His research group aims to develop computational and mathematical techniques to address various aspects of materials behavior, which exhibit complexity and structure on varying length and time scales. The work draws ideas from quantum mechanics, statistical mechanics and homogenization theories to create multi-scale models from fundamental principles, which provide insight into the complex behavior of materials. Topics of research include developing multi-scale methods for density-functional theory (electronic structure) calculations at continuum scales, electronic structure studies on defects in materials, quasi-continuum method, analysis of approximation theories, numerical analysis, and quantum transport in materials.
Hierarchy of triangulations that form the basis of a coarse-graining methods (quasi-continuum reduction) for conducting electronic structure calculations at macroscopic scales.
