KSSOLV-GPU: an Efficient GPU-Enabled MATLAB Toolbox for Solving the Kohn-Sham Equations within Density Functional Theory in Plane-Wave Basis Set<sup>†</sup>

Zhen-lin Zhang; Shi-zhe Jiao; Jie-lan Li; Wen-tiao Wu; Ling-yun Wan; Xin-ming Qin; Wei Hu; Jin-long Yang

doi:10.1063/1674-0068/cjcp2108139

Volume 34 Issue 5

Oct. 2021

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Article Navigation > Chinese Journal of Chemical Physics > 2021 > 34(5): 552-564

Zhen-lin Zhang, Shi-zhe Jiao, Jie-lan Li, Wen-tiao Wu, Ling-yun Wan, Xin-ming Qin, Wei Hu, Jin-long Yang. KSSOLV-GPU: an Efficient GPU-Enabled MATLAB Toolbox for Solving the Kohn-Sham Equations within Density Functional Theory in Plane-Wave Basis Set†[J]. Chinese Journal of Chemical Physics , 2021, 34(5): 552-564. doi: 10.1063/1674-0068/cjcp2108139

Citation:

Zhen-lin Zhang, Shi-zhe Jiao, Jie-lan Li, Wen-tiao Wu, Ling-yun Wan, Xin-ming Qin, Wei Hu, Jin-long Yang. KSSOLV-GPU: an Efficient GPU-Enabled MATLAB Toolbox for Solving the Kohn-Sham Equations within Density Functional Theory in Plane-Wave Basis Set^†[J]. Chinese Journal of Chemical Physics , 2021, 34(5): 552-564. doi: 10.1063/1674-0068/cjcp2108139

Citation:

Zhen-lin Zhang, Shi-zhe Jiao, Jie-lan Li, Wen-tiao Wu, Ling-yun Wan, Xin-ming Qin, Wei Hu, Jin-long Yang. KSSOLV-GPU: an Efficient GPU-Enabled MATLAB Toolbox for Solving the Kohn-Sham Equations within Density Functional Theory in Plane-Wave Basis Set^†[J]. Chinese Journal of Chemical Physics , 2021, 34(5): 552-564. doi: 10.1063/1674-0068/cjcp2108139

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KSSOLV-GPU: an Efficient GPU-Enabled MATLAB Toolbox for Solving the Kohn-Sham Equations within Density Functional Theory in Plane-Wave Basis Set^†

doi: 10.1063/1674-0068/cjcp2108139

Hefei National Laboratory for Physical Sciences at the Microscale, Department of Chemical Physics, Synergetic Innovation Center of Quantum Information and Quantum Physics, and Anhui Center for Applied Mathematics, University of Science and Technology of China, Hefei 230026, China

More Information

Corresponding author: Wei Hu, E-mail: whuustc@ustc.edu.cn
Received Date: 2021-08-16
Accepted Date: 2021-10-08
Publish Date: 2021-10-27

Abstract

Abstract

KSSOLV (Kohn-Sham Solver) is a MATLAB (Matrix Laboratory) toolbox for solving the Kohn-Sham density functional theory (KS-DFT) with the plane-wave basis set. In the KS-DFT calculations, the most expensive part is commonly the diagonalization of Kohn-Sham Hamiltonian in the self-consistent field (SCF) scheme. To enable a personal computer to perform medium-sized KS-DFT calculations that contain hundreds of atoms, we present a hybrid CPU-GPU implementation to accelerate the iterative diagonalization algorithms implemented in KSSOLV by using the MATLAB built-in Parallel Computing Toolbox. We compare the performance of KSSOLV-GPU on three types of GPU, including RTX3090, V100, and A100, with conventional CPU implementation of KSSOLV respectively and numerical results demonstrate that hybrid CPU-GPU implementation can achieve a speedup of about 10 times compared with sequential CPU calculations for bulk silicon systems containing up to 128 atoms.
- Kohn-Sham Solver,
- Density functional theory,
- Iterative eigensolver,
- MATLAB,
- GPU

^†Part of special topic of “the Young Scientist Forum on Chemical Physics: Theoretical and Computational Chemistry Workshop 2020”.

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References(46)

References

[1]	P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964). doi: 10.1103/PhysRev.136.B864
[2]	W. Kohn and L. J. Sham, Phys. Rev. 140, A1133 (1965). doi: 10.1103/PhysRev.140.A1133
[3]	G. B. Wang, H. Q. Zhao, Z. L. Zhang, W. L. Wang, and D. M. Chen, Chin. J. Chem. Phys. 28, 579 (2015). doi: 10.1063/1674-0068/28/cjcp1504067
[4]	J. Y. Weng, T. T. Zhou, and Y. H. Zhang, Chin. J. Chem. Phys. 27, 285 (2014). doi: 10.1063/1674-0068/27/03/285-290
[5]	D. Wu, G. D. Chen, C. Y. Ge, Z. P. Hu, X. H. He, and X. G. Li, Chin. J. Chem. Phys. 30, 295 (2017). doi: 10.1063/1674-0068/30/cjcp1703035
[6]	H. Ehrenreich and M. H. Cohen, Phys. Rev. 115, 786 (1959). doi: 10.1103/PhysRev.115.786
[7]	Q. Jiang, L. Wan, S. Jiao, W. Hu, J. Chen, and H. An, in 2020 IEEE 22nd International Conference on High Performance Computing and Communications; IEEE 18th International Conference on Smart City; IEEE 6th International Conference on Data Science and Systems (HPCC/SmartCity/DSS) IEEE, 197-205 (2020).
[8]	S. Das, P. Motamarri, V. Gavini, B. Turcksin, Y. W. Li, and B. Leback, in Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis, 1-11 (2019).
[9]	W. Jia, L. W. Wang, and L. Lin, in Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis, 1-23 (2019).
[10]	L. Wang, Y. Wu, W. Jia, W. Gao, X. Chi, and L. W. Wang, in SC'11: Proceedings of 2011 International Conference for High Performance Computing, Networking, Storage and Analysis, IEEE, 1-10 (2011).
[11]	W. Jia, J. Fu, Z. Cao, L. Wang, X. Chi, W. Gao, and L. W. Wang, J. Comput. Phys. 251, 102 (2013). doi: 10.1016/j.jcp.2013.05.005
[12]	C. Yang, J. C. Meza, B. Lee, and L. W. Wang, ACM Trans. Math. Softw. 36, 1 (2009).
[13]	G. Kresse and J. Hafner, Phys. Rev. B 47, 558 (1993). doi: 10.1103/PhysRevB.47.558
[14]	P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G. L. Chiarotti, M. Cococcioni, I. Dabo, A. D. Corso, S. d. Gironcoli, S. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos, N. Marzari, F. Mauri, R. Mazzarello, S. Paolini, A. Pasquarello, L. Paulatto, C. Sbraccia, S. Scandolo, G. Sclauzero, A. P. Seitsonen, A. Smogunov, P. Umari, and R. M. Wentzcovitch, J. Phys. : Condens. Matter 21, 395502 (2009). doi: 10.1088/0953-8984/21/39/395502
[15]	J. Hutter and M. Iannuzzi, Z. Kristallogr. Cryst. Mater. 220, 549 (2005). doi: 10.1524/zkri.220.5.549.65080
[16]	S. J. Clark, M. D. Segall, C. J. Pickard, P. J. Hasnip, M. I. Probert, K. Refson, and M. C. Payne, Z. Kristallogr. Cryst. Mater. 220, 567 (2005). doi: 10.1524/zkri.220.5.567.65075
[17]	J. Noffsinger, F. Giustino, B. D. Malone, C. H. Park, S. G. Louie, and M. L. Cohen, Comput. Phys. Commun. 181, 2140 (2010). doi: 10.1016/j.cpc.2010.08.027
[18]	F. Gygi, IBM J. Res. Dev. 52, 137 (2008). doi: 10.1147/rd.521.0137
[19]	S. Boeck, C. Freysoldt, A. Dick, L. Ismer, and J. Neugebauer, Comput. Phys. Commun. 182, 543 (2011). doi: 10.1016/j.cpc.2010.09.016
[20]	M. F. Herbst, A. Levitt, and E. Cancès, Proc. JuliaCon Conf. 3, 69 (2021). doi: 10.21105/jcon.00069
[21]	X. Gonze, J. M. Beuken, R. Caracas, F. Detraux, M. Fuchs, G. M. Rig-nanese, L. Sindic, M. Verstraete, G. Zerah, F. Jollet, M. Torrent, A. Roy, M. Mikami, P. Ghosez, J. Y. Raty, and D. C. Allan, Comput. Mater. Sci. 25, 478 (2002). doi: 10.1016/S0927-0256(02)00325-7
[22]	W. Jia, Z. Cao, L. Wang, J. Fu, X. Chi, W. Gao, and L. W. Wang, Comput. Phys. Commun. 184, 9 (2013). doi: 10.1016/j.cpc.2012.08.002
[23]	C. K. Skylaris, P. D. Haynes, A. A. Mostofi, and M. C. Payne, J. Chem. Phys. 122, 084119 (2005). doi: 10.1063/1.1839852
[24]	A. Marini, C. Hogan, M. Grning, and D. Varsano, Comput. Phys. Commun. 180, 1392 (2009). doi: 10.1016/j.cpc.2009.02.003
[25]	W. Hu, L. Lin, A. S. Banerjee, E. Vecharynski, and C. Yang, J. Chem. Theory Comput. 13, 1188 (2017). doi: 10.1021/acs.jctc.6b01184
[26]	R. Sundararaman, K. Letchworth-Weaver, K. A. Schwarz, D. Gunceler, Y. Ozhabes, and T. Arias, SoftwareX 6, 278 (2017). doi: 10.1016/j.softx.2017.10.006
[27]	N. Jain, E. Bohm, E. Mikida, S. Mandal, M. Kim, P. Jindal, Q. Li, S. Ismail-Beigi, G. J. Martyna, and L. V. Kale, International Conference on High Performance Computing, Springer, 139 (2016).
[28]	J. J. Mortensen, L. B. Hansen, and K. W. Jacobsen, Phys. Rev. B 71, 035109 (2005). doi: 10.1103/PhysRevB.71.035109
[29]	J. A. Duersch, M. Shao, C. Yang, and M. Gu, SIAM J. Sci. Comput. 40, C655 (2018). doi: 10.1137/17M1129830
[30]	C. Davidson, J. Comput. Phys. 17, 87 (1975). doi: 10.1016/0021-9991(75)90065-0
[31]	D. M. Ceperley and B. J. Alder, Phys. Rev. Lett. 45, 566 (1980). doi: 10.1103/PhysRevLett.45.566
[32]	J. P. Perdew and A. Zunger, Phys. Rev. B 23, 5048 (1981). doi: 10.1103/PhysRevB.23.5048
[33]	A. D. Becke, Phys. Rev. A 38, 3098 (1988). doi: 10.1103/PhysRevA.38.3098
[34]	C. Lee, W. Yang, and R. G. Parr, Phys. Rev. B 37, 785 (1988). doi: 10.1103/PhysRevB.37.785
[35]	J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 3865 (1996). doi: 10.1103/PhysRevLett.77.3865
[36]	J. Tao, J. P. Perdew, V. N. Staroverov, and G. E. Scuseria, Phys. Rev. Lett. 91, 146401 (2003). doi: 10.1103/PhysRevLett.91.146401
[37]	J. Sun, A. Ruzsinszky, and J. P. Perdew, Phys. Rev. Lett. 115, 036402 (2015). doi: 10.1103/PhysRevLett.115.036402
[38]	A. D. Becke, J. Chem. Phys. 98, 1372 (1993). doi: 10.1063/1.464304
[39]	J. P. Perdew, M. Ernzerhof, and K. Burke, J. Chem. Phys. 105, 9982 (1996). doi: 10.1063/1.472933
[40]	J. Heyd, G. E. Scuseria, and M. Ernzerhof, J. Chem. Phys. 118, 8207 (2003). doi: 10.1063/1.1564060
[41]	A. Stroppa and G. Kresse, New J. Phys. 10, 063020 (2008). doi: 10.1088/1367-2630/10/6/063020
[42]	L. Schimka, J. Harl, A. Stroppa, A. Grneis, M. Marsman, F. Mittendorfer, and G. Kresse, Nat. Mater. 9, 741 (2010). doi: 10.1038/nmat2806
[43]	H. Sun, D. J. Mowbray, A. Migani, J. Zhao, H. Petek, and A. Rubio, ACS Catal. 5, 4242 (2015). doi: 10.1021/acscatal.5b00529
[44]	Y. Zhou, Y. Saad, M. L. Tiago, and J. R. Chelikowsky, J. Comput. Phys. 219, 172 (2006). doi: 10.1016/j.jcp.2006.03.017
[45]	J. Lu and H. Yang, Multiscale Model. Simul. 15, 254 (2017). doi: 10.1137/16M1068670
[46]	L. Lin, J. Lu, and L. Ying, Acta Numer. 28, 405 (2019). doi: 10.1017/S0962492919000047