特邀香港理工大学李步扬教授作线上学术报告

发布者:朱亚宾发布时间:2020-05-22浏览次数:10

报告题目:A Hodge decomposition method for dynamic Ginzburg-Landau equations in nonsmooth domains-a second approach

报告时间:2020524日(周15:2516:10

人:李步扬教授

报告地点:Zoom云会议(ID937 6354 7091, 密码:nanxinda60

报告摘要:In a general polygonal domain,possibly nonconvex and multi-connected (with holes), the time-dependent Ginzburg-Landau equation is reformulated into a new sys-tem of equations. The magnetic field B:=×A is introduced as an unknown solution in the new system , while the magnetic potential A is solved implicitly through its Hodge decomposition into divergence-free part,curl-free and harmonic parts,separately.Global well-posedness of the new system and its equivalence to the original problem are proved.A linearized and decoupled Galerkin finite element method is proposed for solving the new system.The convergence of numerical solutions is proved based on a compactness argument by utilizing the maximal Lp-regularity of the discretized equations. Compared with the Hodge decomposition method proposed in[27], the new method has the advan-tage of approximating the magnetic field B directly and converging for initial conditions that are incompatible with the external magnetic field. Several numerical examples are provided to illustrate the efficiency of the proposed numerical method in both simply connected and multi-connected nonsmooth domains. We observe that even in simply connected domains, the new method is superior to the method in[27]for approximating the magnetic field.

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数学与统计学院

2020522

附:专家简介

李步扬2012年在香港城市大学获得博士学位,2013年至2015年在南京大学作助理研究员,2015-2016年在德国图宾根大学作洪堡学者,自2016年起李步扬博士在香港理工大学担任助理教授。李步扬博士的研究方向主要是偏微分方程的数值解,包括非线性抛物方程、相场方程、几何曲面演化方程等,至今已在 SIAM Journal on Numerical Analysis, Numerische Mathematik Mathematics of Computation 三个经典的计算数学杂志发表论文27篇。