Generalised finite difference methods for the Monge-Ampere equation


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

标题:Generalised finite difference methods for the Monge-Ampere equation

时间地点2017613日(星期二)15:00-16:00  理科A304


摘要The introduction of viscosity solutions and the Barles-Souganidis convergence 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 of Monge-Ampere type equations on general meshes or point clouds.  These schemes easily handle complex geometries and non-uniform distributions of discretisation points.  Moreover, they are proven to converge via a modification of the Barles-Souganidis framework.  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。