Hypercube algorithms and implementations
Parallel algorithms are presented for important components of computational fluid dynamics algorithms along with implementations on hypercube computers. These programs, used to solve hyperbolic and elliptic equations, achieve high efficiency on 5- and 7-dimensional hypercubes. For elliptic equations, a parallel preconditioned conjugate gradient method is described which has been used to solve pressure equations discretized with high order finite elements on irregular grids. A parallel full multigrid method and a parallel fast Poisson solver are also presented. Hyperbolic conservation laws have been discretized with parallel versions of finite difference methods and with the random choice method. The performance of these algorithms is analyzed in terms of machine efficiency, communication time, bottlenecks and software development costs. A key aspect of this work is the development of a library of parallel operators for distributed vectors and matrices, efficient for both full and sparse data. The implementation of these operators on hypercubes is described along with measurements of communication effects. Using the library, the PDE algorithms mentioned above have been implemented on both serial computers and on hypercubes without any code modification. All interprocess communication is hidden in library routines. A general parallel computer simulator is described along with its use in the development of the algorithms. The relation of the model problems solved here to the more complex physical problems encountered in real fluids is discussed. Techniques are developed for comparing the behavior of an algorithm on different architectures as a function of problem size and local computational effort.
- Research Organization:
- Courant Institute of Mathematical Sciences, New York Univ., New York, NY
- OSTI ID:
- 6576353
- Journal Information:
- SIAM J. Sci. Stat. Comput.; (United States), Journal Name: SIAM J. Sci. Stat. Comput.; (United States) Vol. 8:2; ISSN SIJCD
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
990210* -- Supercomputers-- (1987-1989)
ALGORITHMS
ANALOG SYSTEMS
COMMUNICATIONS
COMPUTER ARCHITECTURE
COMPUTER CODES
COMPUTERS
CONSERVATION LAWS
COST
DATA TRANSMISSION
DIFFERENTIAL EQUATIONS
DIGITAL COMPUTERS
EFFICIENCY
EQUATIONS
FLUID MECHANICS
FUNCTIONAL MODELS
LIBRARIES
MATHEMATICAL LOGIC
MATRICES
MECHANICS
PARALLEL PROCESSING
PARTIAL DIFFERENTIAL EQUATIONS
PERFORMANCE
POISSON EQUATION
PROGRAMMING
SIMULATORS
SUPERCOMPUTERS
TENSORS
TIME DEPENDENCE
VECTORS