## Schedule

### Jully 22 - 26 (week 1):

lecture | Mon Jul 22 | Tue Jul 23 | Wed Jul 24 | Thu Jul 25 | Fri Jul 26 |

08:00-10:00 | Higham | Higham | Higham | Higham | Hochbruck |

10:00-10:20 | Break | Break | Break | Break | Break |

10:20-12:20 | Hochbruck | Hochbruck | Hochbruck | Hochbruck | Higham |

exercise | |||||

14:30-16:30 | Tutorial | Tutorial | Tutorial | Tutorial | Tutorial |

16:30-17:30 | Seminar |

### July 29 - August 2 (week 2):

lecture | Mon Jul 29 | Tue Jul 30 | Wed Jul 31 | Thu Aug 1 | Fri Aug 2 |

08:00-10:00 | R.-C. Li | R.-C. Li | X. Li | X. Li | X. Li |

10:00-10:20 | Break | Break | Break | Break | Break |

10:20-12:20 | Benner | Benner | Benner | Benner | Benner |

exercise | |||||

14:30-16:30 | Tutorial | Tutorial | Tutorial | Tutorial | Tutorial |

16:30-17:30 | Seminar |

### August 5 - 9 (week 3):

lecture | Mon Aug 5 | Tue Aug 6 | Wed Aug 7 | Thu Aug 8 | Fri Aug 9 |

08:00-10:00 | X. Li | X. Li | R.-C. Li | Workshop | Open |

10:00-10:20 | Break | Break | Break | Day | |

10:20-12:20 | R.-C. Li | R.-C. Li | Seminar | ||

exercise | |||||

14:30-16:30 | Tutorial | Tutorial | Tutorial | ||

16:30-17:30 | Seminar |

### Research seminars:

- July 25, 4:30pm - 5:30pm,

**Orthogonal eigenvalue problem and structured eigenvalue problem**

**Hongguo Xu**, University of Kansas

Abstract: We review the QR algorithm and some related algorithms. We discuss numerical methods for solving the eigenvalue problem of real orthogonal matrices and show how matrix structures can be used to develop more efficient and reliable algorithms. Finally, we give a brief introduction to the eigenvalue problem of matrices with certain algebraic structures. - August 1, 4:30pm - 5:30pm,

**A (fully?) adaptive rational (global) Arnoldi method for model-order reduction of second-order MIMO systems arising in structural dynamics**

**Heike Fassbender**, AG Numerik, Institut Computational Mathematics

Abstract: Moment-matching model order reduction of second-order dynamical systems with multiple inputs and multiple outputs (MIMO) is considered for damped or proportionally damped systems. It is well-known that moment-matching can be efficiently and numerically sound implemented by Krylov subspace methods. For second-order systems second-order Krylov subspaces and an appropriate second-order Krylov method have to be employed. As model reduction of linear first-order systems is much further developed and understood, it is tempting to transform the original second-order system to a mathematically equivalent first-order system and to employ known model order reduction methods. But this approach doubles the size of the matrices to be considered. Moreover, it may be difficult to retrieve the second-order reduced system from the first-order reduced one. For the problem investigated, it turns out that the second-order Krylov subspaces are identical to certain first-order ones, so that no linearization is necessary, but a first-order model reduction method can be employed. The problem size does not increase. The discussion will be restricted to rational block Arnoldi methods, in particular the global Arnoldi method. A new model reduction algorithm for second order MIMO systems is proposed which automatically generates a reduced system of given order approximating the transfer function in the lower range of frequencies. It determines the expansion points iteratively and the number of moments matched per expansion point adaptively. An extension of the proposed method to a fully automatic one also iteratively determining the order of the reduced system is work in progress. Numerical examples comparing our results to modal reduction for a problem arising in the numerical simulation of mechanical structures are presented. - August 7, 10:20-11:20,

**Linear numerical schemes for epitaxial thin film growth model with energy stability**

**Cheng Wang**, University of Massachusetts Dartmouth

A few linear schemes for nonlinear PDE model of thin film growth model without slope selection are presented in the talk. In the first order linear scheme, the idea of convex-concave decomposition of the energy functional is applied, and the particular decomposition places the nonlinear term in the concave part of the energy, in contrast to a standard convexity splitting scheme. As a result, the numerical scheme is fully linear at each time step and unconditionally solvable, and an unconditional energy stability is guaranteed by the convexity splitting nature of the numerical scheme. To improve the numerical accuracy, a second order temporal approximation for the nonlinear term is recently reported, which preserves an energy stability. To solve this highly non-trivial nonlinear system, a linear iteration algorithm is proposed, with an introduction of a second order artificial diffusion term. Moreover, a contraction mapping property is proved for such a linear iteration. As a result, the highly nonlinear system can be decomposed as an iteration of purely linear solvers. Some numerical simulation results are also presented in the talk.

### Special events

- July 27, Saturday, execusion.
- August 2, Celebration dinner, partially sponsored by Volker Mehrmann of TU Berlin.

*Contact email address: wggao at fudan.edu.cn and/or bai at cs.ucdavis.edu*