报告人：Prof. B.Froese, Department of Mathematical Sciences, New Jersey Institute ofTechnology

标题：Generalisedfinite difference methods for theMonge-Ampereequation

时间地点：2017年6月13日（星期二）15:00-16:00 理科楼A304

摘要：The introduction of viscosity solutions and theBarles-Souganidisconvergence framework have allowed for considerable progress in the numerical solution of fully nonlinear elliptic equations. Monotone finite difference methods now exist for a variety of problems. However, these schemes are defined only on uniform Cartesian meshes over a rectangular domain, are typically inconsistent near the boundary, and rely on a comparison principle that can fail for several important boundary value problems. We introduce a framework for constructing monotone approximations ofMonge-Ampere type equations on general meshes or point clouds. These schemes easily handle complex geometries and non-uniform distributions ofdiscretisationpoints. Moreover, they are proven to converge via a modification of theBarles-Souganidisframework. A range of computational examples demonstrate the effectiveness of these methods.

报告人简介：B.Froese教授2012年毕业于加拿大Simon Fraser University。之后在The University of Texas at Austin做博士后。2015年就职于New Jersey Institute of Technology。她最近在优化输运领域中有一些重要工作，包括Monge-Ampere方程的数值求解，Wasserstein度量的应用等方面。

联系人：吴昊