讲座题目： A robust approach for solving Helmholtz equation with strongnonlinearity
主讲人：Prof. Zhengfu Xu (Michigan Technological University,USA)
主持人：袁健华副教授
时 间：2014年7月1日（周二）上午9:30-10:30
地 点：主楼1214
主要内容：
In this talk, we will discuss a steady state approach solving thenonlinear Helmholtz equations modeling \chi{(2)} (second harmonic generation)and \chi{(3)} (Kerr effect) type nonlinear optical phenomena in photonic bandgap material. These nonlinear phenomena arise as a result of the combination ofhigh electromagnetic mode density and nonlinear reaction from the medium. Theproposed method is designed to deal with the failure of generally usedlinearization technique in the case of strong nonlinearity. We will discuss theperformance of this approach through several numerical results.
主讲人简介：
Prof. Zhengfu Xu ，Michigan Technological University, Houghton，Ph.D. in Applied Mathematics, Division of Applied Mathematics, Brown University。
Academic Experience：
• Associate Professor: Department of Mathematical Sciences, Michigan Technological University, 2014–.
• Assistant Professor: Department of Mathematical Sciences, Michigan Technological University, 2011–2014.
• Visiting Assistant Professor: Department of Mathematics, Michigan State University. Supervisor: Gang Bao, Andrew Christlieb. 2008 – 2011.
• S. Chowla Research Assistant Professor: Department of Mathematics, Penn State University. Supervisor: Jinchao Xu. 2005 – 2008.
• Research Assistant : Division of Applied Mathematics, Brown University. 2003 – 2005.
• Teaching Assistant: Division of Applied Mathematics, Brown University. 2002 – 2003.
Awards and grants：
1. Junior faculty research award, Department of Mathematical Science, 2012-2013.
2. Sole PI, NSF grant- DMS-1316662 “High Order Maximum Principle Preserving Finite Difference Schemes for Hyperbolic Conservation Laws,” in the amount of $226,349, 2013–2016.
3. Co-PI, AHA, “How to reduce hemorrhagic stokes: A mathematical imaging approach for evaluating the rupture risk of intracranial aneury”, Pending.
Papers in Preparation：
• J. Jones, Z. Xu, A. Christlieb and K. Promislow, Fast and accurate simulation of long-time adiabatic evolution of functionalized polymer solvent with gradient stable scheme.
• H. Yang, F. Li, Z. Xu, Positivity-preserving and locally divergence-free discontinuous Galerkin methods for the magneto-hydrodynamic equations.
• Y Jiang, Z. Xu, Maximum principle preserving high order IMEX methods for convection diusion equations.
