Multigrid Method for Large Scale Electronic Structure of Materials

摘要

The funding from this grant was utilized to further develop a new approach forthe electronic structure of materials. The method formulates the Kohn-Sham equations of Density Functional Theory directly in real space with a high order Finite Difference approach. The resulting equations were solved using the linear scaling multigrid algorithm developed by Brandt and coworkers. Multigrid techniques were used to solve both the self consistent eigenvalue equations and the Poisson equation for the electrostatic potential at each step of iterations. Accurate numerical results were obtained for finite and periodic electrostatic problems and for the eigenvalue equations for many electron atoms and simple molecules. Recently, conservative grid equations have been developed so that grid refinement strategies can be employed. This allows one to perform extensive numerical work selectively in regions of high electron density. The new method should have wide applications for numerical studies of complex and disordered materials which require a quantum mechanical treatment for many atoms.