A multilevel Newton's method for eigenvalue problems

Yunhui He; Yu Li; Hehu Xie; Chun'guang You; Ning Zhang

Applications of Mathematics (2018)

  • Volume: 63, Issue: 3, page 281-303
  • ISSN: 0862-7940

Abstract

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We propose a new type of multilevel method for solving eigenvalue problems based on Newton's method. With the proposed iteration method, solving an eigenvalue problem on the finest finite element space is replaced by solving a small scale eigenvalue problem in a coarse space and a sequence of augmented linear problems, derived by Newton step in the corresponding sequence of finite element spaces. This iteration scheme improves overall efficiency of the finite element method for solving eigenvalue problems. Finally, some numerical examples are provided to validate the efficiency of the proposed numerical scheme.

How to cite

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He, Yunhui, et al. "A multilevel Newton's method for eigenvalue problems." Applications of Mathematics 63.3 (2018): 281-303. <http://eudml.org/doc/294519>.

@article{He2018,
abstract = {We propose a new type of multilevel method for solving eigenvalue problems based on Newton's method. With the proposed iteration method, solving an eigenvalue problem on the finest finite element space is replaced by solving a small scale eigenvalue problem in a coarse space and a sequence of augmented linear problems, derived by Newton step in the corresponding sequence of finite element spaces. This iteration scheme improves overall efficiency of the finite element method for solving eigenvalue problems. Finally, some numerical examples are provided to validate the efficiency of the proposed numerical scheme.},
author = {He, Yunhui, Li, Yu, Xie, Hehu, You, Chun'guang, Zhang, Ning},
journal = {Applications of Mathematics},
keywords = {eigenvalue problem; finite element method; Newton's method; multilevel iteration},
language = {eng},
number = {3},
pages = {281-303},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A multilevel Newton's method for eigenvalue problems},
url = {http://eudml.org/doc/294519},
volume = {63},
year = {2018},
}

TY - JOUR
AU - He, Yunhui
AU - Li, Yu
AU - Xie, Hehu
AU - You, Chun'guang
AU - Zhang, Ning
TI - A multilevel Newton's method for eigenvalue problems
JO - Applications of Mathematics
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 63
IS - 3
SP - 281
EP - 303
AB - We propose a new type of multilevel method for solving eigenvalue problems based on Newton's method. With the proposed iteration method, solving an eigenvalue problem on the finest finite element space is replaced by solving a small scale eigenvalue problem in a coarse space and a sequence of augmented linear problems, derived by Newton step in the corresponding sequence of finite element spaces. This iteration scheme improves overall efficiency of the finite element method for solving eigenvalue problems. Finally, some numerical examples are provided to validate the efficiency of the proposed numerical scheme.
LA - eng
KW - eigenvalue problem; finite element method; Newton's method; multilevel iteration
UR - http://eudml.org/doc/294519
ER -

References

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