Numerical Solution of the Kohn-Sham Equation by Finite Element Methods with an Adaptive Mesh Redistribution Technique

A finite element method with an adaptive mesh redistribution technique is presented for solving the Kohn-Sham equation. The mesh redistribution strategy is based on the harmonic mapping, and the movement of grid points is partially controlled by the monitor function that depends on the gradient of the electron density. Compared with fixed meshes, both efficiency and accuracy of the solution are improved significantly. Effectiveness and robustness of the solver are illustrated by numerical experiments.