Stabilized Finite Element Methods for the Schrödinger Wave Equation

Abstract

This paper presents two stabilized formulations for the Schrödinger wave equation. First formulation is based on the Galerkin/least-squares (GLS) method, and it sets the stage for exploring variational multiscale ideas for developing the second stabilized formulation. These formulations provide improved accuracy on cruder meshes as compared with the standard Galerkin formulation. Based on the proposed formulations a family of tetrahedral and hexahedral elements is developed. Numerical convergence studies are presented to demonstrate the accuracy and convergence properties of the two methods for a model electronic potential for which analytical results are available.

Multiscale real-space quantum-mechanical tight-binding calculations of electronic structure in crystals with defects using perfectly matched layers

“…LSMS hence provides a natural framework for the use of the methods described here to appropriately truncate the domain without spurious effects. Extending our method to LSMS and related numerical methods for electronic structure [KM09,MK12] is an area of our current activity.…”