Abstract
The choice of data structures influences the parallelization, efficiency and the manageability of a mesh refinement program. We introduce a mixed directed-undirected graph that combines both communication and scheduling needs. An inverted index is maintained for the directed graph to improve code performance and readability.
Similar content being viewed by others
References
Babuska, I., J. Chandra and J. E. Flaherty:Adaptive computational methods for partial differential equations, SIAM, Philadelphia, Pa., 1983, (0-89871-191-6).
Bell, J. L.:Data Structures For Scientific Simulation Programs, Ph.D. Thesis, University of Colorado, 1983.
Berger, M. J.:Adaptive Mesh Refinement for Hyperbolic Partial Differential Equations, Ph.D. Dissertation, Stanford University, 1982.
Berger, M. J.:Data Structures for Adaptive Mesh Refinement, inAdaptive Computational Methods for Partial Differential Equations, SIAM, Philadelphia, Pa., 1983, (0-89871-191-6).
Berger, M. J. and P. Colella:Local adaptive mesh refinement for shock hydrodynamics, to appear in J. Comput. Phys.
Bolstad, J. H.:An Adaptive Finite Difference Method for Hyperbolic Systems in One Space Dimension, Lawrence Berkeley Lab Report LBL 13287 Rev., 1982.
Chin, R. C. Y., G. W. Hedstrom, J. R. McGraw and F. A. Howes:Parallel Computation of Multiple-Scale Problems, Lawrence Livermore National Laboratory Report UCRL-92007, Rev. 1, 1985.
Ewing, Richard E.:Adaptive local grid refinement, inMathematical and Computational Methods in Seismic Exploration and Reservoir Modeling, SIAM, Philadelphia 1986.
Gropp, William D. and David E. Keyes:Complexity of parallel implementation of domain decomposition techniques for elliptic partial differential equations, SIAM J. Sci. Stat. Comput., Vol. 9 No. 2, March 1988.
Oran, E. S. and J. P. Boris:Numerical Simulation of Reactive Flow, Elsevier Science Publishing Co., New York, 1987, (0-444-01251-6).
Perkins, A. L.:Tailoring Domain Decomposition to The Network Structure for Parallel Processing of Fluid Dynamics, Lawrence Livermore National Laboratory Report UCID-21609, 1988.
Perkins, A. L.:Parallel Heterogeneous Mesh Refinement for Multidimensional Convection-Diffusion Equations Using an Euler-Lagrange Method, Ph.D. Thesis, June 1989, UCRL-53950.
Schlichting, H.:Boundary Layer Theory, McGraw Hill Book Company, New York, N.Y., 1979, 47–69, (0-07-055334-3).
Schwarz, H. A.:Über einen Grenzübergang durch alternierendes Verfahren, Gesammelte Mathematische Abhandlungen 2, Springer Verlag, Berlin, 1869, (translation).
Scroggs, J. S.:The Solution of a Parabolic Partial Differential Equation via Domain Decomposition: The Synthesis of Asymptotic and Numerical Analysis, Ph.D. Thesis, University of Illinois, 1988.
Spall, M. A. and W. R. Holland:A nested primitive equation model for oceanic applications, to appear in J. Phys. Ocean.
Author information
Authors and Affiliations
Additional information
This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under contract No. W-7405-Eng-48.
Rights and permissions
About this article
Cite this article
Perkins, A.L. A mixed directed-undirected data structure for a parallel implementation of a domain decomposition algorithm. BIT 32, 598–608 (1992). https://doi.org/10.1007/BF01994844
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01994844