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.

该项目涉及对电子结构计算的密度功能理论（DFT）产生的非线性特征值问题的后验误差估计。该项目建立在初步工作的基础上，该工作是为了简单的毛利语特征值问题而建立的。目的是提供近似能量和确切能量之间误差的确保界限。 DFT模型主要使用所谓的自洽场（SCF）迭代来解决，在SCF-词法过程中的每个步骤都解决了线性特征值问题。将设计估计器，以使总误差的每个误差组件可以量化，即由于PlaneWave离散化而导致的离散误差，由于未交配的SCF迭代而导致的迭代误差以及由于线性特征值问题的迭代求解器而引起的误差。这种分裂允许设计自适应算法，并在不同的错误源之间具有错误平衡。估计器将是凸DFT模型误差的保证上限，最终的工作包将处理到非凸模型。开发的方法和估计器将在开源DFTK软件包中实现和测试。