| Issue |
ESAIM: M2AN
Volume 55, Number 5, September-October 2021
|
|
|---|---|---|
| Page(s) | 1779 - 1802 | |
| DOI | https://doi.org/10.1051/m2an/2021039 | |
| Published online | 17 September 2021 | |
A type of full multigrid method for non-selfadjoint Steklov eigenvalue problems in inverse scattering
1
Center for Applied Mathematics, Tianjin University, Tianjin 300072, China
mtxie@tju.edu.cn
2
Beijing Institute for Scientiic and Engineering Computing, College of applied sciences, Beijing University of Technology, Beijing 100124, China
xufei@lsec.cc.ac.cn
3
School of Mathematics and Statistics, Beijing Technology and Business University, Beijing 100048, China
* Corresponding author: yuemeiling@lsec.cc.ac.cn
Received:
19
August
2020
Accepted:
28
July
2021
In this paper, a type of full multigrid method is proposed to solve non-selfadjoint Steklov eigenvalue problems. Multigrid iterations for corresponding selfadjoint and positive definite boundary value problems generate proper iterate solutions that are subsequently added to the coarsest finite element space in order to improve approximate eigenpairs on the current mesh. Based on this full multigrid, we propose a new type of adaptive finite element method for non-selfadjoint Steklov eigenvalue problems. We prove that the computational work of these new schemes are almost optimal, the same as solving the corresponding positive definite selfadjoint boundary value problems. In this case, these type of iteration schemes certainly improve the overfull efficiency of solving the non-selfadjoint Steklov eigenvalue problem. Some numerical examples are provided to validate the theoretical results and the efficiency of this proposed scheme.
Mathematics Subject Classification: 35Q99 / 65N30 / 65M12 / 65M70
Key words: Non-selfadjoint steklov eigenvalue problem / full multigrid method / multilevel correction method / adaptive finite element method
© The authors. Published by EDP Sciences, SMAI 2021
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