Implicit application of polynomial filters in a k-step Arnoldi method
SIAM Journal on Matrix Analysis and Applications
The symmetric eigenvalue problem
The symmetric eigenvalue problem
Thick-restart Lanczos method for electronic structure calculations
Journal of Computational Physics
Parallel methods and tools for predicting material properties
Computing in Science and Engineering
Thick-Restart Lanczos Method for Large Symmetric Eigenvalue Problems
SIAM Journal on Matrix Analysis and Applications
KSSOLV—a MATLAB toolbox for solving the Kohn-Sham equations
ACM Transactions on Mathematical Software (TOMS)
Efficient solution of the Schroedinger-Poisson equations in layered semiconductor devices
Journal of Computational Physics
A block Chebyshev-Davidson method with inner-outer restart for large eigenvalue problems
Journal of Computational Physics
SelInv---An Algorithm for Selected Inversion of a Sparse Symmetric Matrix
ACM Transactions on Mathematical Software (TOMS)
Dimensional Reductions for the Computation of Time-Dependent Quantum Expectations
SIAM Journal on Scientific Computing
Practical acceleration for computing the HITS ExpertRank vectors
Journal of Computational and Applied Mathematics
Quantum algorithms for predicting the properties of complex materials
Proceedings of the 1st Conference of the Extreme Science and Engineering Discovery Environment: Bridging from the eXtreme to the campus and beyond
Dissecting the FEAST algorithm for generalized eigenproblems
Journal of Computational and Applied Mathematics
Hi-index | 31.46 |
The power of density functional theory is often limited by the high computational demand in solving an eigenvalue problem at each self-consistent-field (SCF) iteration. The method presented in this paper replaces the explicit eigenvalue calculations by an approximation of the wanted invariant subspace, obtained with the help of well-selected Chebyshev polynomial filters. In this approach, only the initial SCF iteration requires solving an eigenvalue problem, in order to provide a good initial subspace. In the remaining SCF iterations, no iterative eigensolvers are involved. Instead, Chebyshev polynomials are used to refine the subspace. The subspace iteration at each step is easily five to ten times faster than solving a corresponding eigenproblem by the most efficient eigen-algorithms. Moreover, the subspace iteration reaches self-consistency within roughly the same number of steps as an eigensolver-based approach. This results in a significantly faster SCF iteration.