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

• Applicant: Professor Dr. Benjamin Stamm
• Subject Area: Mathematics
• Term: since 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 516782692

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.

• DFG Programme: Research Grants
• International Connection: France
• Cooperation Partner: Dr. Geneviève Dusson