Workshop on Computational Mathematics
10 May (Friday) 2013
Room: 118
Graduate School of Mathematical Sciences
The University of Tokyo
http://www.ms.u-tokyo.ac.jp/ac
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 on fine grid are computationally prohibitive. While in some cases, effective medium theories may be useful, in other situations the distribution of heterogeneities may have more complex effects on waves. We present our results of a new multiscale finite element algorithm for simulating acoustic wave propagation in heterogeneous media. The wave equation is solved on a coarse grid using multiscale basis functions. These multiscale basis functions are chosen as the most dominant modes among the set of all fine grid basis functions, and thus allowing a coarse representation of complex wave structures. Numerical results demonstrate the performance of the 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 for inversion.
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 of these 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 for these models. By using the energy stable schemes, an adaptive time-stepping strategy has been introduced. The energy is used to monitor the change of the 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 are resolved accurately.
13:30-14:15
Professor Manabu Machida
(University of Michigan)
"Numerical Calculation of the Magnetization Correlation Function with Random Vectors"
14:30-15:15
Professor Leevan Ling
(Hong Kong Baptist University)
TBA
15:15-16:00
Professor Kazufumi Ito
(North Carolina State University)
TBA
10 May (Friday) 2013
Room: 118
Graduate School of Mathematical Sciences
The University of Tokyo
http://www.ms.u-tokyo.ac.jp/ac
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 on fine grid are computationally prohibitive. While in some cases, effective medium theories may be useful, in other situations the distribution of heterogeneities may have more complex effects on waves. We present our results of a new multiscale finite element algorithm for simulating acoustic wave propagation in heterogeneous media. The wave equation is solved on a coarse grid using multiscale basis functions. These multiscale basis functions are chosen as the most dominant modes among the set of all fine grid basis functions, and thus allowing a coarse representation of complex wave structures. Numerical results demonstrate the performance of the 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 for inversion.
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 of these 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 for these models. By using the energy stable schemes, an adaptive time-stepping strategy has been introduced. The energy is used to monitor the change of the 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 are resolved accurately.
13:30-14:15
Professor Manabu Machida
(University of Michigan)
"Numerical Calculation of the Magnetization Correlation Function with Random Vectors"
14:30-15:15
Professor Leevan Ling
(Hong Kong Baptist University)
TBA
15:15-16:00
Professor Kazufumi Ito
(North Carolina State University)
TBA
Categories:
Past Seminar