Matrix ordering strategies for process engineering: graph partitioning algorithms for parallel computation
The solution of large-scale chemical process simulation and optimization problems using parallel computation requires algorithms that can take advantage of multiprocessing when solving the large, sparse matrices that arise. Parallel algorithms require that the matrices be partitioned in order to dis...
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| Vydané v: | Computers & chemical engineering Ročník 23; číslo 8; s. 1063 - 1073 |
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| Jazyk: | English |
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Oxford
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01.08.1999
Elsevier |
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| ISSN: | 0098-1354, 1873-4375 |
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| Abstract | The solution of large-scale chemical process simulation and optimization problems using parallel computation requires algorithms that can take advantage of multiprocessing when solving the large, sparse matrices that arise. Parallel algorithms require that the matrices be partitioned in order to distribute computational work across processors. One way to accomplish this is to reorder the matrix into a bordered block-diagonal form. Since this structure is not always obtained from the equation generation routine, an algorithm to reorder the rows and columns of the coefficient matrix is needed. We describe here a simple graph partitioning algorithm that creates a bordered block-diagonal form that is suitable for use with parallel algorithms for the solution of the highly asymmetric sparse matrices arising in process engineering applications. The method aims to create a number of similarly sized diagonal blocks while keeping the size of the interface matrix, which may represent a bottleneck in the parallel computation, reasonably small. Results on a wide range of test problems indicate that the reordering algorithm is able to find such a structure in most cases, and requires much less reordering time than previously used graph partitioning methods. |
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| AbstractList | The solution of large-scale chemical process simulation and optimization problems using parallel computation requires algorithms that can take advantage of multiprocessing when solving the large, sparse matrices that arise. Parallel algorithms require that the matrices be partitioned in order to distribute computational work across processors. One way to accomplish this is to reorder the matrix into a bordered block-diagonal form. Since this structure is not always obtained from the equation generation routine, an algorithm to reorder the rows and columns of the coefficient matrix is needed. We describe here a simple graph partitioning algorithm that creates a bordered block-diagonal form that is suitable for use with parallel algorithms for the solution of the highly asymmetric sparse matrices arising in process engineering applications. The method aims to create a number of similarly sized diagonal blocks while keeping the size of the interface matrix, which may represent a bottleneck in the parallel computation, reasonably small. Results on a wide range of test problems indicate that the reordering algorithm is able to find such a structure in most cases, and requires much less reordering time than previously used graph partitioning methods. |
| Author | Camarda, Kyle V. Stadtherr, Mark A. |
| Author_xml | – sequence: 1 givenname: Kyle V. surname: Camarda fullname: Camarda, Kyle V. email: markst@nd.edu organization: Department of Chemical Engineering, University of Illinois, 600 S. Mathews Avenue, Urbana, IL 61801 USA – sequence: 2 givenname: Mark A. surname: Stadtherr fullname: Stadtherr, Mark A. organization: Department of Chemical Engineering, University of Notre Dame, Notre Dame, IN 46556, USA |
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| Cites_doi | 10.1145/800153.804930 10.1016/0098-1354(93)80024-H 10.1016/S0167-8191(96)00047-6 10.1002/aic.690431207 10.1002/j.1538-7305.1970.tb01770.x 10.1016/S0098-1354(97)87541-2 10.1109/DAC.1982.1585498 10.1002/aic.690430417 10.1016/0098-1354(88)85069-5 10.1016/0098-1354(95)00074-7 10.1016/0098-1354(94)00081-6 10.1145/355958.355963 10.1137/0911048 10.1016/0098-1354(78)80008-8 10.1109/SUPERC.1992.236662 |
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| Keywords | Design Graph partitioning Parallel computation Simulation Sparse matrices Optimization Parallel algorithm Sparse matrix Problem solving Large scale system |
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| References_xml | – volume: 20 start-page: 1123 year: 1996 end-page: 1132 ident: BIB3 article-title: Reliability of iterative linear solvers in chemical process simulation publication-title: Computers & Chemical Engineering – volume: 7 start-page: 315 year: 1981 end-page: 330 ident: BIB5 article-title: On algorithms for obtaining a maximum transversal publication-title: ACM Transactions in Math Software – reference: Schweikert, D. G. and Kernighan B. W. (1972). A proper model for the partitioning of electrical circuits. In Proceedings of the ninth ACM-IEEE Design Automation Workshop, ACM, Dallas. – volume: 43 start-page: 1032 year: 1997 end-page: 1040 ident: BIB11 article-title: A parallel frontal solver for large scale process simulation and optimization publication-title: American Institute of Chemical Engineers Journal – reference: (pp. 414–423). IEEE Press, Los Alamitos, CA. – reference: -way partitioning scheme for irregular graphs. 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SIAM J publication-title: Science of Statistical Computing doi: 10.1137/0911048 – ident: 10.1016/S0098-1354(99)00271-9_BIB10 – ident: 10.1016/S0098-1354(99)00271-9_BIB8 – volume: 91 start-page: 313 issue: 304 year: 1995 ident: 10.1016/S0098-1354(99)00271-9_BIB17 article-title: Plantwide dynamic simulation on supercomputers: modelling a Bayer distillation process publication-title: American Institute of Chemical Engineers Symposium Series – volume: 2 start-page: 61 year: 1978 ident: 10.1016/S0098-1354(99)00271-9_BIB15 article-title: Decomposition of very large scale Newton-Raphson based flowsheeting problems publication-title: Computers & Chemical Engineering doi: 10.1016/0098-1354(78)80008-8 – ident: 10.1016/S0098-1354(99)00271-9_BIB16 doi: 10.1109/SUPERC.1992.236662 |
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| SubjectTerms | Applications of mathematics to chemical engineering. Modeling. Simulation. Optimization Applied sciences Chemical engineering Design Exact sciences and technology Graph partitioning Optimization Parallel computation Simulation Sparse matrices |
| Title | Matrix ordering strategies for process engineering: graph partitioning algorithms for parallel computation |
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