We describe the design and implementation of KSSOLV, a MATLAB toolbox for solving a class of nonlinear eigenvalue problems known as the Kohn-Sham equations. These types of problems arise in electronic structure calculations, which are nowadays essential for studying the microscopic quantum mechanical properties of molecules, solids, and other nanoscale materials. KSSOLV is well suited for developing new algorithms for solving the Kohn-Sham equations and is designed to enable researchers in computational and applied mathematics to investigate the convergence properties of the existing algorithms. The toolbox makes use of the object-oriented programming features available in MATLAB so that the process of setting up a physical system is straightforward and the amount of coding effort required to prototype, test, and compare new algorithms is significantly reduced. All of these features should also make this package attractive to other computational scientists and students who wish to study small- to medium-size systems.

This software is also peer reviewed by journal TOMS.

References in zbMATH (referenced in 35 articles , 1 standard article )

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  1. Gao, Yijin; Mayfield, Jay; Bao, Gang; Liu, Di; Luo, Songting: An asymptotic Green’s function method for time-dependent Schrödinger equations with application to Kohn-Sham equations (2022)
  2. An, Dong; Lin, Lin; Xu, Ze: Split representation of adaptively compressed polarizability operator (2021)
  3. Oviedo, Harry; Dalmau, Oscar; Lara, Hugo: Two adaptive scaled gradient projection methods for Stiefel manifold constrained optimization (2021)
  4. Figueroa, Edgar Fuentes; Dalmau, Oscar: Transportless conjugate gradient for optimization on Stiefel manifold (2020)
  5. Kelley, C. T.; Bernholc, J.; Briggs, E. L.; Hamilton, Steven; Lin, Lin; Yang, Chao: Mesh independence of the generalized Davidson algorithm (2020)
  6. Xu, Fei: A cascadic adaptive finite element method for nonlinear eigenvalue problems in quantum physics (2020)
  7. Gao, Bin; Liu, Xin; Yuan, Ya-Xiang: Parallelizable algorithms for optimization problems with orthogonality constraints (2019)
  8. Hu, Jiang; Jiang, Bo; Lin, Lin; Wen, Zaiwen; Yuan, Ya-Xiang: Structured quasi-Newton methods for optimization with orthogonality constraints (2019)
  9. Lin, Lin; Zepeda-Nunez, Leonardo: Projection-based embedding theory for solving Kohn-Sham density functional theory (2019)
  10. Shen, Yedan; Kuang, Yang; Hu, Guanghui: An asymptotics-based adaptive finite element method for Kohn-Sham equation (2019)
  11. Cancès, Eric (ed.); Friesecke, Gero (ed.); Helgaker, Trygve Ulf (ed.); Lin, Lin (ed.): Mathematical methods in quantum chemistry. Abstracts from the workshop held March 18--24, 2018 (2018)
  12. Dalmau Cedeño, Oscar Susano; Oviedo Leon, Harry Fernando: Projected nonmonotone search methods for optimization with orthogonality constraints (2018)
  13. Gao, Bin; Liu, Xin; Chen, Xiaojun; Yuan, Ya-xiang: A new first-order algorithmic framework for optimization problems with orthogonality constraints (2018)
  14. Hu, Guanghui; Xie, Hehu; Xu, Fei: A multilevel correction adaptive finite element method for Kohn-Sham equation (2018)
  15. Hu, Jiang; Milzarek, Andre; Wen, Zaiwen; Yuan, Yaxiang: Adaptive quadratically regularized Newton method for Riemannian optimization (2018)
  16. Zhang, Xiaoping; Su, Shuai; Wu, Jiming: A vertex-centered and positivity-preserving scheme for anisotropic diffusion problems on arbitrary polygonal grids (2017)
  17. Cancès, Eric; Dusson, Geneviève; Maday, Yvon; Stamm, Benjamin; Vohralík, Martin: A perturbation-method-based post-processing for the planewave discretization of Kohn-Sham models (2016)
  18. Imakura, Akira; Li, Ren-Cang; Zhang, Shao-Liang: Locally optimal and heavy ball GMRES methods (2016)
  19. Shao, MeiYue; Lin, Lin; Yang, Chao; Liu, Fang; Da Jornada, Felipe H.; Deslippe, Jack; Louie, Steven G.: Low rank approximation in (G_0W_0) calculations (2016)
  20. Vecharynski, Eugene; Knyazev, Andrew: Preconditioned steepest descent-like methods for symmetric indefinite systems (2016)

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