Abstract
Efficient numerical algorithms for the solution of fluid flow problems on sequential machines are the major focus of research within our group. However with the recent acquisition of a MIMD machine, attempts have been made to obtain parallel implementations of these algorithms. This paper will describe the difficulties involved in two such attempts: the solution of a triple—layer diffusion problem used in modelling electrochemical sensors; and the solution of the Navier—Stokes equations in a driven cavity using multigrid.
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References
Shah, T.M. Analysis of the Multigrid Method, DPhil thesis, Oxford University Computing Laboratory, Oxford, 1989.
Clark, L.C. Monitor and Control of Blood and Tissue Oxygen Tensions, Trans. Am. Soc. Art. Intern. Organs, Vol.2, pp. 41–60, 1956.
Peaceman, D.W. and Rachford, H.H. The Numerical Solution of Parabolic and Elliptic Differential Equations, J. Soc. Indust. Appl. Math., Vol.3, pp. 28–41, 1955.
Gavaghan, D.J. and Rollett, J.S. The Correction of Boundary Singularities in Numerical Simulation of Time-dependent Diffusion Processes at Unshielded Disc Electrodes, J. Electroanal. Chem., Vol. 295, pp. 1–14, 1990.
Inmos. Transputer Development System, Prentice Hall, London, 1988.
Gourlay, G.R. Hopscotch: A Fast Second Order Partial Differential Equation Solver, J. Inst. Maths. Applies., Vol.6, pp. 375–390, 1970.
Gwilliam, C.S. A Parallel Algorithm for the Navier-Stokes Equations in a Driven CavitY, MSc thesis, Oxford University Computing Laboratory, Oxford, 1990.
Harlow, F.H. and Welch, J.E. Numerical Calculation of Time-dependent Viscous Incompressible Flow of Fluid with Free Surface, The Physics of Fluids, Vol.8(12), pp. 2182–2189, Dec 1965.
Brandt, A. Multi-level Adaptive Solutions to Boundary-value Problems, Mathematics of Computation, Vol.31(138), pp. 333–390, April 1977.
Sivaloganathan, S. and Shaw, G. A Multigrid Method for Recirculating Flows, International Journal for Numerical Methods in Fluids, Vol.8, pp. 417–440, 1988.
Stäben, K. and Trottenberg, U. Multigrid Methods: Fundamental Algorithms, Model Problem Analysis and Applications, Springer Verlag Lecture Notes in Mathematics, Vol.960, pp. 1–176, 1981.
Johnsson, S.L. Saad, Y. and Schultz, M.H. Research Report, YALEU/DCS/RR-382, Oct. 1985.
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© 1991 Computational Mechanics Publications
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Gavaghan, D.J., Gwilliam, C.S., Rollett, J.S. (1991). Difficulties in Parallelising Efficient Sequential Codes. In: Brebbia, C.A., Peters, A., Howard, D. (eds) Applications of Supercomputers in Engineering II. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-3660-0_2
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DOI: https://doi.org/10.1007/978-94-011-3660-0_2
Publisher Name: Springer, Dordrecht
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