@Article{CiCP-18-1211,
author = {Gu , QunGao , Weiguo and J. García-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 = {<p style="text-align: justify;">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.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.260514.101214a},
url = {http://global-sci.org/intro/article_detail/cicp/11066.html}
}