Abstract
We propose asynchronous parallel algorithms for numerically solving systems of hyperbolic partial differential equations. The algorithms are based on the solutions along the characteristic directions. We show that the characteristic directions can be computed in parallel without the need for sharing information or synchronizing on a common time step. This permits the development of efficient asynchronous parallel algorithms. Our solutions cover the cases when the characteristic lines are intersected to form shock waves. We discuss the time performance of our algorithms as well as their implementation on a parallel computer.
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References
Amitai, D., Averbuch, A., Israeli, M., and Itzikowitz, S. (1991). An asynchronous approach to the numerical solution of pdes on mimd multiprocessors (unpublished manuscript).
Courant, R. and Hilbert, D. (1962).Methods of Mathematical Physics Volume II, Interscience Publishers.
Godunov, S. K. and Ryabenkii, V. S. (1987).Difference Schemes, North Holland.
Mertens, J. and Becker, K. (1989). Numerical solution of flow equations: An aircraft design's view. In allman, J. and Jeltsch, R., editors,Nonlinear Hyperbolic Equations—Theory, Computation Methods, and Applications, theProc. of the Second Int'l. Conf. on Nonlinear Hyperbolic Problems, Aachen, Germany, March, 1988, pp. 40–412, Friedr. Vieweg & Sohn, 1989.
Morton, K. W. and Childs, P. N. (1989). Characteristic Galerkin methods for hyperbolic systems. In Ballman, J. and Jeltsch, R., editors,Nonlinear Hyperbolic Equations-Theory, Computation Methods, and Applications, theProc. of the Second Int'l. Conf. on Nonlinear Hyperbolic Problems, Aachen, Germany, March, 1988, pp. 435–455, Friedr. Vieweg & Sohn, 1989.
Rozdestvenskii, and Janenko, N. N. (1983).Systems of Quasilinear Equations and Their Applications to Gas Dynamics, AMS Vol. 53.
Smith, G. D. (1986).Numerical Solution of Partial Differential Equations: Finite Difference Methods, Clarendon Press Oxford.
Zukov, A. I. (1967). Application of the method of characteristics to the numerical solution of one-dimensional problem in gas dynamics.Trudy Math. Inst. Steklov, 58.
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Supported by the R&D administration of the Ministry of Defense and the Ministry of Immigration Absorption, Israel.
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Ioffe, L., Pinter, S.S. Applying asynchronous parallel characteristic methods for solving systems of hyperbolic PDEs. J Sci Comput 8, 195–218 (1993). https://doi.org/10.1007/BF01060930
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DOI: https://doi.org/10.1007/BF01060930