High performance sparse solver for unsymmetrical linear equations with out-of-core strategies and its application on meshless methods

Applied Mathematics and Mechanics (English Edition)

Volumn 27, Issue 10, 2006, Pages 1339-1348

  Yuan, Wei Ran ^a   Chen, Pu ^a   Liu, Kai Xin ^a  

^a PEKING UNIVERSITY   (China)

Author keywords

High performance computation; Linear equation; Meshless method; Sparse matrix

Indexed keywords

ALGORITHMS; CODES (SYMBOLS); LINEAR SYSTEMS; MATRIX ALGEBRA; PERFORMANCE; SPEED;

FACTORIZATION PROCESS; HIGH PERFORMANCE COMPUTATION; MESHLESS METHOD; SPARSE MATRICES;

LINEAR EQUATIONS;

EID: 33845372047     PISSN: 02534827     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10483-006-1006-1     Document Type: Article

References (19)

1. Chen Pu, Runesha H, Nguyen D T, Tong P, Chang T Y P. Sparse algorithms for indefinite systems of linear equations[J]. Comput Mech J, 2000, 25(1): 33-42.
2. Damhaug A C, Reid J, Bergseth A. The impact of an efficient linear solver on finite element analysis[J]. Comput Struct, 1999, 72(4/5): 594-604.
3. Weinberg D J. A performance assessment of NE/Nastran's new sparse direct and iterative solvers[J]. Adv Engng Software, 2000, 31(8/9): 547-554.
4. Wilson E L, Bathe K J, Doherty W P. Direct solution of large system of linear equations[J]. Comput Struct, 1974, 4(2): 363-372.
5. Atluri S N, Zhu T. A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics[J]. Comput Mech, 1998, 22(2): 117-127.
6. Atluri S N, Zhu T. The meshless local Petrov-Galerkin (MLPG) approach for solving problems in elasto-statics[J]. Comput Mech, 2000, 25(2/3): 169-179.
7. Ng E G, Peyton B W. Block sparse Cholesky algorithm on advanced uniprocessor computers[J]. SIAM J Sci Comput, 1993, 14(5): 1034-1055.
8. Pissanetzky S. Sparse Matrix Technology[M]. Academic Press, London, Orlando, 1984.
9. Demmel W J, Eisenstat C S, Gilbert J R, Li S X, Liu W H J. A supernodal approach to sparse partial pivoting[J]. SIAM J Matrix Analysis and Applications, 1999, 20(3): 720-755.
10. Li S X. An Overview of superLU: algorithms, implementation, and user interface[J]. ACM Trans Math Soft, 2005, 31(3): 302-325.
11. Runesha H B, Nguyen D T. Vector-sParse solver for unsymmetrical matrices[J]. Adv Engng Software, 2000, 31(8/9): 563-569.
12. Sherman A H. On the efficient solution of sparse systems of linear and nonlinear equations[D]. Rept No. 46 (Ph D Dissertation), Dept of Computer Science, Yale University, New York, 1975.
13. Chen Pu, Zheng Dong, Sun Shuli, Yuan Mingwu. High performance sparse static solver in finite element analyses with loop-unrolling[J]. Adv Engng Software, 2003, 34(4): 203-215.
14. Fellipa C A. Solution of linear equations with skyline-stored symmetric matrix[J]. Comput Struct, 1975, 5(1): 13-29.
15. Wilson E L, Dovey H H. Solution or reduction of equilibrium equations for large complex structural system[J]. Adv Engng Software, 1978, 1(1): 19-26.
16. Amestoy R P, Enseeiht-Irit, Davis A T, Duff S I. Algorithm 837: AMD, an approximate minimum degree ordering algorithm[J]. ACM Trans Math Soft, 2004, 30(3): 381-388.
17. Karypis G, Kumar V. A fast and high quality multilevel scheme for partitioning irregular graphs[J]. SIAM J Sci Comput, 1998, 20(1): 359-392.
18. Zheng D, Chang T Y P. Parallel Cholesky method on MIMD with shared memory[J]. Comput Struct, 1995, 56(1): 25-38.
19. Dowd K, Severance C R. High Performance Computing[M]. 2nd Ed. Sebastopol, CA: O'Reilly and Associates, Cambridge, 1998.