Conversion Methods, Block Triangularization, and Structural Analysis of Differential-Algebraic Equation Systems
| Autor: | Tan, Guangning, Nedialkov, Nedialko S., Pryce, John D. |
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| Rok vydání: | 2016 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In a previous article, the authors developed two conversion methods to improve the $\Sigma$-method for structural analysis (SA) of differential-algebraic equations (DAEs). These methods reformulate a DAE on which the $\Sigma$-method fails into an equivalent problem on which this SA is more likely to succeed with a generically nonsingular Jacobian. The basic version of these methods processes the DAE as a whole. This article presents the block version that exploits block triangularization of a DAE. Using a block triangular form of a Jacobian sparsity pattern, we identify which diagonal blocks of the Jacobian are identically singular and then perform a conversion on each such block. This approach improves the efficiency of finding a suitable conversion for fixing SA's failures. All of our conversion methods can be implemented in a computer algebra system so that every conversion can be automated. Comment: 25 pages, 1 figure |
| Databáze: | arXiv |
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