Multigrid Methods for Simulation of Complex Materials

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Thomas Beck, University of Cincinnati, is funded by a grant from the Theoretical and Computational Chemistry Program to continue his work in the use of multigrid methods for simulations of complex materials. Beck will continue his development of multigrid methods for solving the Kohn-Sham equations of density functional theory and the Poisson electrostatic equation. New algorithms will be developed for use on massively parallel computers such as the Cray T3D. Once the methods have been developed test computations will be carried out on small molecules and periodic lattice systems for direct comparison with existing ab initio and plane wave computations. Applications include: 1) calculations involving the chemical binding of sulfur compounds on gold surfaces; and 2) Monte Carlo simulations to compute thermodynamic information in hydrogen and hydrogen/helium plasmas at high pressures not available to experiment. Understanding chemical processes at the molecular level requires a quantum treatment to accurately describe chemical bonds and rearrangements occuring in complex condensed phase environments. Existing algorithms for studying these processes have been limited both by the inherent difficulties in such calculations and by the scaling properties of the methods. The multigrid methods being pursued by Beck offer promising alternatives to more traditional electronic structure approaches due to their rigorous linear scaling capabilities and computational flexibility.