SparSol: Sparse linear systems solver

Russian Journal of Numerical Analysis and Mathematical Modelling

Volumn 22, Issue 4, 2007, Pages 325-339

  Diyankov, O V ^a   Koshelev, S V ^a   Kotegov, S S ^a   Krasnogorov, I V ^a   Kuznetsova, N N ^a   Pravilnikov, V Y ^a   Beckner, B L ^b   Maliassov, S Y ^b   Mishev, I D ^b   Usadi, A K ^b  

^a Neurok TechSoft LLC   (Russian Federation)

^b EXXONMOBIL UPSTREAM RESEARCH COMPANY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; COMPUTER SIMULATION; PROBLEM SOLVING; SOFTWARE PACKAGES;

HYDROCARBON RESERVOIR SIMULATIONS; LARGE SPARSE LINEAR SYSTEMS;

LINEAR SYSTEMS;

EID: 34249306139     PISSN: 09276467     EISSN: 15693988     Source Type: Journal    
DOI: 10.1515/rnam.2007.016     Document Type: Article

References (24)

1. V. F. de Almeida, A. M. Chapman, and J. J. Derby, On equilibration and sparse factorization of matrices arising in finite element solutions of partial differential equations. Numer. Meth. Partial Diff. Equations (2000) 16, 11-29.
2. J. R. Appleyard and I. M. Cheshire, Nested Factorization. In: The 7th SPE Symposium on Reservoir Simulation, 1983.
3. R. Barrett, M. Berry, T. Chan, J. Demmel, J. Donato, J. Dongarra, V.Eijkhout, R. Pozo, Ch. Romine, and H. van der Vorst, Templates for the Solution of Linear Systems: Building Blocks for Iterative Methods (electronic version).
4. T. F. Chan and H. van der Vorst, Approximate and Incomplete Factorizations. http://igitur-archive.library.uu.nl/math/2001-0621-115821/ proc.pdf
5. ExxonMobil public matrix collection. http://www.aconts.com/XOMMarrices
6. I. E. Kaporin, Explicitly preconditioned conjugate gradient method for the solution of nonsymmetric linear systems. J. Comp. Math. (1992) 50, 169-187.
7. T U -decomposition. Numer. Linear Algebra Appl. (1998) 5, 483-509.
8. I. E. Kaporin, Second order ILU preconditioning for nonsymmetric matrices. In: International Conference on Matrix Methods and Operator Equations, June 20 - 25, Moscow, 2005.
9. I. E. Kaporin, Superlinear convergence in minimum residual iterations. Numer. Linear Algebra Appl. (2005) 12, 453-470.
10. I. E. Kaporin and I. N. Konshin, Optimization of Matrix Scaling in CGSOL code. NeurOK Techsoft Report, June, 2003.
11. D. Kershaw, The incomplete Choleskyconjugate gradient method for the iterative solution of systems of linear equations. J. Comp. Phys. (1978) 26, 43-65.
12. N. N. Kuznetsova et al., The family of Nested Factorizations. Russ. J. Numer. Anal. Math. Modelling (2007) 22, No. 4, 393-412.
13. PETSc Home Portable, Extensible Toolkit for Scientific Computation. http://www-unix.mcs.anl.gov/petsc/
14. V. Y. Pravilnikov et al., FILU: an efficient incomplete LU preconditioner. Russ. J. Numer. Anal. Math. Modelling (2007) 22, No. 4, 413-430.
15. Y. Saad, Iterative Methods for Sparse Linear Systems. PWS Publishing, New York, 1996.
16. Y Saad, GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comp. (1986) 7, 856-869.
17. Y. Saad, SPARSEKIT: A basic tool for sparse matrix computations. Tech. Report No. 90-20, Research Institute for Advanced Computer Science. NASA Aimes Research Center, Moffet Field, CA, 1990.
18. Y. Saad and B. Suchomel, ARMS: An algebraic recursive multilevel solver for general sparse linear systems. Numer. Linear Algebra Appl. (2002) 9, 359-378
19. O. Sheck and K. Gärtner, PARDISO: a high performance serial and parallel sparse liner solver in semiconductor device simulations. Future Generation Comp. Systems (2001) 789, No. 1, 1-9.
20. G. L. G. Sleijpen and D. R. Fokkema, BiCGStab(L) for Linear Equations Involving Unsymmetric Matrices with Complex Spectrum (electronic version).
21. P. Sonneveld, CGS, a fast Lanczos type solver for nonsymmetric linear systems. SIAM J. Sci. Stat. Comp. (1989) 10, 36-52.
22. H. A. van der Vorst, Bi-CGSTAB: A fast and smooth converging variant of Bi-CG for the solution of non-symmetric linear systems. SIAM J. Sci. Stat. Comp. (1992) 12, 631-644.
23. H. A. van der Vorst and T. F. Chan, Linear system solvers: sparse iterative methods. In: Parallel Numerical Algorithms (Eds. D. E. Keyes, A. Sanuh, and V. Venkatokrishman). Kluwer Academic, Dordecht, 1997, pp. 91-118.
24. J. W. Watts, III, A conjugate gradient truncated direct method for the iterative solution of the reservoir simulation pressure equation. Soc. Petrol. Engrg. (1981) 21, 345-353.