TY - JOUR
T1 - An Extrapolation Cascadic Multigrid Method for Elliptic Problems on Reentrant Domains 
AU - Pan , Kejia
AU - He , Dongdong
AU - Chen , Chuanmiao
JO - Advances in Applied Mathematics and Mechanics
VL - 6
SP - 1347
EP - 1363
PY - 2017
DA - 2017/09
SN - 9
DO - http://doi.org/10.4208/aamm.OA-2016-0019
UR - https://global-sci.org/intro/article_detail/aamm/10182.html
KW - Richardson extrapolation, Cascadic multigrid, graded mesh, elliptic problems, corner
singularity.
AB - <p style="text-align: justify;">This paper proposes an extrapolation cascadic multigrid (EXCMG) method
to solve elliptic problems in domains with reentrant corners. On a class of λ-graded
meshes, we derive some new extrapolation formulas to construct a high-order approximation
to the finite element solution on the next finer mesh using the numerical solutions
on two-level of grids (current and previous grids). Then, this high-order approximation
is used as the initial guess to reduce computational cost of the conjugate
gradient method. Recursive application of this idea results in the EXCMG method
proposed in this paper. Finally, numerical results for a crack problem and an $L$-shaped
problem are presented to verify the efficiency and effectiveness of the proposed EXCMG
method.</p>