TY - JOUR T1 - High Order Finite Difference Discretization for Composite Grid Hierarchy and Its Applications AU - Gu , Qun AU - Gao , Weiguo AU - J. GarcĂ­a-Cervera , Carlos JO - Communications in Computational Physics VL - 5 SP - 1211 EP - 1233 PY - 2018 DA - 2018/04 SN - 18 DO - http://doi.org/10.4208/cicp.260514.101214a UR - https://global-sci.org/intro/article_detail/cicp/11066.html KW - AB -

We introduce efficient approaches to construct high order finite difference discretizations for solving partial differential equations, based on a composite grid hierarchy. We introduce a modification of the traditional point clustering algorithm, obtained by adding restrictive parameters that control the minimal patch length and the size of the buffer zone. As a result, a reduction in the number of interfacial cells is observed. Based on a reasonable geometric grid setting, we discuss a general approach for the construction of stencils in a composite grid environment. The straightforward approach leads to an ill-posed problem. In our approach we regularize this problem, and transform it into solving a symmetric system of linear of equations. Finally, a stencil repository has been designed to further reduce computational overhead. The effectiveness of the discretizations is illustrated by numerical experiments on second order elliptic differential equations.