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Volume 12, Issue 2
An Adaptive Mesh Refinement Strategy for Immersed Boundary/Interface Methods

Zhilin Li & Peng Song

Commun. Comput. Phys., 12 (2012), pp. 515-527.

Published online: 2012-12

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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.

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@Article{CiCP-12-515, author = {}, title = {An Adaptive Mesh Refinement Strategy for Immersed Boundary/Interface Methods}, journal = {Communications in Computational Physics}, year = {2012}, volume = {12}, number = {2}, pages = {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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.070211.150811s}, url = {http://global-sci.org/intro/article_detail/cicp/7302.html} }
TY - JOUR T1 - An Adaptive Mesh Refinement Strategy for Immersed Boundary/Interface Methods JO - Communications in Computational Physics VL - 2 SP - 515 EP - 527 PY - 2012 DA - 2012/12 SN - 12 DO - http://doi.org/10.4208/cicp.070211.150811s UR - https://global-sci.org/intro/article_detail/cicp/7302.html KW - AB -

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.

Zhilin Li & Peng Song. (2020). An Adaptive Mesh Refinement Strategy for Immersed Boundary/Interface Methods. Communications in Computational Physics. 12 (2). 515-527. doi:10.4208/cicp.070211.150811s
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