ABSTRACT
This paper presents the design, development and application of a computational infrastructure to support the implementation of parallel adaptive algorithms for the solution of sets of partial differential equations. The infrastructure is separated into multiple layers of abstraction. This paper is primarily concerned with the two lowest layersof this infrastructure: a layer which defines and implements dynamic distributed arrays (DDA), and a layer in which several dynamic data and programming abstractions are implemented in terms of the DDAs. The currently implemented abstractions are those needed for formulation of hierarchical adaptive finite difference methods, hp-adaptive finite element methods, and fast multipole method for solution of linear systems. Implementation of sample applications based on each of these methods are described and implementation issues and performance measurements are presented.
- M. Parashar and J. C. Browne, System Engineering for High Performance Computing Software: The HDDA/DAGH Infrastructure for Implementation of Parallel Structured Adaptive Mesh Refinement, to be published in Structured Adaptive Mesh Refinement Grid Methods, IMA Volumes in Mathematics and its Applications, Springer-Verlag, 1997.Google Scholar
- Harold Carter Edwards,A Parallel Infrastructure for Scalable Adaptive Finite Element Methods and its Application to Least Squares C-infinity Collocation, PhD Thesis, The University of Texas at Austin, May 1997.Google Scholar
- Hans Sagan, Space Filling Curves, Springer-Verlag, 1994.Google Scholar
- H. F. Korth, A. Silberschatz, Database System Concepts,. McGraw Hill. New York, 1991. Google ScholarDigital Library
- W. Litwin. Linear Hashing: a New Tool for File and Table Addressing, Proceedings of the 6th Conference on VLDB, Montreal, Canada, 1980.Google Scholar
- Robert Sedgewick. Algorithms, Addison-Wesley, Reading, Massachusetts, 1983. Google ScholarDigital Library
- Marsha J. Berger, Joseph Oliger, Adaptive Mesh-Refinement for Hyperbolic Partial Differential Equations, Journal of Computational Physics, pp. 484-512, 1984.Google Scholar
- Manish Parashar and James C. Browne, Distributed Dynamic Data-Structures for Parallel Adaptive Mesh-Refinement, Proceedings of the International Conference for High Performance Computing, pp. 22-27, Dec. 1995.Google Scholar
- Manish Parashar and James C. Browne, On Partitioning Dynamic Adaptive Grid Hierarchies, Proceedings of the 29th Annual Hawaii International Conference on System Sciences, 1:604-613, Jan. 1996. Google ScholarDigital Library
- J. Masso and C. Bona, Hyperbolic System for Numerical Relativity, Physics Review Letters, 68(1097), 1992.Google Scholar
- Robert van de Geijn, Using PLAPACK: Parallel Linear Algebra Package, The MIT Press, 1997. Google ScholarDigital Library
- Leslie Greengard, The rapid evaluation of potential fields in particle systems, 1987. Google ScholarDigital Library
- Jürgen K. Singer, The Parallel Fast Multipole Method in Molecular Dynamics, PhD thesis, The University of Houston, August 1995. Google ScholarDigital Library
- Jürgen K. Singer, Parallel Implementation of the Fast Multipole Method with Periodic Boundary Conditions, East-West Journal on Numerical Mathematics, 3(3), October 1995.Google Scholar
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