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The presented method is used in finite-element analysis software developed for multicore and multiprocessor shared-memory computers, or it can be used on single-processor personal computers under the operating systems Windows 2000, Windows XP, or Windows Vista, widely popular in small or medium-sized design offices. The method has the following peculiar features: it works with any ordering; it uses an object-oriented approach on which a dynamic, highly memory-efficient algorithm is based; it performs a block factoring in the frontal matrix that entails a high-performance arithmetic on each processor and ensures a good scalability in shared-memory systems. Many years of experience with this solver in the SCAD software system have shown the method's high efficiency and reliability with various large-scale problems of structural mechanics (hundreds of thousands to millions of equations).
Rocznik
Tom
Strony
117--131
Opis fizyczny
Bibliogr. 14 poz., il., wykr., tab.
Twórcy
autor
- Institute of Computer Modeling, Cracow University of Technology, ul. Warszawska 24, 31-155 Cracow
Bibliografia
- [1] C. Ashcraft, J.W.-H. Liu. Robust Ordering of Sparse Matrices Using Multisection. Technical Report CS 96-01. Department of Computer Science, York University, Ontario, Canada, 1996.
- [2] J.W. Demmel. Applied Numerical Linear Algebra. SIAM, Philadellphia, 1997.
- [3] F. Dobrian, A. Pothen. Oblio: a sparse direct solver library for serial and parallel computations. Technical Report describing the OBLIO software library. 2000.
- [4] I.S. Duff, J.K. Reid. The multifrontal solution of indefinite sparse symmetric linear systems. ACM Transactions on Mathematical Software, 9: 302-325, 1983.
- [5] I.S. Duff, J.K. Reid, J.A. Scott. The use of profile reduction algorithms-with a frontal code. International Journal for Numerical Methods in Engineering, 28: 2555-2568, 1989.
- [6] S.Yn. Fialko. A block sparse direct multifrontal solver in SCAD software. Proceedings of the CMM-2005 - Computer Methods in Mechanics, June 21-24, 2005, Częstochowa, Poland, pp.73-74, 2005.
- [7] S.Yu. Fialko. Stress-Strain Analysis of Thin-Walled Shells with Massive Ribs. Int. App. Mech.. 40(4): 432-439, 2004.
- [8] A. George A., J.W.-H. Liu. Computer solution of sparse positive definite systems. Prentice-Hall, New Jersey, Inc. Eiiglewood Cliffs, 1981.
- [9] A. George A., J.W.-H. Liu. The Evolution of the Minimum degree Ordering Algorithm. SIAM Rev., 31(March): 1-19, 1989.
- [10] N J.M. Gould, Y. Hu, J. A. Scott. A numerical evaluation o f sparse direct solvers for the solution of large sparse, symmetric linear systems of eąuations. Technical report RAL-TR-2005-005.Rutherford Appleton Laboratory, 2005.
- [11] B.M. Irons. A frontal solution program for finite-element analysis. International Journal for Numerical Methods in Engineering, 2: 5-32, 1970.
- [12] G. Karypis, V. Kumar. A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs. Technical Report TR 95-035. Department of Computer Science, University of Minnesota, Minneapolis, 1995.
- [13] J.A. Scott. A frontal solver for the 21st century. Communications m Numerical Methods in Engineering, 22: 1015-1029, 2006.
- [14] S.W. Sloan. An algorithm for profile and wavefront reduction of sparse matrices. International Journal for Numerical Methods in Engineering, 23: 1315-1324, 1986.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPB8-0009-0013