An improved numerical method for balanced truncation for symmetric second-order systems.
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| Title: | An improved numerical method for balanced truncation for symmetric second-order systems. |
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| Authors: | Benner, Peter1 (AUTHOR), Kürschner, Patrick1 (AUTHOR) kuerschner@mpi-magdeburg.mpg.de, Saak, Jens1 (AUTHOR) |
| Source: | Mathematical & Computer Modelling of Dynamical Systems. Dec2013, Vol. 19 Issue 6, p593-615. 23p. |
| Subjects: | Numerical analysis, Balanced truncation, Mathematical symmetry, Lyapunov functions, Iterative methods (Mathematics), Mathematical models |
| Abstract: | We consider balanced truncation model order reduction for symmetric second-order systems. The occurring large-scale generalized and structured Lyapunov equations are solved with a specially adapted low-rank alternating directions implicit (ADI) type method. Stopping criteria for this iteration are investigated, and a new result concerning the Lyapunov residual within the low-rank ADI method is established. We also propose a goal-oriented stopping criterion which tries to incorporate the balanced truncation approach already during the ADI iteration. The model reduction approach using the ADI method with different stopping criteria is evaluated on several test systems. [ABSTRACT FROM AUTHOR] |
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| Database: | Engineering Source |
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| Abstract: | We consider balanced truncation model order reduction for symmetric second-order systems. The occurring large-scale generalized and structured Lyapunov equations are solved with a specially adapted low-rank alternating directions implicit (ADI) type method. Stopping criteria for this iteration are investigated, and a new result concerning the Lyapunov residual within the low-rank ADI method is established. We also propose a goal-oriented stopping criterion which tries to incorporate the balanced truncation approach already during the ADI iteration. The model reduction approach using the ADI method with different stopping criteria is evaluated on several test systems. [ABSTRACT FROM AUTHOR] |
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| ISSN: | 13873954 |
| DOI: | 10.1080/13873954.2013.794363 |
