|Scientific Computing Seminar, 中國科學院 石鐘慈院士|
Wednesday, December 7, 15:10—16:00 數學系3F會議室
Title: Studies on Wilson Nonconforming Finite Element
Abstract: Wilson nonconforming finite element (1973) is a very useful rectangular element in practice. It has been shown in many engineering applications that the convergence behavior of this element is better than that of the commonly used bilinear element. However, mathematical studies carried out so far cannot justify it. I have spent many years on this problem. The results obtained by use of standard finite element analysis are not satisfied. Recently we tackle this problem from a different view point, i.e. from Mechanics, where the Wilson element was originated. We have succeeded in proving mathematically that the Wilson element is free of shear locking for a wide class of bending dominated plane elasticity problems, while the bilinear element suffers from shear locking. Therefore, we elucidate a long-standing folklore: why Wilson element does a better job in many practical applications than the bilinear one.
|Scientific Computing Seminar, 中國科學院計算科學所 趙旭鷹 研究員|
Wednesday, December 7, 16:10—17:00 數學系3F會議室
Title: Decomposition of Nonlocal Norms and Quantitative Dependence Analysis for Nonlocal Diffusion Models
Abstract: In this talk, several decomposition properties for nonlocal norms of double integrals arising from nonlocal models will be presented. Based on it, how the equivalence between the energy norm and the Sobolev space norm depends on the horizon and other parameters for nonlocal diffusion models will be revealed. More results with quantitative dependence on the horizon and other parameters are further established, such as the nonlocal Poincar\'e inequality, the priori error estimation, and condition numbers of the stiffness matrix and preconditioned stiffness matrix by diagonal scaling on quasi-uniform meshes. Both the case of integrable kernels and the case of non-integrable kernels are considered herein.
|創校85週年暨創系60週年系列演講, 中央研究院數學研究所 程舜仁 教授|
Thursday, December 8, 15:10—16:00 數學系3174教室
Title: On Supercharacter of Modules over the Queer Lie Superalgebra
|創校85週年暨創系60週年系列演講, 台灣大學數學系 陳俊全 國家講座教授|
Thursday, December 15, 16:10—17:00 數學系3174教室
Title: Traveling Waves for the FitzHugh-Nagumo System on an Infinite Channel
Abstract: We are concerned with the traveling wave solutions for the FitzHugh-Nagumo system on an in finite channel. Based on a variational formulation depending on a parameter, the speed of a traveling wave can be selected out. Furthermore, to show the existence of a traveling wave solution with such a speed, we seek a minimizer subject to a constraint. In the way of finding a solution located in a bounded region of a function space, we utilize a truncation technique which causes the analysis in dealing with a nonlocal term more involved.
|創校85週年暨創系60週年系列演講, 交通大學應用數學系 林文偉 教授|
Monday, December 19, 16:10—17:00 數學系3174教室
Title: Structure-Preserving Algorithms for Palindromic Quadratic Eigenvalue Problems with Applications
Abstract: In this talk we mainly study palindromic quadratic eigenvalue problems (P-QEPs) and the related nonlinear matrix equations (NMEs), typically arising in the vibration analysis for fast trains, the Green's function calculation in nano research and the surface accoustic wave filtering problems etc. We prove the existence and uniqueness of the (weakly) stabilizing solution for the NME, and develop structure-preserving (doubling) algorithms for solving the P-QEPs and the associated NMEs. Numerical results show that our proposed SDAs are efficiently and accurately in real engineering and chemistrical applicaition problems.
|85週年暨創系60週年系列演講, Stanford University and University of California, Irvine, Prof. Richard Schoen|
Wednesday, December 21, 16:10—17:00 三系館成功共同教室 A1302
Title: Geometries that Optimize Eigenvalues
Abstract: When we choose a metric on a manifold we determine the spectrum of the Laplace operator. Thus an eigenvalue may be considered as a functional on the space of metrics. For example the first eigenvalue would be the fundamental vibrational frequency. In some cases the normalized eigenvalues are bounded independent of the metric. In such cases it makes sense to attempt to find critical points in the space of metrics. In this talk we will survey two cases in which progress has been made focusing primarily on the case of surfaces with boundary. We will describe the geometric structure of the critical metrics which turn out to be the induced metrics on certain special classes of minimal (mean curvature zero) surfaces in spheres and euclidean balls. The eigenvalue extremal problem is thus related to other questions arising in the theory of minimal surfaces.
|PDE Seminar, 京都大學 川越大輔博士|
Wednesday, December 27, 14:10—15:00 數學系3F會議室
Title: Propagation of Boundary-Induced Discontinuity in Stationary Radiative Transfer
Abstract: We consider the boundary value problem of the stationary transport equation, the integro-differential equation of spatial and velocity variables, in the three dimensional slab domain. In this talk, we discuss the relation between discontinuity of the boundary data and that of the solution to the stationary transport equation. Under the suitable assumption poses on the boundary data, discontinuity of the boundary data propagates along the positive characteristic lines.