Accelerated Block Preconditioned Gradient method for large scale wave functions calculations in Density Functional Theory

An Accelerated Block Preconditioned Gradient (ABPG) method is proposed to solve electronic structure problems in Density Functional Theory. This iterative algorithm is designed to solve directly the non-linear Kohn–Sham equations for accurate discretization schemes involving a large number of degrees of freedom. It makes use of an acceleration scheme similar to what is known as RMM-DIIS in the electronic structure community. The method is illustrated with examples of convergence for large scale applications using a finite difference discretization and multigrid preconditioning.