A posteriori error estimates and adaptive strategies for nonlinear models in electronic structure calculations

电子结构计算中非线性模型的后验误差估计和自适应策略

• 批准号: 516782692
• 负责人: Professor Dr. Benjamin Stamm
• 金额: --
• 依托单位: Lehrstuhl für Numerische Mathematik für Höchstleistungsrechner
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/516782692?language=en
• 关键词: posteriori; error; estimates; adaptive; strategies

This project deals with certified a posteriori error estimations of nonlinear eigenvalue problems arising in Density-Functional Theory (DFT) of electronic structure calculations. The project builds upon preliminary work established for the simpler Gross-Piteavskii eigenvalue problem. The goal is to provide guaranteed bounds of the error between the approximate energy and the exact energy. DFT models are dominantly solved using the so-called Self-Consistent Field (SCF) iterations where a linear eigenvalue problem is solved at each step within the SCF-iterative procedure. The estimator will be designed such that each error component of the total error can be quantified, namely the discretization error due to the planewave discretization, the iteration error due to the non-converged SCF- iterations, and the error due to the iterative solver of the linear eigenvalue problems. This splitting allows the design of an adaptive algorithm with error balancing between the different error sources. The estimator will be a guaranteed upper bound of the error for convex DFT-models and the final work-package will treat the extension to non-convex models. The developed methods and estimators will be implemented and tested in the open-source DFTK software package.

该项目处理电子结构计算的密度泛函理论 (DFT) 中出现的非线性特征值问题的经过认证的后验误差估计。该项目建立在为更简单的 Gross-Piteavskii 特征值问题所做的初步工作的基础上。目标是提供近似能量和精确能量之间误差的有保证的界限。 DFT 模型主要使用所谓的自洽场 (SCF) 迭代来求解，其中线性特征值问题在 SCF 迭代过程中的每个步骤中求解。估计器将被设计为使得总误差的每个误差分量都可以被量化，即由于平面波离散化引起的离散化误差、由于非收敛的SCF迭代引起的迭代误差以及由于迭代求解器引起的误差线性特征值问题。这种划分允许设计一种在不同误差源之间具有误差平衡的自适应算法。估计器将是凸 DFT 模型的误差上限，最终工作包将处理对非凸模型的扩展。开发的方法和估计器将在开源 DFTK 软件包中实施和测试。