@Article{CiCP-18-1211, author = {Gu , QunGao , Weiguo and J. GarcĂ­a-Cervera , Carlos}, title = {High Order Finite Difference Discretization for Composite Grid Hierarchy and Its Applications}, journal = {Communications in Computational Physics}, year = {2018}, volume = {18}, number = {5}, pages = {1211--1233}, abstract = {

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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.260514.101214a}, url = {http://global-sci.org/intro/article_detail/cicp/11066.html} }