Efficient real-space solution of the Kohn–Sham equations with multiscale techniques
Jian Wang, Thomas L. Beck · The Journal of Chemical Physics · 2000
We present a multigrid algorithm for a self-consistent solution of the Kohn–Sham equations in real space. The entire problem is discretized on a real-space mesh with a high-order finite difference representation. The resulting self-consistent equations are solved on a hierarchy of grids of increasing resolution with a nonlinear full approximation scheme, full multigrid algorithm. The self-consistency is effected by updates of the Poisson equation and the exchange-correlation potential at the end of each eigenfunction correction cycle. The algorithm leads to highly efficient solution of the equations, whereby the ground-state electron distribution is obtained in only two or three self-consistency iterations on the finest scale.