2018.8.10-8.16 学术活动预告
2018/8/9 9:02:46 中国科学院数学与系统科学研究院

     Speaker:

     Cheng Wang, Department of Mathematics, University of Massachusetts Dartmouth

     Title:

     Energy stable fourth order finite difference scheme for the Cahn-Hilliard equation

     Time & Venue:

     2018.8.10 10:00-11:00 Z311

     Abstract:

     An energy stable numerical scheme for the Cahn-Hilliard equation is proposed and analyzed, with second order accuracy in time and the fourth order finite difference approximation in space. In particular, the truncation error for the long stencil fourth order finite difference approximation is estimated, over a uniform numerical grid with a periodic boundary condition,via the help of discrete Fourier analysis instead of the the standard Taylor expansion. This in turn results in a reduced regularity requirement for the test function. In the temporal approximation, we apply a second order BDF stencil, combined with a second order extrapolation formula applied to the concave diffusion term, as well as a second order artificial Douglas-Dupont regularization term, for the sake of energy stability. As a result, the unique solvability, energy stability are established for the proposed numerical scheme, and an optimal rate convergence analysis is derived. A few numerical experiments are also presented.

     Speaker:

     Professor Stefano de Gironcoli, Scuola Internazionale Superiore di Studi Avanzati (SISSA)

     Title:

     Global Minimization vs Self-Consistent Field approach to the Electronic Structure Problem Solution

     Time & Venue:

     2018.8.10 16:00-17:00 N702

     Abstract:

     I will briefly review the two main approaches to the solution of a general Electronic Structure problem: the self-consistent field approch and the global minimization approach. I'll draw attention advantages and remaining problems of the two approches.

     Speaker:

     苏长剑博士, IHES

     Title:

     On a conjecture of Bump-Nakasuji -Naruse about the Casselman basis

     Time & Venue:

     2018.8.13 10:00-11:00 N913

     Abstract:

     Let G be a split p-adic reductive group. In the Iwahori invariants of a unramified principal series representation of G, there are two bases. One of them is the Casselman basis, which played an important role in the proof of the Casselman--Shalika formula. In this talk, I will prove a conjecture of Bump, Nakasuji and Naruse about the transition matrix between these two bases. The idea is to transform the problem into the Langlands dual side, and use motivic Chern classes introduced by Brasselet-Schurmann-Yokura and the K-theoretic stable envelope for the dual Springer resolution introduced by Maulik and Okounkov. This is based on joint work with Aluffi, Mihalcea and Schurmann.

     来源：中国科学院数学与系统科学研究院

     中国科学院数学与系统科学研究院

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