This workshop is devoted to discussions on recent progresses in modern numerical analysis, including some topics from high-performance computations.
We welcome participants from related areas for joining in the discussions.
The main lecture is provided also as a part of UTokyo Numerical Analysis Seminar (UTNAS).
Workshop date and venue
March 12 (Mon.), 2018
Seminar room AD (on the 3rd floor)
Engineering building No.6 (See Hongo Campus map; the building is marked as “78” in violet, circled)
Hongo campus
The University of Tokyo (See Access map for transportations)
Program
| 14:00–14:30 | S. Sato (UTokyo) |
Numerical and theoretical treatment of evolutionary differential equations with a mixed derivative [su_spoiler title=”abstract” open=”no” style=”default” icon=”chevron-circle” anchor=”” class=””]In this talk, we deal with the initial value problem of evolutionary differential equations with a mixed derivative on the periodic domain. Here, “mixed derivative” indicates the case where a spatial differential operator is operating on the time derivative, obscuring the vector field describing the flow. Therefore, some reformulation to reveal it is the first step of PDE-theoretical and numerical studies. However, it is nontrivial because the spatial differential operator is not invertible and cannot be easily eliminated. Though this issue was already settled for linear cases, general theory has been undeveloped. In this talk, we propose a novel procedure for wider class of equations, which provides us with the unified viewpoint for the numerical and theoretical treatment of these equations. [/su_spoiler] |
| 14:45–15:15 | D. Lee (Nagoya Univ.) |
On the k-th eigenvalue problem in materials simulation[su_spoiler title=”abstract” open=”no” style=”default” icon=”chevron-circle” anchor=”” class=””]In this talk, we consider computing the k-th eigenvalue and its associated eigenvector of large sparse generalized Hermitian eigenvalue problems. The k-th eigenvalue problem arises in quantum materials simulation, where several properties of materials are governed by the eigenpair with a material-specific index k. We present a numerical algorithm for the problem and demonstrate the efficiency of the algorithm in numerical experiments.[/su_spoiler] |
| 15:30–16:00 | T. Kemmochi (UTokyo) |
An analytic semigroup approach for DG time-stepping methods [su_spoiler title=”abstract” open=”no” style=”default” icon=”chevron-circle” anchor=”” class=””]The discontinuous Galerkin time-stepping method (DG time-stepping method) is a time-discretization method based on the discontinuous Galerkin finite element method. In contrast to one-step methods, the approximated solution is well-defined at each time in the DG time-stepping method. Therefore, it gives an efficient numerical algorithm with space-time methods for moving boundary problems such as fluid structure interaction. However, there are few studies on theoretical analysis for the behavior of approximated solutions at each time. In this talk, we address the DG time-stepping method for parabolic problems in the framework of analytic semigroup theory. We present optimal order error estimates for the homogeneous heat equation. The key point is rigorous estimates for rational functions that express the approximated solutions.[/su_spoiler] |
| 16:30–18:00 | L. Einkemmer (Univ. Innsbruck) |
(main lecture；UTNAS#98) Strategies and challenges in numerically solving kinetic equations [su_spoiler title=”abstract” open=”no” style=”default” icon=”chevron-circle” anchor=”” class=””]Many phenomena in both space and laboratory plasmas require a kinetic description. However, these equations are posed in a high dimensional phase space and the corresponding solutions exhibit small-scale oscillations. In addition, traditional numerical methods suffer from a restrictive CFL condition. In this talk we will present strategies that are able to overcome these difficulties. This will lead us from time splitting based semi-Lagrangian discontinuous Galerkin schemes to low-rank approximations of the Vlasov equation. The importance of preserving the physical structure of the problem under consideration will be a common thread. Although splitting (and related) methods are a staple in such, and many other, applications domains, their convergence suffers from order reduction in the presence of non-trivial boundary conditions. This behavior will be investigated in a mathematically rigorous way and a procedure to avoid order reduction will be presented.[/su_spoiler] |
How to participate
There is no need of registration.
You can just come to the workshop venue.
Contact
If you have any questions or requests, please contact T. Matsuo at matsuo(at_mark)mist.i.u-tokyo.ac.jp