Domain decomposition methods for electronic structure calculations

• Applicant: Professor Dr. Benjamin Stamm
• Subject Area: Mathematics
• Term: from 2019 to 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 411724963

• Final Report Year: 2025

Final Report Abstract

This project presents the construction and analysis of scalable preconditioning strategies for the linear Schrödinger eigenvalue problem with periodic potentials in anisotropic structures which is the first step towards the theoretical understanding of domain decomposition methods for electronic structure calculations. The anisotropic nature of the geometrical structures model the characteristics of many applications such as nano-tubes and sheets, or proteins. As only some dimensions of the computational domain expand to infinity, the resulting eigenvalue gap between the first and second eigenvalue vanishes, posing a significant challenge for numerical methods.

Publications

• A Quasi-Optimal Factorization Preconditioner for Periodic Schrödinger Eigenstates in Anisotropically Expanding Domains. SIAM Journal on Numerical Analysis, 60(5), 2508-2537.
  Stamm, Benjamin & Theisen, Lambert
  
• ddEigenLab.Jl: Domain-Decomposition Eigenvalue Problem Lab (v0.2). Zenodo. May
  Lambert Theisen & Benjamin Stamm
  
• A Scalable Two-Level Domain Decomposition Eigensolver for Periodic Schrödinger Eigenstates in Anisotropically Expanding Domains. SIAM Journal on Scientific Computing, 46(5), A3067-A3093.
  Theisen, Lambert & Stamm, Benjamin
  
• ddEigenLab.Jl: Domain-Decomposition Eigenvalue Problem Lab (v0.4). Zenodo. Apr.
  Lambert Theisen & Benjamin Stamm