High Order Finite Difference Discretization for Composite Grid Hierarchy and Its Applications. (November 2015)

• Record Type: Journal Article
• Authors: Gu, Qun; Gao, Weiguo; García-Cervera, Carlos J.
• Is Part Of: Communications in computational physics. Volume 18:Number 5(2015:Nov.)
• Page Start: 1211
• Page End: 1233
• Publication Date: 2015-11
• Subjects: 35J57, -- 47A52, -- 65M50, -- 65N06; High order, -- point clustering algorithm, -- finite difference method, -- composite grid, -- stencil, -- regularization; Mathematical physics -- Data processing -- Periodicals; Physics -- Data processing -- Periodicals; 530.150285
• DOI: 10.4208/cicp.260514.101214a
• Languages: English
• ISSNs: 1815-2406

Abstract

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.