A Two-Grid Algorithm of the Finite Element Method for the Two-Dimensional Time-Dependent Schrödinger Equation

Jianyun Wang, Zixin Zhong, Zhikun Tian () and Ying Liu ()
Additional contact information
Jianyun Wang: School of Science, Hunan University of Technology, Zhuzhou 412007, China
Zixin Zhong: School of Science, Hunan University of Technology, Zhuzhou 412007, China
Zhikun Tian: School of Computational Science and Electronics, Hunan Institute of Engineering, Xiangtan 411104, China
Ying Liu: College of Information and Intelligence, Hunan Agricultural University, Changsha 410128, China

Mathematics, 2024, vol. 12, issue 5, 1-12

Abstract: In this paper, we construct a new two-grid algorithm of the finite element method for the Schrödinger equation in backward Euler and Crank–Nicolson fully discrete schemes. On the coarser grid, we solve coupled real and imaginary parts of the Schrödinger equation. On the fine grid, real and imaginary parts of the Schrödinger equation are decoupled, and we solve the elliptic equation about real and imaginary parts, respectively. Then, we obtain error estimates of the exact solution with the two-grid solution in the H 1 -norm and carry out two numerical experiments.

Keywords: two-grid algorithm; Schrödinger equation; finite element method; backward Euler scheme; Crank–Nicolson scheme (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/12/5/726/pdf (application/pdf)
https://www.mdpi.com/2227-7390/12/5/726/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:12:y:2024:i:5:p:726-:d:1348672

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().