Title: Partition-of-unity finite elements and iterative solvers for large-scale ab initio electronic- Speaker: John E. Pask, Lawrence Livermore National Laboratory Date/Time: Wednesday, December 6, 2006, 10:30am – 11:30 am Location: CSRI Building, Room 90 (Sandia NM) Brief Abstract: Over the course of the past few decades, density functional theory (DFT) has proven to be an accurate and reliable basis for the understanding and prediction of a wide variety of materials properties from the first principles of quantum mechanics (ab initio), with no empirical parameters.However, the solution of the equations of DFT remains a formidable task and this has limited the range of materials problems which can be investigated by such rigorous, quantum mechanical means. We discuss work on a new finite-element (FE) based method [1,2] for large-scale ab initio electronic-structure calculations, with the goal of extending the range of materials systems that can be investigated by such means, by exploiting the strict locality, and associated natural parallelization, of the FE basis. We review the basic quantum mechanical equations to be solved and discuss their formulation in a form appropriate for solution in a general C^0 (continuous but not necessarily smooth) basis. We discuss recent work on the incorporation of modern partition-of-unity FE techniques, which allow the known physics to be built into the FE basis, thus reducing the required degrees of freedom substantially; and recent work on iterative solvers for the large, sparse, generalized eigenproblems produced by the method. Initial results show order-of-magnitude improvements relative to modern state-of-the-art electronic structure methods such as planewaves and AMR-FE for systems with localized states such as d- and f- electron metals. This work was performed under the auspices of the U.S. Department of Energy by University of California, Lawrence Livermore National Laboratory under Contract W-7405-Eng-48. [1] J.E. Pask and P.A. Sterne, "Finite element methods in ab initio electronic structure calculations," Modelling Simul. Mater. Sci. Eng. 13, [2] J.E. Pask and P.A. Sterne, "Real-space formalism for the electrostatic potential and total energy of solids," Phys. Rev. B 71, 113101 (2005). Collaborators: Natarajan Sukumar, University of California, Davis, Kristopher Andersen, Naval Research Laboratory, Philip Sterne, Lawrence Livermore National Laboratory CSRI POC: Richard Lehoucq, (505) 845-8929 |