Pole-based approximation of Fermi-Dirac function

Abstract

Two approaches for the efficient rational approximation of the Fermi-Dirac function are discussed: one uses the contour integral representation and conformal mapping and the other is based on a version of the multipole representation of the Fermi-Dirac function that uses only simple poles. Both representations have logarithmic computational complexity. They are of great interest for electronic structure calculations.

16 pages, 8 figures, dedicated to Professor Andy Majda on the occasion of his 60th birthday

References in corpus (3)

• An efficient and accurate decomposition of the Fermi operator
• Multipole Representation of the Fermi Operator with Application to the Electronic Structure Analysis of Metallic Systems
• A hybrid approach to Fermi operator expansion

Cited by in corpus (25)

• Adaptive local basis set for Kohn-Sham density functional theory in a discontinuous Galerkin framework I: Total energy calculation
• RESCU: a Real Space Electronic Structure Method
• Accelerating Atomic Orbital-based Electronic Structure Calculation via Pole Expansion and Selected Inversion
• Cubic scaling algorithms for RPA correlation using interpolative separable density fitting
• A subquadratic-scaling subspace projection method for large-scale Kohn-Sham density functional theory calculations using spectral finite-element discretization
• Cubic-scaling algorithm and self-consistent field for the random-phase approximation with second-order screened exchange
• Stochastic density functional theory
• Self-consistent field theory based molecular dynamics with linear system-size scaling
• SIESTA-PEXSI: Massively parallel method for efficient and accurate \textit{ab initio} materials simulation without matrix diagonalization
• Minimax rational approximation of the Fermi-Dirac distribution
• Optimized local basis set for Kohn-Sham density functional theory
• PSelInv -- A Distributed Memory Parallel Algorithm for Selected Inversion : the Symmetric Case
• Spectrum-splitting approach for Fermi-operator expansion in all-electron Kohn-Sham DFT calculations
• Assessment of localized and randomized algorithms for electronic structure
• Efficient iterative method for solving the Dirac-Kohn-Sham density functional theory
• Element orbitals for Kohn-Sham density functional theory
• Enhancing the scalability and load balancing of the parallel selected inversion algorithm via tree-based asynchronous communication
• Robust Determination of the Chemical Potential in the Pole Expansion and Selected Inversion Method for Solving Kohn-Sham density functional theory
• QM/MM methods for crystalline defects. Part 1: Locality of the tight binding model
• Interior Eigensolver for Sparse Hermitian Definite Matrices Based on Zolotarev's Functions
• PEXSI-$\Sigma$: A Green's function embedding method for Kohn-Sham density functional theory
• Numerical solution of large scale Hartree-Fock-Bogoliubov equations
• Pole expansion for solving a type of parametrized linear systems in electronic structure calculations
• Incomplete selected inversion for linear-scaling electronic structure calculations
• Split representation of adaptively compressed polarizability operator