High performance inverse preconditioning

Archives of Computational Methods in Engineering

Volumn 16, Issue 1, 2009, Pages 77-108

  Gravvanis, George A ^a  

^a DEMOCRITUS UNIVERSITY OF THRACE   (Greece)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATE INVERSE; COMPUTATIONAL PROCEDURES; DESIGN ISSUES; DISTRIBUTED SYSTEMS; JAVA MULTITHREADING; MODERN COMPUTER SYSTEMS; PARALLEL METHOD; PARALLEL NUMERICAL ALGORITHMS; PARALLEL PERFORMANCE; PRECONDITIONED CONJUGATE GRADIENT; SPARSE LINEAR SYSTEMS; SYMMETRIC MULTIPROCESSOR SYSTEMS; WAVE PATTERNS;

COMPUTATIONAL EFFICIENCY; CONJUGATE GRADIENT METHOD; INVERSE PROBLEMS; JAVA PROGRAMMING LANGUAGE; LINEAR SYSTEMS; MULTITASKING; NETWORK SECURITY;

PARALLEL ALGORITHMS;

EID: 70350230201     PISSN: 11343060     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11831-008-9026-x     Document Type: Article

References (71)

1. Akl SG (1997) Parallel computation: models and methods. Prentice-Hall, Englewood Cliffs.
2. Baker M, Carpenter B, Fox G, Ko SH, Lim S (1999) mpiJava: an object-oriented Java interface to MPI. In: Proceedings of the 11th IPPS/SPDP'99 workshops held in conjunction with the 13th international parallel processing symposium and 10th symposium on parallel and distributed processing, pp 748-762.
3. Benzi M (2002) Preconditioning techniques for large linear systems: a survey. J Comput Phys 182:418-477.
4. Benzi M, Meyer CD, Tuma M (1996) A sparse approximate inverse preconditioner for the conjugate gradient method. SIAM J Sci Comput 17:1135-1149.
5. Boisvert RF (1991) Algorithms for special tridiagonal systems. SIAM J Sci Stat Comput 12(2):423-442.
6. Bull M, Kambites ME (2000) JOMP-an OpenMP-like interface for Java. In: Proceedings of the 2000 ACM Java grande conference, pp 44-53.
7. Bull M, Telford S (2000) Programming models for parallel Java applications. UKHEC Newslett 2:9.
8. Bull J, Smith L, Pottage L, Freeman R (2001) Benchmarking Java against C and Fortran for scientific applications. In: ACM 2001 Java grande/ISCOPE conference, pp 97-105.
9. Christofer TW, Thiruvathukal GK (2000) High-performance Java platform computing. Sun Microsystems Press, Santa Clara.
10. Chronopoulos AT, Gear CW (1989) s-Step iterative methods for symmetric linear systems. J Comput Appl Math 25:153-168.
11. Cosgrove JDF, Dias JC, Griewank A (1992) Approximate inverse preconditioning for sparse linear systems. Int J Comput Math 44:91-110.
12. D'Azevedo E, Eijkhout V, Romine C (1993) A matrix framework for conjugate gradient methods and some variants of CG with less synchronization overhead. In: Proceedings of the sixth SIAM conference on parallel processing for scientific computing. SIAM, Philadelphia, pp 644-646.
13. de Brozolo CR, Robert Y (1988) Parallel and vector conjugate gradient-like algorithms for sparse nonsymmetric linear systems. In: Proceedings of the 2nd international conference on supercomputing, pp 478-487.
14. Demmel J, Heath M, van der Vorst H (1993) Parallel numerical linear algebra. In: Acta numerica 1993. Cambridge University Press, Cambridge.
15. Dongarra J, van der Vorst H (1992) Performance of various computers using standard sparse linear equations solving techniques. Super computer 9(5):17-29.
16. Dongarra J, Duff I, Sorensen D, van der Vorst H (1998) Numerical linear algebra for high-performance computers. SIAM, Philadelphia.
17. Dubois P, Greenbaum A, Rodrigue G (1979) Approximating the inverse of a matrix for use in iterative algorithms on vector processors. Computing 22:257-268.
18. Duff I (2000) The impact of high performance computing in the solution of linear systems: trends and problems. J Comput Appl Math 123:515-530.
19. Duff I, Erisman M, Reid J (1986) Direct methods for sparse matrices. Oxford University Press, Oxford.
20. Epitropou VN, Giannoutakis KM, Gravvanis GA (2007) Java multithreading based parallel preconditioned generalized conjugate gradient type methods. In: Kranzlmuller D, Schreiner W, Volkert J (eds) Proc. of the sixth intern symposium on parallel and distributed computing 2007. IEEE Computer Society Press, Los Alamitos, pp 311-318.
21. Evans DJ (1967) The use of preconditioning in iterative methods for solving linear equations with symmetric positive definite matrices. J Inst Math Appl 4:295-314.
22. Evans DJ (1983) Preconditioning methods: theory and applications. Gordon and Breach, New York.
23. Giannoutakis KM, Gravvanis GA (2007) On the design of parallel finite element approximate inverses. In: Arabnia HR (ed) Proceedings of the 2007 international conference on parallel and distributed processing techniques and applications (PDPTA '2007), vol I. CSREA Press, Las Vegas, pp 292-298.
24. Giannoutakis KM, Gravvanis GA (2008) Parallel approximate finite element inverses on symmetric multiprocessor systems. In: Bubak M, van Albada GD, Dongarra J, Sloot PMA (eds) Computational science-ICCS 2008: 8th international conference proceedings. Lecture notes of computer science, vol 5101, Part I. Springer, New York, pp 925-934.
25. Giannoutakis KM, Gravvanis GA (2008) Design and implementation of parallel approximate inverse classes using OpenMP. Concurr Comput: Pract Exp, to appear.
26. Giannoutakis KM, Gravvanis GA (2008) High performance finite element approximate inverse preconditioning. Appl Math Comput 201:293-304.
27. Giannoutakis KM, Gravvanis GA, Clayton B, Patil A, Enright T, Morrison JP (2007) Matching high performance approximate inverse preconditioning to architectural platforms. J Supercomput 42(2):145-163.
28. Grama A, Gupta A, Karypis G, Kumar V (2003) Introduction to parallel computing. Addison-Wesley, Reading.
29. Gravvanis GA (1996) The rate of convergence of explicit approximate inverse preconditioning. Int J Comput Math 60:77-89.
30. Gravvanis GA (1998) Parallel matrix techniques. In: Papailiou KD, Tsahalis D, Periaux J, Hirsch C, Pandolfi M (eds) Computational fluid dynamics 98, vol I, Part 1. Wiley, New York, pp 472-477.
31. Gravvanis GA (1998) An approximate inverse matrix technique for arrowhead matrices. Int J Comput Math 70:35-45.
32. Gravvanis GA (1999) Parallel preconditioned algorithms for solving special tridiagonal systems. In: Proceedings of dynamical systems and applications, vol III. Dynamic Publishers, Atlanta, pp 241-248.
33. Gravvanis GA (2000) Explicit isomorphic iterative methods for solving arrow-type linear systems. Int J Comput Math 74(2):195-206.
34. Gravvanis GA (2000) Solving parabolic and nonlinear 1D problems with periodic boundary conditions. In: CD-ROM proceedings of the European congress on computational methods in applied sciences and engineering 2000.
35. Gravvanis GA (2002) Explicit approximate inverse preconditioning techniques. Arch Comput Methods Eng 9(4):371-402.
36. Gravvanis GA (2009) OpenMP based parallel normalized direct methods for sparse finite element linear systems. J Supercomput 47(1):44-52.
37. Gravvanis GA, Epitropou VN (2008) Java multithreading based parallel approximate arrow-type inverses. Concurr Comput: Pract Exp 20(10):1151-1172.
38. Gravvanis GA, Giannoutakis KM (2003) On the rate of convergence and complexity of finite element normalized explicit approximate inverse preconditioning. In: Bathe KJ (ed) Computational fluid and solid mechanics 2003, vol 2. Elsevier, Amsterdam, pp 1963-1967.
39. Gravvanis GA, Giannoutakis KM (2003) Normalized explicit finite element approximate inverses. Int J Differ Equ Appl 6(3):253-267.
40. Gravvanis GA, Giannoutakis KM (2004) Parallel approximate finite element inverse preconditioning on distributed systems. In: Proceedings of the third international symposium on parallel and distributed computing 2004 (ISPDC 2004) and the third international workshop on algorithms, models and tools for parallel computing on heterogeneous networks (HeteroPar 2004). IEEE Computer Society Press, Los Alamitos, pp 277-283.
41. Gravvanis GA, Giannoutakis KM (2004) Normalized explicit finite element approximate inverse preconditioning. Int J Comput Struct 82(28):2377-2388.
42. Gravvanis GA, Giannoutakis KM (2006) On the performance of parallel normalized explicit preconditioned conjugate gradient-type methods. In: CD-ROM proceedings of the 20th international parallel and distributed processing symposium 2006 (IPDPS 2006), General Co-Chair: Paul Spirakis and H.J. Siegel, IEEE Computer Society.
43. Gravvanis GA, Giannoutakis KM (2006) Parallel exact and approximate arrow-type inverses on symmetric multiprocessor systems. In: ICCS 2006, Part I. LNCS, vol 3991. Springer, New York, pp 506-513.
44. Gravvanis GA, Giannoutakis KM (2006) Normalized explicit preconditioned methods for solving 3D boundary value problems on uniprocessor and distributed systems. Int J Numer Methods Eng 65(1):84-110.
45. Gravvanis GA, Giannoutakis KM (2008) An improved parallel algorithm for computing approximate inverses by reducing synchronizations. In: Proc of the seventh intern symposium on parallel and distributed computing 2008. IEE Computer Society Press, to appear.
46. Gravvanis GA, Giannoutakis KM (2008) Fast parallel finite element approximate inverses. Comput Model Eng Sci 32(1):35-44.
47. Gravvanis GA, Lipitakis EA (1996) An explicit sparse unsymmetric finite element solver. Commun Numer Methods Eng 12:21-29.
48. Gravvanis GA, Platis AN, Giannoutakis KM, Violentis JB, Lipitakis EA (2003) Performability evaluation of multitasking and multiprocessor systems by explicit approximate inverses. In: Arabnia HR, Mun Y (eds) Proceedings of the international conference on parallel and distributed processing techniques and applications (PDPTA 2003), vol III. CSREA Press, Las Vegas, pp 1324-1331.
49. Gravvanis GA, Epitropou VN, Giannoutakis KM (2007) On the performance of parallel approximate inverse preconditioning using Java multithreading techniques. Appl Math Comput 190:255-270.
50. Grote MJ, Huckle T (1997) Parallel preconditioning with sparse approximate inverses. SIAM J Sci Comput 18:838-853.
51. Grunwald D, Vajracharya S (1994) Efficient barriers for distributed shared memory computers. In: Proceedings of the 8th international parallel processing symposium. IEEE Computer Society Press, Los Alamitos.
52. Hackbusch W (1994) Iterative solution of large linear systems of equations. Springer, New York.
53. Hestenes MR, Stiefel E (1954) Methods of conjugate gradients for solving linear systems. J Res Natl Bur Stand 49:409-436.
54. Huckle T (1998) Efficient computations of sparse approximate inverses. Numer Linear Algorithms Appl 5:57-71.
55. Huckle T (1999) Approximate sparsity patterns for the inverse of a matrix and preconditioning. Appl Numer Math 30:291-303.
56. Kolotilina LY, Yeremin AY (1993) Factorized sparse approximate inverse preconditioning. SIAM J Matrix Anal Appl 14:45-58.
57. Li W, Li E, Meng R, Wang T, Dulong C (2006) Performance analysis of Java concurrent programming: a case study of video mining system. In: CD-ROM proceedings of the 20th international parallel and distributed processing symposium 2006 (IPDPS 2006). IEEE Computer Society, Los Alamitos.
58. Lipitakis EA (1983) A normalized sparse linear equation solver. J Comput Appl Math 9:287-298.
59. Lipitakis EA, Evans DJ (1984) Solving linear finite element systems by normalized approximate matrix factorization semi-direct methods. Comput Methods Appl Mech Eng 43:1-19.
60. Lipitakis EA, Evans DJ (1987) Explicit semi-direct methods based on approximate inverse matrix techniques for solving boundary-value problems on parallel processors. Math Comput Simul 29:1-17.
61. Lipitakis EA, Gravvanis GA (1995) Explicit preconditioned iterative methods for solving large unsymmetric finite element systems. Computing 54:167-183.
62. Marr DT, Binns F, Hill D, Hinton G, Koufaty D, Miller A, Upton M (2002) Hyper-threading technology architecture and microarchitecture, hyper-threading technology. Intel Technol J 6(1):4-13.
63. O'Leary D, Stewart G (1990) Computing the eigenproblem and eigenvectors of arrowhead matrices. J Comput Phys 90:497-505.
64. Parlett B, Nour-Omid B (1985) The use of refined error bound when updating eigenvalues of tridiagonals. Linear Algebra Appl 68:179-219.
65. Quinn MJ (2003) Parallel programming in C with MPI and OpenMP. Mc-Graw Hill, New York.
66. Saad Y (1996) Iterative methods for sparse linear systems. PWS, Boston.
67. Saad Y, van der Vorst HA (2000) Iterative solution of linear systems in the 20th century. J Comput Appl Math 123:1-33.
68. Sonneveld P (1989) CGS: a fast Lanczos-type solver for nonsymmetric linear systems. SIAM J Sci Stat Comput 10:36-52.
69. Tian X, Bik A, Girkar M, Grey P, Saito H, Su E (2002) Intel OpenMP C++/Fortran compiler for hyper-threading technology: implementation and performance, hyper-threading technology. Intel Technol J 6(1):36-45.
70. van der Vorst HA (1989) High performance preconditioning. SIAM J Sci Stat Comput 10:1174-1185.
71. van der Vorst HA (1992) Bi-CGSTAB: a fast and smoothly converging variant of Bi-CG for the solution of non-symmetric linear systems. SIAM J Sci Stat Comput 13:631-644.