Year: 2021
Author: Hongmei Zhang, Jianghua Yin, Jicheng Jin
Advances in Applied Mathematics and Mechanics, Vol. 13 (2021), Iss. 1 : pp. 176–190
Abstract
In this paper, some two-grid finite-volume methods are constructed for solving the steady-state Schrödinger equation. The method projects the original coupled problem onto a coarser grid, on which it is less expensive to solve, and then prolongates the approximated coarse solution back to the fine grid, on which it is not much more difficult to solve the decoupled problem. We have shown, both theoretically and numerically, that our schemes are more efficient and achieve asymptotically optimal accuracy as long as the mesh sizes satisfy $h=\mathcal{O}(H^2)$.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.OA-2019-0212
Advances in Applied Mathematics and Mechanics, Vol. 13 (2021), Iss. 1 : pp. 176–190
Published online: 2021-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 15
Keywords: Schrödinger equation coupled equation finite volume two-grid.
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