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High Order Finite Difference Discretization for Composite Grid Hierarchy and Its Applications

Published online by Cambridge University Press:  23 November 2015

Qun Gu
Affiliation:
School of Mathematical Sciences, Fudan University, Shanghai 200433, P.R. China
Weiguo Gao*
Affiliation:
MOE Key Laboratory of Computational Physical Sciences and School of Mathematical Sciences, Fudan University, Shanghai 200433, P.R. China
Carlos J. García-Cervera
Affiliation:
Department of Mathematics, University of California, Santa Barbara, CA 93106, USA
*
*Corresponding author. Email addresses: 081018018@f udan.edu.cn (Q. Gu), [email protected] (W. Gao), [email protected] (C.J.García-Cervera)
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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.

Type
Research Article
Copyright
Copyright © Global-Science Press 2015 

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