## Dimension Reduction of Large-Scale Systems: Proceedings of a Workshop held in Oberwolfach, Germany, October 19-25, 2003Peter Benner, Volker Mehrmann, Danny C. Sorensen In the past decades, model reduction has become an ubiquitous tool in analysis and simulation of dynamical systems, control design, circuit simulation, structural dynamics, CFD, and many other disciplines dealing with complex physical models. The aim of this book is to survey some of the most successful model reduction methods in tutorial style articles and to present benchmark problems from several application areas for testing and comparing existing and new algorithms. As the discussed methods have often been developed in parallel in disconnected application areas, the intention of the mini-workshop in Oberwolfach and its proceedings is to make these ideas available to researchers and practitioners from all these different disciplines. |

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### Contents

Model Reduction Based on Spectral Projection Methods | 5 |

SmithType Methods for Balanced Truncation of Large Sparse Systems | 49 |

Balanced Truncation Model Reduction for LargeScale Systems in Descriptor Form | 83 |

On Model Reduction of Structured Systems | 117 |

Model Reduction of TimeVarying Systems | 131 |

Model Reduction of SecondOrder Systems | 149 |

Arnoldi Methods for StructurePreserving Dimension Reduction of SecondOrder Dynamical Systems | 173 |

FadeType Model Reduction of SecondOrder and HigherOrder Linear Dynamical Systems | 191 |

Microhotplate Gas Sensor | 333 |

Tunable Optical Filter | 337 |

Convective Thermal Flow Problems | 341 |

Boundary Condition Independent Thermal Model | 345 |

The Butterfly Gyro | 349 |

A SemiDiscretized Heat Transfer Model for Optimal Cooling of Steel Profiles | 353 |

Model Reduction of an Actively Controlled Supersonic Diffuser | 357 |

Second Order Models LinearDrive MultiMode Resonator and Axi Symmetric Model of a Circular Piston | 363 |

Controller Reduction Using AccuracyEnhancing Methods | 225 |

Proper Orthogonal Decomposition Surrogate Models for Nonlinear Dynamical Systems Error Estimates and Suboptimal Control | 261 |

Oberwolfach Benchmark Collection | 311 |

A File Format for the Exchange of Nonlinear Dynamical ODE Systems | 317 |

Nonlinear Heat Transfer Modeling | 327 |