
9月演講

Colloquium, 國立成功大學數學系 舒宇宸副教授
Thursday, September 10, 15:10—17:00 數學系3174
Title: 專題討論課程介紹 Abstract: 說明各個課程學習架構，讓研究生對修課規劃有明確的瞭解。

Colloquium, 交通大學應用數學系 賴明治講座教授
Thursday, September 17, 16:10—17:00 數學系3174
Title: An immersed boundary projection method for simulating the inextensible vesicle dynamics Abstract: this talk, we introduce an immersed boundary projection method (IBPM) based on an unconditionally energy stable scheme to simulate the vesicle dynamics in a viscous fluid. Utilizing the block LU decomposition of the algebraic system, a novel fractional step algorithm is introduced by decoupling all solution variables, including the fluid velocity, fluid pressure, and the elastic tension. In contrast to previous works, the present method preserves both the fluid incompressibility and the interface inextensibility at a discrete level simultaneously. In conjunction with an implicit discretization of the bending force, the present method alleviates the timestep restriction, so the numerical stability is assured by nonincreasing total discrete energy during the simulation. The numerical algorithm takes a linearithmic complexity by using preconditioned GMRES and FFTbased solvers. The grid convergence studies con firm that the solution variables exhibit firstorder convergence rate in L2norm. We demonstrate the numerical results of the vesicle dynamics in a quiescent flow, Poiseuille flow, and shear flow, which are congruent with the results in the literature.

Colloquium, 臺灣大學資訊工程學系 李彥寰教授
Thursday, September 24, 16:10—17:00 數學系3174
Title: NonAsymptotic Analysis of EM in Poisson Inverse Problems Abstract:Poisson inverse problems arise in many realworld applications, such as positron emission tomography and astronomical image deblurring. Expectation maximization (EM) is a standardand perhaps the most popularapproach to solving a Poisson inverse problem. Vardi et al. proved EM asymptotically converges more than three decades ago; however, it was unclear how fast EM converges. In this talk, I will present a nonasymptotic convergence guarantee for EM. Our analysis exploits an interesting connection between EM and a portfolio selection method due to Cover.





