Three-scale finite element discretizations for quantum eigenvalue problems

Based on globally and locally coupled discretizations, some three-scale finite element schemes are proposed in this paper for a class of quantum eigenvalue problems. It is shown that the solution of a quantum eigenvalue problem on a fine grid may be reduced to the solution of an eigenvalue problem on a relatively coarse grid, and the solutions of linear algebraic systems on a globally mesoscopic grid and the locally fine grid, and the resulting solution is still very satisfactory.