Abstract
We present a parallel algorithm for the solution of partial differential equations representing a 3-D diffusion process of the underground water by a finite difference method. The algorithm belongs to a class of the incomplete LU factorization methods, where corresponding system of linear algebraic equations is solved by a quasi LU decomposition in every time step. A code realizing the algorithm was written in Fortran 90 programming language using the MPI message passing interface system and was tested on a SGI Origin 2000 parallel computer.
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References
Hofhaus, J., van de Velde, E.F.: Alternating-direction line-relaxation methods on multicomputers. SIAM J. Sci. Comput., Vol 27, No. 2, March 1996 454–478
Ortega, J.M.: Introduction to Parallel and Vector Solution of Linear Systems, Plenum Press, New York and London, (1988)
Benzi, M., Tuma, M.: A sparse approximate inverse preconditioner for nonsymmetric linear systems. SIAM Journal of Scientific Computing 19, (1998) 968–994
Chow, E., Saad, Y.: Approximate inverse preconditioners via sparse-sparse iterations. SIAM Journal of Scientific Computing 19, (1998) 995–1023
Gould, N.I.M., Scott, J.A.: Sparse approximate-inverse preconditioners using normminimization techniques. SIAM Journal of Scientific Computing 19, (1998) 605–625
Bruno, J., Cappello, P.: Implementing the 3-D alternating direction method on the hypercube. Journal of Parallel and Distributed Computing 23, (1994) 411–417
Tsompanopoulou, P., Vavalis, E.: ADI methods for cubic spline discretizations of elliptic PDEs. SIAM Journal of Scientific Computing 19, (1998) 341–363
Walters, R.W., Dwoyer, D.L., Hassan, H.A.: A strongly implicit procedure for the compressible Navier-Stokes equations. AIAA Journal, Vol. 24, No. 1, (1985) 6–12
Alden, J.A., Booth J., Compton, R.G., Dryfe, R.A.W., Sanders, G.H.W.: Diffusional mass transport to microband electrodes of practical geometries: A simulation study using the strongly implicit procedure. Journal of Electroanalytical Chemistry 389, (1995) 4554
Stone, H.L.: Iterative solution of implicit approximations of multidimensional partial differential equations. SIAM J. Numer. Anal., Vol. 5, No. 3, (1968)530–558
Technical Overview of the Origin Family, http://www.sgi.com/Products/hardware/servers/technology/
Snir, M., Otto, S., Huss-Lederman, S., Walker, D., Dongarra, J.: MPI: The Complete Reference, The MIT Press, Cambridge, Massachusetts, London,England (1996)
Hluchy, L., Godlevsky A., Halada, L., Dobrucky, M., Tran, D.V.: Ground water flow modeling in distributed environment. Proc. of DAPSY’98, Budapest, (Sept. 27–29, 1998) 155–161.
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© 1999 Springer-Verlag Berlin Heidelberg
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Halada, L., Lucká, M. (1999). A Parallel Strongly Implicit Algorithm for Solving of Diffusion Equations. In: Zinterhof, P., Vajteršic, M., Uhl, A. (eds) Parallel Computation. ACPC 1999. Lecture Notes in Computer Science, vol 1557. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-49164-3_8
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DOI: https://doi.org/10.1007/3-540-49164-3_8
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