KOHN-SHAM DENSITY FUNCTIONALS ACCURATELY SOLVED BY A FINITE-ELEMENT MULTIGRID (FEM-MG) METHOD FOR LIGHTER ATOMS AND DIATOMIC-MOLECULES

The finite-element multi-grid method combines the stability and high a ccuracy of FEM with the ability of MG to solve sparse matrix equations very quickly, scaling basically linear with the number of unknowns. I t is applied to effectively two-dimensional problems like atoms and di atomic molecules under axial symmetry described by density and orbital functionals, respectively. The high solution efficiency (accuracy and speed) of FEM-MG obtained already is demonstrated for Bet which in ma ny respects is a particularly difficult case. Thus our finite-element multi-grid method allows large-scale investigations with controlled ac curacy of various combinations of exchange-correlation density functio nals for the description of lighter atoms and diatomic molecules.