Abstract
The solution of linear systems of equations on advanced parallel and/or vector computers is an important area of ongoing research. The development of efficient equation solvers is particularly important for static and dynamic (linear and non-linear) structural analyses, sensitivity and structural optimization, control-structure interactions, ground water flows, panel flutters, eigenvalue analysis etc…. [10.1–10.19]. Modern high-performance computers (such as Cray-YMP, Cray-C90, Intel Paragon, IBM-SP2) have both parallel and vector capability, thus algorithms that exploit parallel and/or vector capabilities are the most desirable.
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10.13 References
Pissanetzky, S., “Sparse Matrix Technology,” Academic Press, Inc., London (1984).
Agarwal, T.K., Storaasli, O.O., and Nguyen, D.T., “A Parallel-Vector Algorithm for Rapid Structural Analysis on High Performance Computers,” to appear in Computers and Structures Journal.
Nguyen, D.T., Storaasli, O.O., Carmona, E.A., Al-Nasra, M., Zhang, Y., Baddourah, M.A. and Agarwal, T.K., “Parallel-Vector Computation for Linear Structural Analysis and Nonlinear Unconstrained Optimization Problems,” Computing Systems in Engineering, An International Journal, Vol.2, No.2/3, September 1991, (Pergamon Press), pp. 175–182.
Qin, J., Gray,Jr, C.E., Mei, C. and Nguyen, D.T., “A Parallel-Vector Equation Solver for Unsymmetric Matrices on Supercomputers,” Computing Systems in Engineering, An International Journal, Vol.2, No.2/3, September 1991 (Pergamon Press), pp. 197–202.
Zhang, Y. and Nguyen, D.T., “Parallel-Vector Sensitivity Calculations in Linear Structural Dynamics,” Computing Systems in Engineering Journal, Vol.3, No. 1-4, pp.365–378, (1992).
Belvin, W.K., Maghami, P.G. and Nguyen, D.T., “Efficient Use of High Performance Computers for Integrated Controls and Structures Design,” Computing Systems in Engineering Journal, Vol.3, No. 1-4, pp. 181–188, (1992).
Qin, J. and Nguyen, D.T., “A Parallel-Vector Equation Solver for Distributed Memory Computers,” Computing Systems in Engineering journal, Vol.5, No. 1, (1994).
Maker, B.N., Qin, J. and Nguyen, D.T., “Performance of NIKE3D with PVSOLVE on Vector and Parallel Computers,” to appear in Computing Systems in Engineering Journal.
Qin, J. and Nguyen, D.T., “A Parallel-Vector Simplex Algorithm on Distributed Memory Computers,” to appear in Optimization Journal.
Akan, A.O., Qin, J., Nguyen, D.T., and Basco, D.R., “Parallel Computation for Groundwater Flow,” Proceedings of the International Groundwater Management Symposium, San Antonio, TX (August 1995)
Qin, J., Nguyen, D.T. and Zhang, Y., “Parallel-Vector Lanczos Eigen-Solver for Structural Vibration Problems,” Proceedings of the 4th International Conference on Recent Advances in Structural Dynamics, Institute of Sound and Vibration Research, University of Southampton, Southampton, England (July 15-18, 1991).
Bailey, D.H., Barszcz, E., Dagum, L., and Simon, H.D., “NAS Parallel Benchmark Results 10-93,” NASA Ames Research Center Report, ARC275, Moffett Field, CA.
Sporzynski, Steven R., “Vector/Parallel Skyline Matrix Routines for the IBM-3090,” Technical Report, Washington Systems Center, IBM Corp., 18100 Frederick Pike, Gaithersburg, MD 20879 (May 1990).
Zheng, D. and Chang, T.Y.P., “Parallel Cholesky Method on MIMD with Shared Memory,” Computers and Structures, Vol.56, No.l, pp.25–38 (1995).
Tong, Pin, Rossettos, John N., “Finite Element Method: Basic Technique and Implementation.” the MIT Press, Cambridge, Massachusetts, and London, England.
Ortega, J.M., “Introduction to Parallel and Vector Solution of Linear Systems,” Plenum Press (1988).
Khan, A.I. and Topping, B.H.V., “Parallel-Finite Element Analysis Using the Jacobi-Conditioned Conjugate Gradient Algorithm,” Information Technology for Civil and Structural Engineers,” B.H.V. Topping & A.I. Khan (Eds.), Civil-Comp. Press, Edinburgh, 245–255 (1993).
Khan, A.I., and Topping, B.H.V., “A Transputer Routing Algorithm for Nonlinear or Dynamic Finite Element Analysis,” Engineering Computations, Vol.11, pp.549–564 (1994).
Topping, B.H.V. and Khan, A.I., “Parallel Computations for Structural Analysis, Re-Analysis and Optimization,” Optimization of Large Structural Systems, Vol.11, pp.767–792 (G.I.N. Rozvany, Ed., 1993 Kluwer Academic Publishers, Netherlands).
Duff, I.S. and Stewart, G.W. (Editors), “Sparse Matrix Proceedings 1979,” SIAM (1979)
Duff, I.S., Grimes, R.G. and Lewis, J.G., “Sparse Matrix Test Problems,” ACM Trans. Math Software, 15, pp.1–14 (1989).
George, J.A. and Liu, W.H., “Computer Solution of Large Sparse Positive Definite Systems,” Prentice-Hall, Englewood Cliffs, NJ (1981).
Damhaug, A.C., Mathisen, K.M., and Okstad, K.M., “The Use of Sparse Matrix Methods in Finite Element Codes for Structural Mechanics Applications,” Department of Structural Engineering, The Norwegian Institute of Technology, N-7034 Troudheim, Norway (1993).
Noor, A.K., “Parallel Processing In Finite Element Structural Analysis,” in Parallel Computations and Their Impact on Mechanics, ASME, pp.253–277, A.K. Noor (Ed.) 1987.
Law, K.H. and Mackay, D.R., “A Parallel Row-Oriented Sparse Solution Method for Finite Element Structural Analysis,” Inter. Journal for Num. Meth. in Engr., Vol.36, pp.2895–2919 (1993).
Bathe, K.J., Finite Element Procedures, Prentice-Hall (1996).
Golub, G.H. and VanLoan, C.F., “Matrix Computations,” Johns Hopkins University Press, Baltimore, MD, Second Edition (1989).
Cuthill, E. and McKee, J., “Reducing the Bandwidth of Sparse Symmetric Matrices,” Proc. 24thNat’l. Conf. Assoc. Comput. Mach., ACM Publ., pp.157–172 (1969).
Crane, H.L., Jr., Gibbs, N.E., Poole, Jr., W.G., and Stockmeyer, P.K., “Algorithm 508: Matrix Bandwidth and Profile Reduction,” ACM Trans, on Math. Software, 2, pp.375–377 (1976).
Lewis, J.G., Peyton, B.W. and Pothen, A., “A Fast Algorithm for Reordering Sparse Matrices for Parallel Factorization,” SIAM J. Sci. Statist. Comput., 6, pp.1146–1173 (1989).
Liu, J.W.H., “Reordering Sparse Matrices for Parallel Elimination,” Tech. Report 87-01, Computer Science, York University, North York, Ontario, Canada (1987).
Pothen, A., Simon, H.D. and Liou, K-P., “Partitioning Sparse Matrice with Eigenvectors of Graphic,” Siam J. Matrix, Vol.11, No.l, pp.430–452 (1990).
George, J.A., “Nested Dissection of a Regular Finite Element Mesh,” Siam J. Numer. Anal., 15,pp.l053–1069(1978).
Gilbert, J.R. and Zmijewski, E., “A Parallel Graph Partitioning Algorithm for a Message Passing Multiprocessor,” Inter. J. Parallel Programming, 16, pp.427–449 (1987).
Leiserson, C.E. and Lewis, J.G., “Orderings for Parallel Sparse Symmetrix Factorization,” Third SIAM Conference on Parallel Processing for Scientific Computing (1987).
Simon, H.D., Vu, P. and Yang, C., “Performance of a Supernodal General Sparse Solver on the Cray-YMP: 1.68 GFLOPS with Autotasking,” Applied Mathematics Technical Report (SCA-TR-117), Boeing Computer Service, Scientific Computing and Analysis Division, G-8910, M/S 7L-21, P.O. Box 24346, Seattle, Washington, 98124-0346, USA.
Wang, S.M., Chang, T.Y.P. and Tong, P., “Nonlinear Deformation Responses of Rubber Components by Finite Element Analysis,” Computational Mechanics ’95: Theory and Applications Proceedings of the International Conference on Computational Engineering Science, July 30-August 3, 1995, Hawaii, USA (Volume 2, pp.3135–3140).
Chang, T.Y.P., Saleeb, A.F. and Li, G., “Large Strain Analysis of Rubber-like Materials Based on a Perturbed Lagrangian Variational Principal,” J. Comput. Mech., Vol.8, pp.221–233, (1991).
Gunderson, R.H., “Fatigue Life of TLP Flexelements,” 24th Annual OTC Conference, Houston, Texas, May 4-7, 1992.
Storaasli, O.O., NASA Langley Research Center, Hampton, VA (Private Communication).
Ng, E. and Peyton, B.W., “Block Sparse Choleski Algorithm On Advanced Uniprocessor Computer,” SIAM J. of Sci. Comput., Volume 14, pp. 1034–1056, 1993.
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Nguyen, D.T. (2002). Sparse Equation Solver with Unrolling Strategies. In: Parallel-Vector Equation Solvers for Finite Element Engineering Applications. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-1337-7_10
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DOI: https://doi.org/10.1007/978-1-4615-1337-7_10
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