TY - JOUR
T1 - A Two-Grid Finite-Volume Method for the Schrödinger Equation
AU - Zhang , Hongmei
AU - Yin , Jianghua
AU - Jin , Jicheng
JO - Advances in Applied Mathematics and Mechanics
VL - 1
SP - 176
EP - 190
PY - 2020
DA - 2020/10
SN - 13
DO - http://doi.org/10.4208/aamm.OA-2019-0212
UR - https://global-sci.org/intro/article_detail/aamm/18346.html
KW - Schrödinger equation,  coupled equation, finite volume,  two-grid.
AB - <p style="text-align: justify;">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,&nbsp; that our schemes are more efficient and achieve asymptotically optimal accuracy as long as the mesh sizes satisfy $h=\mathcal{O}(H^2)$.</p>