Collaborative Research: CMG: Quantum Monte Carlo Calculations of Deep Earth Materials

合作研究：CMG：地球深部材料的量子蒙特卡罗计算

• 批准号: 0530110
• 负责人: Lubos Mitas
• 金额: $ 27.63万
• 依托单位: North Carolina State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-09-15 至 2010-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0530110&HistoricalAwards=false
• 关键词: Collaborative; Research; CMG; Quantum; Monte

New mathematical methods in quantum Monte Carlo (QMC) simulation will be applied and developed to obtain more accurate properties of Earth materials than is possible using current electronic structure methods. QMC is one among the most precise known techniques to study realistic materials in physics and chemistry and provide a significant gain in precision compared traditional density functional theory (DFT) approaches. This will bring electronic structure quantum Monte Carlo methodology to a qualitatively higher level of applicability to complex materials and lead to increased accuracy. The new QMC techniques will be applied to forefront problems in the properties of Earth materials in order to obtain accurate equations of state, phase transitions, and elasticity of solid materials that are of high interest in geophysics. One significant limitation of today's QMC methods is the high computational demand, which currently makes applications to larger systems including solid solutions prohibitively expensive. A substantial portion of the QMC computation is spent on forming and evaluating a Slater determinant, which is constructed from one-particle orbitals. The team plans to develop and apply different localization transformations in order to obtain a sparse determinant. Two linear algebra methods will be developed for their efficient evaluation. First, Krylov's method for the iterative evaluation of a determinant will be incorporated into QMC. Secondly, the trace of the determinant will be calculated with Monte Carlo methods. Both techniques will further the goal of obtaining an order-N QMC techniques that are more efficient and applicable to a wider range of materials, well beyond the current possibilities.Computational mineral physics is part of the large effort to use computer simulations to predict and understand properties of the Earth. New mathematical techniques will be derived to make advance quantum Monte Carlo simulations more precise and significantly more efficient. The properties of important Earth materials at high pressure will be predicted with unprecedented accuracy. This work will also lead to a more precise description of a number of fundamental phase transitions in solid deep Earth. This project is a close collaboration between a mathematician, mathematical physicists, and geophysicists. It will bring new applied math methods into geoscience, with broad applicability to all Earth materials. The broader impact will include the development of new computational techniques applicable to many areas as well as the education of graduate students and post-docs in state-of-the-art materials simulations, teaching of new computational techniques in graduate level classes and during two workshops that will be organized.

将应用和开发量子蒙特卡洛（QMC）模拟中的新数学方法，以获得与使用当前电子结构方法相比，获得更准确的地球材料特性。 QMC是研究物理和化学中逼真的材料的最精确的已知技术之一，并在与传统密度功能理论（DFT）方法相比，精确地增长了显着增长。这将使电子结构量子蒙特卡洛方法论在质量上更高的适用性水平，并提高准确性。新的QMC技术将应用于地球材料特性中的最前沿问题，以获得对地球物理学高度兴趣的固体材料的准确方程。当今QMC方法的一个重要局限性是高计算需求，目前将其应用于较大的系统，包括固体解决方案过高的昂贵。 QMC计算的很大一部分用于形成和评估由单粒子轨道构建的Slater决定因素。团队计划开发和应用不同的本地化转换，以获得稀疏的决定因素。将开发两种线性代数方法，以进行有效的评估。首先，Krylov的迭代评估方法将纳入QMC。其次，确定因子的痕迹将使用蒙特卡洛方法计算。这两种技术都将进一步获得更有效且适用于更广泛材料的订单N QMC技术的目标，远远超出了当前的可能性。Computational矿物质物理学是使用计算机模拟来预测和理解地球特性的巨大努力的一部分。将得出新的数学技术，以使进步的量子蒙特卡洛模拟更加精确，更有效。在高压下，重要的地球材料的特性将以前所未有的精度预测。这项工作还将导致对固体深层地球中许多基本相变的更精确描述。这个项目是数学家，数学物理学家和地球物理学家之间的密切合作。它将将新的应用数学方法带入地球科学，并对所有地球材料具有广泛的适用性。更广泛的影响将包括开发适用于许多领域的新计算技术，以及在最先进的材料模拟中的研究生和毕业后的教育，研究生级课程中新的计算技术的教学以及将在两个将要组织的研讨会上。