Year: 2012
Communications in Computational Physics, Vol. 12 (2012), Iss. 2 : pp. 515–527
Abstract
An adaptive mesh refinement strategy is proposed in this paper for the Immersed Boundary and Immersed Interface methods for two-dimensional elliptic interface problems involving singular sources. The interface is represented by the zero level set of a Lipschitz function $ϕ(x,y)$. Our adaptive mesh refinement is done within a small tube of $|ϕ(x,y)|≤δ$ with finer Cartesian meshes. The discrete linear system of equations is solved by a multigrid solver. The AMR methods could obtain solutions with accuracy that is similar to those on a uniform fine grid by distributing the mesh more economically, therefore, reduce the size of the linear system of the equations. Numerical examples presented show the efficiency of the grid refinement strategy.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.070211.150811s
Communications in Computational Physics, Vol. 12 (2012), Iss. 2 : pp. 515–527
Published online: 2012-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 13
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