TY - JOUR
T1 - An Adaptive Mesh Refinement Strategy for Immersed Boundary/Interface Methods
AU - Zhilin Li & Peng Song
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 - <p style="text-align: justify;">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.</p>