Date

  • 24th July, 2015, 13:15 - 17:30
    (The schedule is subject to change)

Venue

  • The University of Tokyo, Faculty of Engineering Bldg.6, room 63 (on the 2nd floor).
    (7-3-1, Hongo, Bunkyo-ku, Tokyo, 113-0033, JAPAN)
  • Access Map (pdf, 762KB)
  • Hongo Campus Map (pdf, 922KB)

Note

We will hold another seminar in the morning, in which Professor Sugihara (Aoyama Gakuin University) will talk about a few decades developments in numerical analysis.

同日午前中に杉原 正顯教授(青山学院大学)による、これまでの数値解析の発展に関するセミナーを開催いたします． ぜひこちらのセミナーにもご参加ください．

Banquet

We will have a banquet at night after the workshop around the venue. Please contact the management committee if you would like to participate it by the 17th July.
* Of course, the speakers are invited and not required to contact.

ワークショップ終了後、会場周辺にて懇親会を開催いたします． ご興味のある方は、7月17日までに下記の運営委員までご連絡下さい．
* 講演者はもちろんご連絡不要です．

Management Committee

Daisuke Furihata (Osaka University, e-mail: furihata at cmc.osaka-u.ac.jp),
Hidenori Ogata (The University of Electro-Communications),
Dai Okano (Ehime University),
Takayasu Matsuo (The University of Tokyo).

RDNACA

RDNACA is a meeting that focuses on recent developments in numerical analysis with special emphasis on complex analysis and related topics.

This is a joint workshop with the JST Starategic Basic Research Programs: CREST "Toward a paradigm shift created by mathematics of vortex-boundary interactions."


RDNACA は数値解析における近年の発展について、特に関数論分野との関係がある研究を対象として開催する研究集会です．

当研究集会は JST戦略的創造研究推進事業 CREST 「数学と諸分野の協働によるブレークスルーの探索 渦・境界相互作用が創出するパラダイムシフト」との共催です．

Program

(The order of talks is subject to change)

  • #1.    13:15 - 14:00,
    Christopher Green (University of California, San Diego),
    Title: Green's function for the Laplace-Beltrami operator on a toroidal surface,
    Abstract: Green's function for the Laplace-Beltrami operator on the surface of a three-dimensional ring torus is constructed. An integral ingredient of our approach is the stereographic projection of the torus surface onto a planar concentric annulus. The representation for Green's function that we find is explicit. It is written in terms of a single complex variable using two special functions: the Schottky-Klein prime function associated with an annulus, and the dilogarithm function. Applications of this work and possible extensions will be discussed. (This is joint work with Jonathan Marshall.)

  • #2.    14:00 - 14:45,
    Kenichiro Tanaka (Musashino University),
    Title: Potential theoretic approach for unified design of a highly accurate formula for function approximation in a weighted Hardy space,
    Abstract: We propose a method to design an highly accurate interpolation formula on the real axis for function approximation in a weighted Hardy space. Among various approximation formulas, the SE- and DE-Sinc formula for functions with single- and double-exponential weights are known to be very accurate, respectively. In each case, however, the optimal formula corresponding to each weight is more accurate than the Sinc formula. We adopt potential theoretic approach to obtain an accurate formula in an explicit form for the weighted Hardy space in the case of a general weight function. Some numerical results show the validity of the method.

  • coffee break    14:45 - 15:00,

  • #3.    15:00 - 15:45,
    Rhodri Nelson (Kyoto University),
    Title: Linear feedback stabilization of point vortex equilibria near a Kasper Wing,
    Abstract: This talk will begin by reviewing the stability (and robustness) of point vortex equilibria in the vicinity of a Kasper Wing (three thin plate) configuration and compare these results to those of the single plate case (previously studied by Saffman and Sheffield). Following this, a Linear-Quadratic-Gaussian (LQG) control is designed and applied to both the single plate and Kasper Wing systems. With pressure difference across the main plate being used as the output, the systems are shown to be fully observable. A sink-source placed along the main plate is used to perform flow actuation. It is then shown that Kasper Wing configurations are generally more controllable than their single plate counterparts and exhibit larger basins of convergence under LQG feedback control. The control is then applied with additional perturbations added to the flow. These perturbations include vorticity shedding to satisfy so called Kutta conditions in time and random perturbations to the angle of the free stream background flow. It is seen that under these conditions the control performs well provided the system does not deviate too far from its original state.

  • #4.    15:45 - 16:30,
    Bartosz Protas (McMaster University),
    Title: On some optimization problems in fluid dynamics,
    Abstract: The presentation will survey applications of optimization techniques to a number of classical and emerging problems in fluid mechanics and related fields. Our main focus will be on problems which can be formulated in terms of PDE-constrained optimization and solved with gradient-based techniques. We will review numerical approaches to the calculation of gradients (sensitivities) in problems with different structure based on suitably-defined adjoint systems. The specific examples will include optimal control of vortex flows, reconstruction of constitutive relations in multiphysics systems and shape optimization. While the main focus will be on techniques and results of large-scale computations, the lectures will also feature a number of rigorous developments.

  • coffee break    16:30 - 16:45,

  • #5.    16:45 - 17:30,
    Takaharu Yaguchi (Kobe University),
    Title: Structure-preserving numerical integrators for the KdV equation using an almost complex structure,
    Abstract: Structure-preserving numerical integrators are the numerical methods for solving differential equations while preserving a structure or a property of the equation. When the Hamilton equation on the cotangent bundle of a manifold is of interest, structure-preserving methods are often designed by using the variational principle in classical mechanics. On the other hand, the variational principle is also obtained on general symplectic spaces from almost complex structures of the spaces. In this talk, we derive a numerical scheme for the KdV equation using this structure. (This is a joint work with Ai Ishikawa.)