Ordering Strategies for Sparse Matrices in Chemical Process Simulation
Camarda, Kyle Vincent
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Permalink
https://hdl.handle.net/2142/82438
Description
Title
Ordering Strategies for Sparse Matrices in Chemical Process Simulation
Author(s)
Camarda, Kyle Vincent
Issue Date
1997
Doctoral Committee Chair(s)
Stadtherr, Mark A.
Department of Study
Chemical Engineering
Discipline
Chemical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Chemical
Language
eng
Abstract
The effective application of supercomputers in the areas of chemical process simulation, design and optimization requires the use of novel computational strategies. Frontal methods have been shown to effectively use the vector and parallel capabilities of such machines to solve the large, sparse matrices which arise from such problems. Since the row and column ordering of these matrices has a direct impact on the efficiency of frontal methods, this work has developed a number of ordering strategies specifically designed for use with frontal methods. The strategies investigated include local heuristic strategies, graph, partitioning techniques, and iterative methods. These methods were compared with previously used orderings, in terms of structural criteria, solution time, and parallel speedup. For the one processor frontal method, the local heuristic ordering RMCD was found to outperform other methods when the matrix is to be solved a small number of times. A new version of the MNC orderings of Coon (1989), known as NMNC, is presented which runs in linear time and produces orderings which are amenable to solution using frontal methods. Iterative algorithms based on a combinatorial optimization formulation of the reordering problem also showed promise. The graph-partitioning algorithms MNC and NMNC were tested for the creation of bordered block-diagonal matrix orderings for use with the parallel frontal method. The NMNC ordering was found to create more diagonal blocks, and have a lower running time than MNC. The parameters used with NMNC must be carefully chosen so as to keep the size of the interface matrix small and maximize the parallel speedup obtainable.
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