparsity patterns for the inverse of a matrix and preconditioning. Appl Numer Math 1999;30:291-303.
7. Lipitakis EA, Gravvanis GA. Explicit preconditioned iterative methods for solving large unsymmetric finite element systems. Computing 1995;54(2):167-83.
8. Gravvanis GA. Generalized approximate inverse finite element matrix techniques. Neural Parallel Sci Comput 1999;7(4):487-500.
9. Toh KC, Phoon KK, Chan SH. Block Preconditioners for symmetric indefinite linear systems. Int J Numer Methods Eng, in press.
10. Van der Vorst H. Iterative methods for large linear systems. Cambridge: Cambridge University Press; 2003.
11. Saad Y. Iterative methods for sparse linear systems. Boston: PWS Publishing Company; 1996.
12. Dayde MJ, L'Excellent, Gould NIM. Element-by-element preconditioners for large partially separable optimization problems. SIAM J Sci Comput 1997;18(6):1767-87.
13. George A, Liu J. Computer solution of large sparse positive definite systems. Englewood Cliffs, NJ: Prentice Hall; 1981.
14. Lee LQ, Siek JG, Lumsdaine A. Generic graph algorithms for sparse matrix ordering. In: Third International Symposium ISCOPE 99. Lecture Notes in Computer Science, vol. 1732. Springer-Verlag; 1999.
15. Ng EG, Peyton BW. Block sparse Cholesky algorithms on advanced uniprocessor computers. SIAM J Sci Comput 1993;14:1034-56.
16. Barrett R, Berry M, Chan T, Demrael J, Donato J, Dongarra J, et al. Templates for the solution of linear systems: building blocks for iterative methods. Philadelphia: SIAM Press; 1994.
17. Driscoll TA. A MATLAB toolbox for Schwarz-Christoffel mapping. ACM Trans Math Software 1996;22:168-86.