The Efficient Use of Vector Computers with Emphasis on Computational Fluid Dynamics pp 1-34 | Cite as

# Introduction to the Workshop: Some Bottlenecks and Deficiencies of Existing Vector Computers and Their Consequences for the Development of General PDE Software

## Summary

In the first part of this introductory paper a review of the different types of vector computer programs and algorithms is presented. Then the hardware of the presently most relevant vector computers together with their bottlenecks will be discussed as well as the trends in development. The weakest point of the existing vector computers is the compiler, this problem is closely related to the lacking vector statements of Fortran 77. Therefore some proposals of Fortran 8X will be presented. In the second part of this paper the authors report about some experiences which have been obtained in the development of “black-box software” for PDE’s. There will be given a pragmatic definition of a “data flow algorithm”, and the separation of data selection and processing will be demonstrated for the evaluation of difference formulae. Then the i/o bottleneck is discussed for the iterative solution of large linear systems in diagonal storing. There will be presented our view of portability of software for different vector computers. The numerical example for ILU-preconditioning demonstrates how vecto-risation might invert experiences gained on general purpose computers. Finally some examples demonstrate the application of the Fidisol program package on different vector computers.

## Keywords

Main Memory Vector Length Peak Performance Vector Computer Secondary Storage## Preview

Unable to display preview. Download preview PDF.

## References

- [1]HOCKNEY, R.W., JESSHOPE, C.R.: “Parallel Computers”, Adam Hilger Ltd, Bristol 1983.zbMATHGoogle Scholar
- [2]GENTZSCH, W.: “Vectorization of Computer Programs with Application to Computational Fluid Dynamics”, Notes on Numerical Fluid Mechanics, vol.8, Friedr.Vieweg & Sohn, Braunschweig/Wiesbaden 1984.CrossRefGoogle Scholar
- [3]HOLLENBERG, J., “SX, NEC Corporation’s supercomputer”, Supercomputer 1, Amsterdam Universities Computing Centre (SARA) , May 1984, 6–8.Google Scholar
- [4]ARNOLD, C.N., “Performance Evaluation of Three Automatic Vectorizer Packages”, Proceedings of the 1982 Internat* Conf. on Parallel Processing, IEEE Computer Society Press, 235–242 (1982).Google Scholar
- [5]KUCK, D.J., “Automatic Prosram Restructuring for High Speed Computation”, Conpar 81 , Lecture Notes in Computer Science 111, Springer-Verlag, Berlin, New York 1981, 66–84.Google Scholar
- [6]MIURA, K., UCHIDA, K., “Facom Vector Processor VP-100/VP-200”, High-Speed Computation, edited by J.S. Kowalik, Springer-Verlag, Berlin, New York, 127–138 (1984).Google Scholar
- [7]Proposals Approved for Fortran 8X, X3J3 Committee, Document SS, January 1985.Google Scholar
- [8]REID, J. K., “The Array Features in Fortran 8X”, PDE-Soft-ware: Modules, Interfaces and Systems, edited by B. Engquist and T. Smedsaas, North-Holland, Amsterdam, New York, 351–354 (1984).Google Scholar
- [9]REID, J. K., WILSON, A., “Array Processing in Fortran 8X”, to appear in the Proceedings of the Conference “Vector and Parallel Processors in Computational Science II”, Oxford, August 28–31, 1984, as a supplement to Computer Physics Communications (1985).Google Scholar
- [10]WAGNER, J. L., “Status of Work Toward Revision of Programming Language Fortran”, Signum Newsletter, vol.19, Nr. 3, July 1984.Google Scholar
- [11]DENNIS, J. B., “Data Flow Supercomputers”, Computer 13, 48–56 (1980).CrossRefGoogle Scholar
- [12]SCHÖNAUER, W., SCHNEPF, E., MÜLLER, H., “Designing PDE software for vector computers as a “data flow algorithm””, to appear in the Proceedings of the Conference “Vector and Parallel Processors in Computational Science II”, Oxford, August 28–31, 1984, as a supplement to Computer Physics Communications (1985).Google Scholar
- [13]SCHÖNAUER, W., MÜLLER, H., SCHNEPF, E., “Numerical tests with biconjugate gradient type methods”, Zamm 65, T391–393 (1984).Google Scholar
- [14]VAN DER VORST, H.A, “Preconditioning by Incomplete Decompositions”, ACCU-reeks 32, Academisch Computer Centrum Utrecht (1982).Google Scholar
- [15]KIGHTLEY, J. R., JONES, I. P., “A comparison of conjugate gradient preconditionings for three-dimensional problems on a CRAY-1”, CSS 162, Computer Science and Systems Division, AERE Harwell (1934).Google Scholar
- [16]SCHÖNAUER, W., SCHNEPF, E., RAITH, K., “The redesign and vectorization of the SLDGL-program package for the self-adaptive solution of nonlinear systems of elliptic and parabolic PDE’s”, PDE Software: Modules, Interfaces and Systems, edited by B. Engquist and T. Smedsaas, North-Holland, Amsterdam (1984 pp. 41–66.Google Scholar
- [17]SCHÖNAUER, W., SCHNEPF, E., MÜLLER, H., “PDE software for vector computers”, Advances in Computer Methods for Partial Differential Equations — V, edited by R. Vichnevetsky and R. S. Stepleman, IMACS 1984, pp. 258–267.Google Scholar
- [18]SCHÖNAUER, W., SCHNEPF, E., MÜLLER, H., “Variable step size/ variable order PDE solver with global optimisation”, to appear in the Proceedings of the 11th IMACS World Congress, Oslo, August 5–9, 1985.Google Scholar
- [19]OERTEL, H, jun., “Thermische Zellularkonvektion”, Habilitationsschrift Universität Karlsruhe (1979).Google Scholar