TY - JOUR
T1 - An Algebraic Multigrid Method for Eigenvalue Problems and Its Numerical Tests
AU - Zhang , Ning
AU - Han , Xiaole
AU - He , Yunhui
AU - Xie , Hehu
AU - You , Chun'guang
JO - East Asian Journal on Applied Mathematics
VL - 1
SP - 1
EP - 19
PY - 2020
DA - 2020/11
SN - 11
DO - http://doi.org/10.4208/eajam.210918.090519
UR - https://global-sci.org/intro/article_detail/eajam/18410.html
KW - Algebraic multigrid, multilevel correction, eigenvalue problem.
AB - <p style="text-align: justify;">In order to solve eigenvalue problems, an algebraic multigrid method based
on a multilevel correction scheme and the algebraic multigrid method for linear equations is developed. The algebraic multigrid method setup procedure is used for construction of an hierarchy and intergrid transfer operators. In this approach, large scale
eigenvalue problems are solved by algebraic multigrid smoothing steps in the hierarchy
and by low-dimensional eigenvalue problems. The efficacy and flexibility of the method
is demonstrated by a number of test examples and the global convergence, which does
not depend on the number of eigenvalues wanted, is obtained.</p>