Parallel algorithms for panel methods. (English) Zbl 0744.76095
Summary: A parallel algorithm for the solution of potential flow problems using the panel method of J. L. Hess and A. M. O. Smith [Prog. Aeronaut. Sci. 8, 1-138 (1967)] and conjugate and bi-conjugate gradient techniques is presented. Analysis of the parallelism for the matrix solvers shows the algorithms to have scalable properties as the problem size grows indefinitely large. Speed-up and efficiency values are presented along with experimental and theoretical values for the optimum number of processors for maximum speed-up. It is envisaged that the parallel techniques presented here have applications using other boundary integral methods for solving engineering problems of a more complex nature.
MSC:
| 76M99 | Basic methods in fluid mechanics |
| 76Bxx | Incompressible inviscid fluids |
| 65Y05 | Parallel numerical computation |
Keywords:
conjugate gradients; potential flow; bi-conjugate gradient techniques; matrix solvers; boundary integral methodsReferences:
| [1] | Introduction to Parallel and Vector Solution of Linear Systems, Plenum, New York, 1988. · doi:10.1007/978-1-4899-2112-3 |
| [2] | and , Supercomputing in Engineering Structures, Springer. New York, 1989. · Zbl 0669.73001 |
| [3] | and , ’Parallel processing for panel methods’, Parallel Processing for Fluid Flow, Methods and Systems, The Royal Institute, London, 27 June 1990, pp. 85-94. |
| [4] | Hees, Prog. Aeronaut. Sci. 8 pp 1– (1967) |
| [5] | ’Development of an efficient and versatile panel method for aerodynamic problems’, Ph.D. Thesis, University of Leeds, March 1979. |
| [6] | ’A field integral method for the calculation of transonic flow over complex aerodynamic shapes’, Ph.D. Thesis, University of Leeds, August 1987. |
| [7] | and , ’Integrating sculptured surface design with the panel method for flow visualisation’, in (ed.), Mathematics of Surfaces III, Clarendon, Oxford, 1989, pp. 301-315. |
| [8] | The Boundary Element Method for Engineers. Pen tech, London, 1978. |
| [9] | Ryan, Notes Numer. Fluid Mech 20 pp 335– (1988) |
| [10] | An Introduction to Fluid Mechanics, Cambridge University Press, Cambridge 1967. |
| [11] | and , ’Blend design as a boundary value problem’, in and (eds), Geometrical Modelling (Theory and Practice), Springer Berlin, 1989, pp. 221-234. · doi:10.1007/978-3-642-61542-9_14 |
| [12] | Bloor, CAD 22 pp 202– (1990) |
| [13] | Foundations of Potential Theory, Dover, New York, 1929. · JFM 55.0282.01 · doi:10.1007/978-3-642-90850-7 |
| [14] | and , ’Iterative methods for non-symmetric linear systems’, in and (eds), Iterative Methods for Large Linear Systems, Academic, New York, 1990. |
| [15] | ’Conjugate gradient methods for indefinite systems’, in Lecture Notes in Mathematics, Vol. 506, 1975, pp. 73-89. |
| [16] | Aeronautical Journal of Royal Aeronautical Society Paper No. 1394, June/July 1986. |
| [17] | Gropp, Comput. Fluids 18 pp 289– (1990) |
| [18] | ’A computational model of the flow of bone. marrow in the vicinity of a needle’. Final Year Report, Department of Mechanical Engineering, University of Leeds, April 1990. |
| [19] | Miller, Parallelogram 32 pp 14– (1990) |
| [20] | and , ’The solution of convective problems in laminar flow’, in Boundary Elements, Proc. 5th Int. Conf. on Boundary Elements, Springer, New York, 1983, pp. 251-274. |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
