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 12 articles )

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  1. Imakura, Akira; Li, Ren-Cang; Zhang, Shao-Liang: Locally optimal and heavy ball GMRES methods (2016)
  2. 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)
  3. Jiang, Bo; Dai, Yu-Hong: A framework of constraint preserving update schemes for optimization on Stiefel manifold (2015)
  4. Liu, Xin; Wen, Zaiwen; Wang, Xiao; Ulbrich, Michael; Yuan, Yaxiang: On the analysis of the discretized Kohn-Sham density functional theory (2015)
  5. Ulbrich, Michael; Wen, Zaiwen; Yang, Chao; Klöckner, Dennis; Lu, Zhaosong: A proximal gradient method for ensemble density functional theory (2015)
  6. Vecharynski, Eugene; Knyazev, Andrew: Preconditioned locally harmonic residual method for computing interior eigenpairs of certain classes of Hermitian matrices (2015)
  7. Zhang, Leihong; Li, Rencang: Maximization of the sum of the trace ratio on the Stiefel manifold, II: computation (2015)
  8. Bao, Gang; Hu, Guanghui; Liu, Di: Numerical solution of the Kohn-Sham equation by finite element methods with an adaptive mesh redistribution technique (2013)
  9. Wen, Zaiwen; Milzarek, Andre; Ulbrich, Michael; Zhang, Hongchao: Adaptive regularized self-consistent field iteration with exact Hessian for electronic structure calculation (2013)
  10. Wen, Zaiwen; Yin, Wotao: A feasible method for optimization with orthogonality constraints (2013)
  11. Bao, Gang; Hu, Guanghui; Liu, Di: An $h$-adaptive finite element solver for the calculations of the electronic structures (2012)
  12. Duminil, Sébastien; Sadok, Hassane: Reduced rank extrapolation applied to electronic structure computations (2011)