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
