Workshop on Computational Mathematics
10 May (Friday) 2013
Room: 118
Graduate School of Mathematical Sciences,The University of Tokyo

10:15-11:00
Professor Eric Chung(Chinese University of Hong Kong)"Multiscale simulation of waves"
Abstract:
Numerical simulation of elastic and acoustic wave propagation utilizes
increasingly large and complex models, providing more realistic and useful
results. However, significant challenges remain as direct simulations onfine grid are computationally prohibitive. While in some cases, effective
medium theories may be useful, in other situations the distribution ofheterogeneities may have more complex effects on waves. We present ourresults of a new multiscale finite element algorithm for simulating
acoustic wave propagation in heterogeneous media. The wave equation issolved on a coarse grid using multiscale basis functions. These multiscalebasis functions are chosen as the most dominant modes among the set of all
fine grid basis functions, and thus allowing a coarse representation ofcomplex wave structures. Numerical results demonstrate the performance ofthe method. Long term developments have strong potential to enhance
inversion algorithms, since the basis functions need not be regenerated,allowing faster simulations for repeated calculations needed forinversion.

11:00-11:45
Professor Zhonghua Qiao
(The Hong Kong Polytechnic University)"Energy stability analysis and adaptive time-stepping strategy for
nonlinear diffusion equations"
Abstract:
In this talk, I will review our recent works on some nonlinear diffusion
equations, which have the dissipative mechanism in energy laws, such as,
the dynamics of the molecular beam epitaxy (MBE) model, the Cahn-Hilliard
model, the phase-field crystal model, etc. The numerical simulations ofthese models require very long time computations to reach the steady state.
In our research, we have developed some unconditionally energy stable
schemes which can preserve the discretized energy decay properties forthese models. By using the energy stable schemes, an adaptive time-stepping
strategy has been introduced. The energy is used to monitor the change ofthe time steps. Large time steps are used when the energy decays rapidly
and small time steps are adopted otherwise. The numerical experiments
demonstrated that the CPU time is significantly saved for long time
simulations, and both the steady states and the dynamical behaviors areresolved accurately.

13:30-14:15
Professor Manabu Machida(University of Michigan)"Recursion algorithm for the inverse Born series”

14:30-15:15
Professor Leevan Ling
(Hong Kong Baptist University)“On method of fundamental solutions for solving Cauchy problems”
Abstract:
The method of fundamental solutions (MFS) introduced by Kupradze andAleksidze in 1964 has become a popular meshless method for solving variousPDEs of practical importance. As a boundary-type meshless method, MFS iscomputationally cheaper than other domain-type meshless methods. More
importantly, the accuracy of some MFS approximations can approach the orderof machine epsilon, or so it is claimed. Users simply provide the locationof the boundary of the domain of the problem. It is unnecessary to createa mesh over the entire region or its boundary, which turns out to be
extremely helpful in solving inverse problems of various types. To
investigate the applicability of the MFS in solving Cauchy problems, aseries of carefully designed numerical experiments, on both direct andinverse problems, is carried out. In this talk, the true approximation powerof MFS will be revealed. (This project was supported by the CERG Grant ofthe Hong Kong Research Grant Council and the FRG Grant of the Hong Kong
Baptist University.)

15:15-16:00
Professor Kazufumi Ito(North Carolina State University)“Control of Variational Inequalities”
Abstract:
We discuss the optimal control problem for parabolic variational inequality
and Cahn-Hillard Navier Stokes system. The Lagrange multiplier formulation
is discussed and the necessary optimality is derived.