TY - JOUR
T1 - Immersed Finite Element Method for Interface Problems with Algebraic Multigrid Solver
AU - Wenqiang Feng, Xiaoming He, Yanping Lin & Xu Zhang
JO - Communications in Computational Physics
VL - 4
SP - 1045
EP - 1067
PY - 2014
DA - 2014/04
SN - 15
DO - http://doi.org/10.4208/cicp.150313.171013s
UR - https://global-sci.org/intro/article_detail/cicp/7127.html
KW - 
AB - <p style="text-align: justify;">This article is to discuss the bilinear and linear immersed finite element (IFE)
solutions generated from the algebraic multigrid solver for both stationary and moving
interface problems. For the numerical methods based on finite difference formulation
and a structured mesh independent of the interface, the stiffness matrix of the linear
system is usually not symmetric positive-definite, which demands extra efforts to design
efficient multigrid methods. On the other hand, the stiffness matrix arising from
the IFE methods is naturally symmetric positive-definite. Hence the IFE-AMG algorithm
is proposed to solve the linear systems of the bilinear and linear IFE methods
for both stationary and moving interface problems. The numerical examples demonstrate
the features of the proposed algorithms, including the optimal convergence in
both $L^2$ and semi-$H^1$ norms of the IFE-AMG solutions, the high efficiency with proper
choice of the components and parameters of AMG, the influence of the tolerance and
the smoother type of AMG on the convergence of the IFE solutions for the interface
problems, and the relationship between the cost and the moving interface location.</p>