An analysis for the DIIS acceleration method used in quantum chemistry calculations
Tóm tắt
Từ khóa
Tài liệu tham khảo
Arioli M., Vlastimil Pták, Strakoš Zdenek: Krylov sequences of maximal length and convergence of GMRES. BIT Numer. Math. 38(4), 636 (1998)
ABINIT is a common project of the Université Catholique de Louvain, Corning Incorporated, and other contributors, for further details see http://www.abinit.org
Beckermann B., Kuijlaars A.B.J.: Superlinear convergence of conjugate gradients. SIAM J. Numer. Anal. 39, 300 (2001)
Beckermann B., Kuijlaars A.B.J.: Superlinear CG convergence for special right-hand sides. Electron. Trans. Numer. Anal. 14, 1 (2002)
bigDFT, http://www-drfmc.cea.fr/sp2m/L_Sim/BigDFT/index.en.html
Broyden C.G.: A class of methods for solving nonlinear simultaneous equations. Math. Comput. 19, 577 (1965)
Broyden C.G., Dennis J.E., Moré J.J.: On the local and superlinear convergence of Quasi-Newton methods. J. Inst. Math. Appl. 12, 223 (1973)
E.J. Bylaska et al., NWChem, A Computational Chemistry Package for Parallel Computers, Version 5.1, Pacific Northwest National Laboratory, Richland, Washington 99352-0999, USA. A modified version, (2007)
Cancès E., Le Bris C.: On the convergence of SCF algorithms for the Hartree-Fock equations. M2AN 34, 749 (2000)
Császár P., Pulay P.: Geometry optimization by direct inversion in the iterative subspace. J. Mol. Struct. 114, 31 (1984)
Dennis J.E. Jr., Schnabel R.B.: Numerical Methods for Unconstrained Optimization and Nonlinear Equations. SIAM, Philadelphia (1996)
Deuflhard P., Freund R., Waltera A.: Fast secant methods for the iterative solution of large nonsymmetric linear systems. Impact Comput. Sci. Eng. 2(3), 2446 (1990)
Eckert F., Pulay P., Werner H.-J.: Ab initio geometry optimization for large molecules. J. Comput. Chem. 18, 1473 (1997)
Fischer T.H., Almlöf J.: General methods for geometry and wave function optimization. J. Phys. Chem. 92, 9768 (1992)
Gay D.M., Schnabel R.B.: Solving Systems of Nonlinear Equations by Broyden’s Method with Projected Updates, Nonlinear Programming 3. Academic Press, London (1978)
Genovese L., Neelov A., Goedecker S., Deutsch T., Ghasemi S.A., Willand A., Caliste D., Zilberberg O., Rayson M., Bergman A., Schneider R.: Daubechies wavelets as a basis set for density functional pseudopotential calculations. J. Chem. Phys. 129, 014109 (2009)
Griewank A.: The local convergence of Broyden-like Methods on Lipschitzian problems in Hilbert spaces. SIAM Numer. Anal. 24(3), 684 (1987)
Harrison R.J.: Krylov subspace accelerated inexact Newton method for linear and nonlinear equations. J. Comput. Chem. 25, 328 (2003)
S. Høst, J. Olsen , B. Jansik, L. Thøgersen, P. Jørgensen, T. Helgaker, The augmented Roothaan-Hall method for optimizing Hartree-Fock and Kohn-Sham density matrices. J. Chem. Phys. 129(12), PMID: 124106 (2008)
Hu X., Yang W.: Accelerating self-consistent field convergence with the augmented RoothaanHall energy function. J. Chem. Phys. 132(5), 054109 (2010)
Y. Huang, H. van der Vorst, Some observations on the convergence behavior of GMRES, Tech. Rep. 89-09, Faculty of Technical Mathematics and Informatics, Delft University of Technology, The Netherlands (1989)
Kawata M., Kortis C.M., Friesner R.A.: Efficient recursive implementation of the modified Broyden method and the direct inversion in the iterative subspace method: acceleration of self-consistent calculations. J. Chem. Phys. 108(11), 4426 (1998)
H.M. Klie, Krylov-secant methods for solving large-scale systems of coupled nonlinear parabolic equations. PhD thesis (Rice University Houston, TX, USA, 1997)
Kresse G., Furthmüller J.: Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54(16), 11169 (1996)
Kudin K.N., Scuseria G.E.: Converging self-consistent field equations in quantum chemistry—recent achievements and remaining challenges. ESAIM: Math. Model. Numer. Anal. 41(2), 281 (2007)
Kudin K.N., Scuseria G.E., Cancès E.: A black-box self-consistent field iteration convergence algorithm: one step closer. J. Chem. Phys. 116, 8255 (2002)
Liesen J., Tichy P.: Convergence analysis of Krylov subspace methods. GAMM-Mitteilungen 27(2), 153 (2004)
Marks L.D., Luke D.R.: Robust mixing for ab initio quantum mechanical calculations. Phys. Rev. B 78(8), 075114 (2008)
Martinez J.M., Lopez T.L.: Combination of the sequential secant method and Broyden’s method with projected updates. Computing 25, 379 (1980)
Ortega J.M., Rheinboldt W.C.: Iterative Solution of Nonlinear Equations in Several Variables. Academic Press, London (1970)
Pulay P.: Convergence acceleration of iterative sequences. The case of SCF iteration. Chem. Phys. Lett. 73(2), 393 (1980)
T. Rohwedder, An analysis for some methods and algorithms of quantum chemistry. PhD thesis, TU Berlin, 2010, available at http://opus.kobv.de/tuberlin/volltexte/2010/2852
T. Rohwedder, R. Schneider, The continuous coupled cluster method. Submitted to M2AN, available at www.dfg-spp1324.de/download/preprints/preprint97.pdf
Saad Y., Schultz M.H.: GMRES: a generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM J. Sci. Stat. Comput. 7, 856 (1986)
Schneider R., Rohwedder T., Blauert J., Neelov A.: Direct minimization for calculating invariant subspaces in density functional computations of the electronic structure. J. Comput. Math. 27, 360 (2009)
H.H.B. Sørensen, O. Østerby, in On one-point iterations and DIIS. Numerical Analysis and Applied Mathematics: International Conference on Numerical Analysis and Applied Mathematics 2009: Volume 1 and Volume 2. AIP Conference Proceedings, vol 1168, p. 468 (2009)
Thogersen L., Olsen J., Köhn A., Jorgensen P., Salek P., Helgaker T.: The trust-region self-consistent field iteration method in Kohn-Sham density functional theory. J. Chem. Phys. 123, 074103 (2005)
van der Vorst H.A., Vuik C.: The superlinear convergence behaviour of GMRES. J. Comput. Appl. Math. 48(3), 327 (1993)
Yang C., Gao W., Meza J.C.: On the convergence of the self-consistent field iteration for a class of nonlinear eigenvalue problems. SIAM J. Matrix Anal. Appl. 30(4), 1773 (2008)
C. Yang, J.C. Meza, L.-W. Wang, A trust region direct constrained minimization algorithm for the Kohn-Sham equation. SIAM J. Sci. Comput. 29(5), 1854 (electronic), 15A18 (65F15 65K10) (2007)