Multigrid Methods for Simulation of Complex Materials

辛辛那提大学的Thomas Beck获得了理论与计算化学项目的资助，继续他在使用多重网格方法模拟复杂材料方面的工作。Beck将继续发展多重网格方法来求解密度泛函理论中的Kohn-Sham方程和泊松静电方程。新的算法将被开发用于大规模并行计算机，如Cray T3D。一旦这些方法被开发出来，将在小分子和周期晶格系统上进行测试计算，以便与现有的从头算和平面波计算进行直接比较。应用包括：1)计算含硫化合物在金表面的化学结合；2)用蒙特卡罗模拟来计算氢和氢/氦等离子体在高压下的热力学信息，这些高压是无法进行实验的。在分子水平上理解化学过程需要量子处理来准确描述在复杂凝聚相环境中发生的化学键和重排。研究这些过程的现有算法受到计算固有的困难和方法的缩放特性的限制。Beck所追求的多重网格方法由于其严格的线性缩放能力和计算灵活性，为更传统的电子结构方法提供了有希望的替代方案。

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.