TY - JOUR
T1 - High Order Finite Difference Discretization for Composite Grid Hierarchy and Its Applications
AU - Gu , Qun
AU - Gao , Weiguo
AU - J. García-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 - <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>