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Preconditioning orbital minimization method for planewave discretization. (English) Zbl 1365.65273

MSC:
65P10 Numerical methods for Hamiltonian systems including symplectic integrators
37M15 Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems
65F08 Preconditioners for iterative methods
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
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[1] S. Baroni and P. Giannozzi, Towards very large-scale electronic-structure calculations, Europhys. Lett., 17 (1992), pp. 547–552, .
[2] F. Bottin, S. Leroux, A. Knyazev, and G. Zérah, Large-scale ab initio calculations based on three levels of parallelization, Comput. Mater. Sci., 42 (2008), pp. 329–336.
[3] F. Corsetti, The orbital minimization method for electronic structure calculations with finite-range atomic basis sets, Comput. Phys. Commun., 185 (2014), pp. 873–883.
[4] A. Damle, L. Lin, and L. Ying, Pole expansion for solving a type of parametrized linear systems in electronic structure calculations, SIAM J. Sci. Comput., 36 (2014), pp. A2929–A2951, . · Zbl 1310.65047
[5] J. W. Demmel, L. Grigori, M. Gu, and H. Xiang, Communication avoiding rank revealing QR factorization with column pivoting, SIAM J. Matrix Anal. Appl., 36 (2015), pp. 55–89, . · Zbl 1327.65078
[6] A. George, Nested dissection of a regular finite element mesh, SIAM J. Numer. Anal., 10 (1973), pp. 345–363, . · Zbl 0259.65087
[7] S. Goedecker, Low complexity algorithms for electronic structure calculations, J. Comput. Phys., 118 (1995), pp. 261–268, . · Zbl 0827.65082
[8] S. Goedecker, Linear scaling electronic structure methods, Rev. Mod. Phys., 71 (1999), pp. 1085–1123, .
[9] N. Hale, N. J. Higham, and L. N. Trefethen, Computing \(a^α, \log(a)\), and related matrix functions by contour integrals, SIAM J. Numer. Anal., 46 (2008), pp. 2505–2523, . · Zbl 1176.65053
[10] N. Halko, P. G. Martinsson, and J. A. Tropp, Finding structure with randomness: Probabilistic algorithms for constructing approximate matrix decompositions, SIAM Rev., 53 (2011), pp. 217–288. · Zbl 1269.65043
[11] A. V. Knyazev, Toward the optimal preconditioned eigensolver: Locally optimal block preconditioned conjugate gradient method, SIAM J. Sci. Comput., 23 (2001), pp. 517–541, . · Zbl 0992.65028
[12] A. Levitt and M. Torrent, Parallel eigensolvers in plane-wave density functional theory, Comput. Phys. Commun., 187 (2015), pp. 98–105.
[13] Y. Li and H. Yang, Interpolative butterfly factorization, SIAM J. Sci. Comput., 2016, accepted. · Zbl 1365.65292
[14] L. Lin, J. Lu, L. Ying, R. Car, and W. E, Fast algorithm for extracting the diagonal of the inverse matrix with application to the electronic structure analysis of metallic systems, Commun. Math. Sci., 7 (2009), pp. 755–777. · Zbl 1182.65072
[15] L. Lin, J. Lu, L. Ying, and W. E, Pole-based approximation of the Fermi-Dirac function, Chin. Ann. Math. Ser. B, 30 (2009), pp. 729–742. · Zbl 1188.41007
[16] L. Lin, C. Yang, J. Lu, L. Ying, and W. E, A fast parallel algorithm for selected inversion of structured sparse matrices with application to 2d electronic structure calculations, SIAM J. Sci. Comput., 33 (2011), pp. 1329–1351, . · Zbl 1230.65039
[17] J. Lu and L. Ying, Sparsifying preconditioner for soliton calculations, J. Comput. Phys., 35 (2016), pp. 458–466. · Zbl 1349.65606
[18] P. G. Martinsson, Blocked Rank-Revealing QR Factorizations: How Randomized Sampling Can Be Used to Avoid Single-Vector Pivoting, 2015, preprint.
[19] F. Mauri and G. Galli, Electronic-structure calculations and molecular dynamics simulations with linear system-size scaling, Phys. Rev. B, 50 (1994), pp. 4316–4326, .
[20] F. Mauri, G. Galli, and R. Car, Orbital formulation for electronic-structure calculations with linear system-size scaling, Phys. Rev. B, 47 (1993), pp. 9973–9976, .
[21] P. Ordejón, D. A. Drabold, M. P. Grumbach, and R. M. Martin, Unconstrained minimization approach for electronic computations that scales linearly with system size, Phys. Rev. B, 48 (1993), pp. 14646–14649, .
[22] P. Ordejón, D. A. Drabold, R. M. Martin, and M. P. Grumbach, Linear system-size scaling methods for electronic-structure calculations, Phys. Rev. B, 51 (1995), pp. 1456–1476, .
[23] M. C. Payne, M. P. Teter, D. C. Allan, T. A. Arias, and J. D. Joannopoulos, Iterative minimization techniques for ab initio total-energy calculations: Molecular dynamics and conjugate gradients, Rev. Mod. Phys., 64 (1992), pp. 1045–1097, .
[24] B. G. Pfrommer, J. Demmel, and H. Simon, Unconstrained energy functionals for electronic structure calculations, J. Comput. Phys., 150 (1999), pp. 287–298, . · Zbl 0923.65089
[25] M. Pippig, PFFT: An extension of FFTW to massively parallel architectures, SIAM J. Sci. Comput., 35 (2013), pp. C213–C236, . · Zbl 1275.65098
[26] E. Polizzi, Density-matrix-based algorithm for solving eigenvalue problems, Phys. Rev. B, 79 (2009), 115112.
[27] J. Poulson, L. Demanet, N. Maxwell, and L. Ying, A parallel butterfly algorithm, SIAM J. Sci. Comput., 36 (2014), pp. C49–C65, . · Zbl 1290.65127
[28] J. Poulson, B. Marker, R. A. van de Geijn, J. R. Hammond, and N. A. Romero, Elemental: A new framework for distributed memory dense matrix computations, ACM Trans. Math. Software, 39 (2013), 13. · Zbl 1295.65137
[29] Y. Saad and M. H. Schultz, GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems, SIAM J. Sci. Statist. Comput., 7 (1986), pp. 856–869, . · Zbl 0599.65018
[30] M. P. Teter, M. C. Payne, and D. C. Allan, Solution of Schrödinger’s equation for large systems, Phys. Rev. B, 40 (1989), pp. 12255–12263, .
[31] L. Ying, Sparsifying preconditioner for pseudospectral approximations of indefinite systems on periodic structures, Multiscale Model. Simul., 13 (2015), pp. 459–471, . · Zbl 1317.65086
[32] L. Ying, Sparsifying preconditioner for the Lippmann–Schwinger equation, Multiscale Model. Simul., 13 (2015), pp. 644–660, . · Zbl 1317.65087
[33] Y. Zhou, J. R. Chelikowsky, X. Gao, and A. Zhou, On the “preconditioning” function used in planewave DFT calculations and its generalization, Commun. Comput. Phys., 18 (2015), pp. 167–179. · Zbl 1388.65195
[34] Y. Zhou, Y. Saad, M. L. Tiago, and J. R. Chelikowsky, Self-consistent-field calculations using Chebyshev-filtered subspace iteration, J. Comput. Phys., 219 (2006), pp. 172–184, . · Zbl 1105.65111
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