|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
|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 time-step restriction, so the numerical stability is assured by non-increasing total discrete energy during the simulation. The numerical algorithm takes a linearithmic complexity by using preconditioned GMRES and FFT-based solvers. The grid convergence studies con firm that the solution variables exhibit first-order convergence rate in L2-norm. 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: Non-Asymptotic Analysis of EM in Poisson Inverse Problems
Abstract:Poisson inverse problems arise in many real-world applications, such as positron emission tomography and astronomical image deblurring. Expectation maximization (EM) is a standard---and perhaps the most popular---approach 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 non-asymptotic convergence guarantee for EM. Our analysis exploits an interesting connection between EM and a portfolio selection method due to Cover.