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An Adaptive Mesh Refinement Strategy for Immersed Boundary/Interface Methods

Published online by Cambridge University Press:  20 August 2015

Zhilin Li*
Affiliation:
Center for Research in Scientific Computation & Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA; and Nanjing Normal University, China
Peng Song*
Affiliation:
Operations Research Program, North Carolina State University, Raleigh, NC 27695, USA
*
Corresponding author.Email:zhilin@math.ncsu.edu
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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.

Type
Research Article
Copyright
Copyright © Global Science Press Limited 2012

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