@Article{AAMM-4-2,
author = {Liu, Chunmei and Shu, Shi and Yunqing, Huang and Zhong, Liuqiang and Wang, Junxian},
title = {An Iterative Two-Grid Method of a Finite Element PML Approximation for the Two Dimensional Maxwell Problem},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2012},
volume = {4},
number = {2},
pages = {175--189},
abstract = {<p style="text-align: justify;">In this paper, we propose an iterative two-grid method for the edge finite
element discretizations (a saddle-point system) of Perfectly Matched Layer (PML)
equations to the Maxwell scattering problem in two dimensions. Firstly, we use
a fine space to solve a discrete saddle-point system of $H(grad)$ variational problems,
denoted by auxiliary system 1. Secondly, we use a coarse space to solve the
original saddle-point system. Then, we use a fine space again to solve a discrete&nbsp;$\boldsymbol{H}(curl)$-elliptic variational problems, denoted by auxiliary system 2. Furthermore,
we develop a regularization diagonal block preconditioner for auxiliary system 1
and use $H$-$X$ preconditioner for auxiliary system 2. Hence we essentially transform
the original problem in a fine space to a corresponding (but much smaller)
problem on a coarse space, due to the fact that the above two preconditioners are
efficient and stable. Compared with some existing iterative methods for solving
saddle-point systems, such as PMinres, numerical experiments show the competitive
performance of our iterative two-grid method.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.10-m11166},
url = {https://global-sci.com/article/73536/an-iterative-two-grid-method-of-a-finite-element-pml-approximation-for-the-two-dimensional-maxwell-problem}
}