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http://hdl.handle.net/11375/21259
Title: | A Tool for Automatic Index Analysis of Differential-Algebraic Equations |
Authors: | Liu, Ning |
Advisor: | Nedialkov, Ned Qiao, Sanzheng |
Department: | Computing and Software |
Keywords: | automatic index analysis, differential-algebraic equations, circuit simulation |
Publication Date: | Sep-2006 |
Abstract: | <p> Systems of differential-algebraic equations (DAEs) arise in applications such as circuit simulation, models of chemical processes, optimal control, and multi-body dynamics. Informally, the index of a DAE is the number of differentiations needed to convert it to an ordinary differential equation. The index generally indicates the difficulty of solving a DAE problem. The higher the index of a DAE, the more difficult it is to solve it numerically.</p> <p> Structural index analysis plays a crucial role in solving DAE problems. In this thesis, we present two methods for index analysis, namely, Pryce's structural analysis (SA) and Linninger's symbolic-numeric (SN) analysis. We provide a Matlab tool implementing these two approaches: an Automatic Structural Index Analyzer (ASIA). We discuss the underlying algorithms, which include generating a signature matrix and computing SA index, computing a system Jacobian, and generating a symbolic-numeric matrix and computing SN index. We also present implementation issues and illustrate how ASIA is used.</p> <p> Numerical experiments show that ASIA can produce reliable structural information. We also show examples on which structural analysis fails, and how ASIA detects such situations.<p> |
URI: | http://hdl.handle.net/11375/21259 |
Appears in Collections: | Digitized Open Access Dissertations and Theses |
Files in This Item:
File | Description | Size | Format | |
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Liu_Ning_2006Sept_Masters..pdf | 2.36 MB | Adobe PDF | View/Open |
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