Volume 18, Issue 5
High Order Finite Difference Discretization for Composite Grid Hierarchy and Its Applications

Qun Gu, Weiguo Gao & Carlos J. García-Cervera

Commun. Comput. Phys., 18 (2015), pp. 1211-1233.

Published online: 2018-04

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  • 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.

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  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

081018018@fudan.edu.cn (Qun Gu)

wggao@fudan.edu.cn (Weiguo Gao)

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@Article{CiCP-18-1211, author = {Gu , Qun and Gao , Weiguo and Carlos J. García-Cervera , }, 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} }
TY - JOUR T1 - High Order Finite Difference Discretization for Composite Grid Hierarchy and Its Applications AU - Gu , Qun AU - Gao , Weiguo AU - Carlos J. García-Cervera , 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.

Qun Gu, Weiguo Gao & Carlos J. García-Cervera. (2020). High Order Finite Difference Discretization for Composite Grid Hierarchy and Its Applications. Communications in Computational Physics. 18 (5). 1211-1233. doi:10.4208/cicp.260514.101214a
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