Hypercube algorithms and implementations
Parallel algorithms are presented for important components of Computational Fluid Dynamics algorithms along with implementations on hypercube computers. Elliptic equations with 1.6 million unknowns and hyperbolic equations with 4 million unknowns have been solved using 128 processors. 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 inter-process communication is hidden in library routines. A general parallel computer simulator is described along with its use in the development of the algorithms.
- Research Organization:
- New York Univ., NY (USA). Courant Mathematics and Computing Lab.
- DOE Contract Number:
- AC02-76ER03077
- OSTI ID:
- 5870655
- Report Number(s):
- DOE/ER/03077-271; CONF-8511169-1; ON: DE86007439
- Country of Publication:
- United States
- Language:
- English
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