Finite difference schemes and block Rayleigh quotient iteration for electronic structure calculations on composite grids

DOI10.1006/jcph.1998.6138zbMath0922.65079OpenAlexW2092002692MaRDI QIDQ1282381

Jean-Luc Fattebert

Publication date: 30 March 1999

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jcph.1998.6138

zbMATH Keywords

finite difference schemeelectronic structuremoleculeKohn-Sham equationspseudopotentialsblock Rayleigh quotient iterationsingular atomic potentials

Mathematics Subject Classification ID

PDEs in connection with quantum mechanics (35Q40) Finite difference methods for boundary value problems involving PDEs (65N06) Applications to the sciences (65Z05) Molecular physics (81V55)

Related Items

Finite element approach for density functional theory calculations on locally-refined meshes, SPARC: accurate and efficient finite-difference formulation and parallel implementation of density functional theory: extended systems, SPARC: accurate and efficient finite-difference formulation and parallel implementation of density functional theory: isolated clusters, An \(h\)-adaptive finite element solver for the calculations of the electronic structures

Uses Software

• LAPACK
• JDQZ

Cites Work

• A new look at the Lanczos algorithm for solving symmetric systems of linear equations
• The iterative calculation of a few of the lowest eigenvalues and corresponding eigenvectors of large real-symmetric matrices
• A block Rayleigh quotient iteration with local quadratic convergence
• An inverse iteration method using multigrid for quantum chemistry
• Einige abstrakte Begriffe in der numerischen Mathematik (Anwendungen der Halbordnung).(Some abstract notions in the numerical mathematic. (Applications et semiorder))
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• Local Mesh Refinement Multilevel Techniques
• Multi-Level Adaptive Solutions to Boundary-Value Problems
• The Davidson Method
• A Jacobi–Davidson Iteration Method for Linear Eigenvalue Problems
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