Paper Info
Title
A parallel adaptive numerical scheme for hyperbolic systems of conservation laws
Abstract
We generalize the rst author's adaptive numerical scheme for scalar rst order conservation laws to systems of equations. The resulting numerical methods generate highly non-uniform, time-dependent grids, and hence are dicult to execute eciently on vector computers such as the Cray or Cyber 205. In contrast, we show that these algorithms may be executed in parallel on alternate computer architectures. We describe a parallel implementation of the algorithm on the Denelcor HEP, a multiple-instruction, multiple-data (MIMD) shared memory parallel computer. ut +f (u)x =0 ;x 2R;t >0; u(x; 0) =u0(x) ;x 2R: The novelty of the method lay in the criteria used to adapt the grid and the experimental demonstration that asymptotic speedup resulted for some problems when compared with a method using the same nite dierence scheme on a xed, uniform grid. Although the adaptive method is unsuitable for execution on vector computers such as the Cray or Cyber 205 because it uses a highly non-uniform, time-dependent computation grid, the algorithm may be executed in parallel on alternate computer architectures. In this paper we extend the algorithm for scalar conservation laws to hyperbolic systems of conservation laws, and we describe a parallel implementation of the algorithm on the Denelcor HEP, a multiple-instruction, multiple- data (MIMD) shared memory parallel computer (16). Because our implementation uses a macro-preprocessor to avoid mention of the specic hardware synchronization primitives provided on the HEP, our programs may be transported to any shared-memory multiprocessor on which the synchronization macro package has been installed.
Year
DOI
Venue
1985
10.1137/0908021
SIAM Journal on Scientific and Statistical Computing
Keywords
DocType
Volume
conservation law,hyperbolic system,parallel adaptive numerical scheme,domain decomposition,parallel processing,load balance,parallel computer,computer architecture,shared memory,numerical method,first order,system of equations
Conference
8
Issue
ISSN
ISBN
2
0196-5204
0-89871-216-5
Citations 
PageRank 
References 
2
0.67
2
Authors
2
Name
Order
Citations
PageRank
Bradley J. Lucier14925.94
Ross Overbeek26213.28