Abstract
A general algorithm for constructing finite element matrices within a multiple input, multiple data stream (MIMD) vector-processing environment is presented. Efficiency of the vectorized code is determined by the number of elements which differs from the more intuitive algorithms based on the number of quadrature points or shape functions. Performance is evaluated analytically and then verified by timings obtained by a series of experimental runs on a Cray Y-MP. A speedup factor of 25 is observed.
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References
Adams, L., and Voight, R. (1984).A Methodology for Exploiting Parallelism in the Finite Element Process, NATO ASI Series, Vol. F7, High-Speed Computations, Springer-Verlag, Berlin.
Axelsson, O., and Barker, V. (1984).Finite Element Solutions of Boundary Value Problems, Academic Press, Orlando, Florida.
Becker, E., Carey, G., and Oden, J. (1981).Finite Elements, Vol. I,An Introduction, Prentice-Hall, Englewood Cliffs, New Jersey.
Carey, G., and Oden, J. (1984).Finite Elements, Vol. III,Computational Aspects, Prentice-Hall, Englewood Cliffs, New Jersey.
Conte, S., and de Boor, C. (1980).Elementary Numerical Analysis, McGraw-Hill, New York.
Cox, C. L. (1986). On Least-Squares Approximations to First-Order Elliptic Systems in Three Dimensions, Technical report, Department of Mathematical Sciences, Clemson University, Clemson, South Carolina.
Edwards, O. (1986). Finite Element Stiffness Calculation on Supercomputers, Thesis, Mathematics Department, Carnegie Mellon University, Pittsburgh, Pennsylvania.
Furey, W. (1988). Lecture notes, Scientific Computing 210, Spring semester, University of Pittsburgh, Pittsburgh, Pennsylvania.
Gustafson, K. (1987).Partial Differential Equations and Hilbert Space Methods, John Wiley & Sons, New York.
Hockney, R., and Jesshope, C. (1981).Parallel Computers, Adam Hilger, Bristol, England.
Johnson, C. (1987).Numerical Solutions of Partial Differential Equations by the Finite Element Method, Cambridge University Press, Cambridge, England.
Layton, W. (1989). Finite Element Methods, manuscript, University of Pittsburgh, Pittsburgh, Pennsylvania.
Lazou, C. (1988).Supercomputers and their Use, Oxford University Press, New York.
Levesque, J., and Williamson, J. (1987).Fortran Programming on the Cray Computers, Pacific-Sierra Research, Placerville, California.
Levesque, J., and Williamson, J. (1989).A Guidebook to Fortran on Supercomputers, Academic Press, San Diego.
O'Neal, D., and Sunmonu, A. (1989). Finite Element Codes—Performance Evaluation and Optimization Techniques, Technical report, University of Pittsburgh, Pittsburgh, Pennsylvania.
Pittsburgh Supercomputing Center (PSC) (1989). Research code QFEPDE, origin unknown, Pittsburgh, Pennsylvania.
Schönauer, W. (1987).Scientific Computing on Vector Computers, Elsevier Science Publishers, Amsterdam.
Silvester, D. (1988). Optimising finite element matrix calculations using the general technique of element vectorisation,Parallel Comput. 6, 157–164.
Strang, G., and Fix, G. (1973).An Analysis of the Finite Element Method, Prentice-Hall, Englewood Cliffs, New Jersey.
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O'Neal, D.C. Optimization of finite element codes. J Sci Comput 5, 245–262 (1990). https://doi.org/10.1007/BF01089167
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DOI: https://doi.org/10.1007/BF01089167