报告主题：A Vertex-centered Positivity-preserving Diamond Scheme for Duffusion equation on Arbitrary Polygonal Meshes
报告人：张晓平 副教授 （武汉大学）
报告时间：2019年4月19日（周五）10：00
报告地点：校本部G507
邀请人：刘东杰
主办部门：理学院数学系
报告摘要： In this talk we discuss a new positivity-preserving finite volume scheme for anisotropic diffusion problems on arbitrary polygonal grids. The scheme has two types of unknowns: the vertex-centered ones are primary and have finite volume equations associated with them; and the edge-midpoint and cell-centered ones are auxiliary ones and are interpolated by the primary unknowns. Thus, the final scheme a pure vertex-centered one. The construction of the scheme is based on a special nonlinear two-point flux approximation that has a fixed stencil and does not require the convex decomposition of the co-normal. In order to solve efficiently the nonlinear systems resulting from the nonlinear scheme, Picard method and its Anderson acceleration are discussed. Some numerical experiments are also presented to show the scheme's efficiency.
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