Efficient Real Space Solution of the Kohn-Sham Equations with Multiscale Techniques

Details Efficient Real Space Solution of the Kohn-Sham Equations with Multiscale Techniques Efficient Real Space Solution of the Kohn-Sham Equations with Multiscale Techniques

1999-05-28

arxiv.org/abs/cond-mat/9905422v1

Physics

Condensed Matter

Materials Science

13 pages, 2 figures

Scientific paper

10.1063/1.481543

We present a multigrid algorithm for 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 heirarchy 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.

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