A parallel multigrid accelerated Poisson solver for ab initio molecular dynamics applications

Computing and Visualization in Science

Volumn 11, Issue 2, 2008, Pages 115-122

  Kostler H ^b   Schmid, R ^a   Rude U ^b   Scheit, Ch ^b  

^a RUHR UNIVERSITY BOCHUM   (Germany)

^b UNIVERSITY OF ERLANGEN NUREMBERG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; ENERGY CONSERVATION; POISSON EQUATION; PROBLEM SOLVING;

DISCRETIZATION ERROR; ENERGY CONSERVING DYNAMICS; MULTIGRID SOLVER; QUANTUM CHEMICAL PROGRAM;

MOLECULAR DYNAMICS;

EID: 39449135624     PISSN: 14329360     EISSN: 14330369     Source Type: Journal    
DOI: 10.1007/s00791-007-0062-0     Document Type: Article

References (41)

1. Dacapo: http://www.fysik.dtu.dk/CAMP/dacapo.html
2. Hpc-cluster: http://www10.informatik.uni-erlangen.de/Cluster/hpc.shtml
3. The MPI forum: The MPI message-passing interface standard. http://www.mcs.anl.gov/mpi/standard.html
4. Numerical python: http://www.pfdubois.com/numpy/
5. Python: http://www.python.org
6. Rsdft: http://www.rsdft.org
7. ± clusters. Phys. Rev. B 59, 7868 (1999)
8. Beck T.L. (2000). Real-space mesh techniques in density-functional theory. Rev. Mod. Phys. 72: 1041-1080
9. Bernert K. (1997). τ-extrapolation-theoretical foundation, numerical experiment and application to Navier-Stokes equations. SIAM J. Sci. Comp. 18: 460-478
10. Bernholc J. (1999). Computational materials science: the era of apllied quantum mechanics. Phys. Today 52(9): 30-35
11. Brandt, A.: Multigrid methods: 1984 guide with applications to fluid dynamics. The Weizmann Institute of Science, Rehovot, Israel (1984)
12. Castro A., Marques M.A.L., Alonso J.A., Bertsch G.F., Yabana K. and Rubio A. (2002). Can optical spectroscopy directly elucidate the ground state of c20?. J. Chem. Phys. 116: 1930-1933
13. Ceperley D.M. and Alder B.J. (1980). Ground state of the electron gas by a stochastic method. Phys. Rev. Lett. 45: 566-569
14. Chelikowsky J.R., Saad Y., Ögüt S., Vasiliev I. and Stathopoulos A. (2000). Electronic structure methods for predicting the properties of materials: grids in space. Phys. Stat. Sol. B 217: 173-195
15. Douglas, C., Haase, G., Langer, U.: A Tutorial on Elliptic PDE Solvers and their Parallelization, SIAM (2003)
16. Gropp W., Lusk E. and Skjellum A. (1999). Using MPI, Portable Parallel Programming with the Mesage-Passing Interface, 2nd edn. MIT Press, Cambridge
17. Hackbusch W. (1985). Multi-Grid Methods and Applications. Springer, Heidelberg
18. Hinsen K. (2000). The molecular modeling toolkit: a new approach to molecular simulations. J. Comput. Chem. 21: 79-85
19. Hohenberg P. and Kohn W. (1964). Inhomogeneous electron gas. Phys. Rev. 136: B864-B871
20. Hülsemann, F., Kowarschik, M., Mohr, M., Rüde, U.: Parallel geometric multigrid. In: Bruaset, A., Tveito, A. (eds.) Numerical Solution of Partial Differential Equations on Parallel Computers, chap. 5, vol. 51 of LNCSE. Springer, Heidelberg, pp. 165-208 (2005). ISBN 3-540-29076-1
21. 2. J. Korean Phys. Soc. 40: 406-415
22. Kendall R.A., Apra E., Bernholdt D.E., Bylaska E.J., Dupuis M., Fann G.I., Harrison R.J., Ju J., Nichols J.A., Nieplocha J., Straatsma T.P., Windus T.L. and Wong, A.T. (2000). High performance computational chemistry: an overview of nwchem a distributed parallel application. Comput. Phys. Commun. 128: 260-283
23. Kohn W. and Sham L.J. (1965). Self-consistent equations including exchange and correlation effects. Phys. Rev. 140: A1133-A1138
24. Martín I. and Tirado F. (1997). Relationships between efficiency and execution time of full multigrid methods on parallel computers. IEEE Trans. Parallel Distrib. Syst. 8: 562-573
25. Marx, D., Hutter, J.: Ab Inition Molecular Dynamics: Theory and Implementation, vol. 1 of NIC Series. John von Neumann Institute for Computing, Julich, pp. 301-449 (2000)
26. Mortensen J.J., Hansen L.B. and Jacobsen K.W. (2005). Real-space grid implementation of the projector augmented wave method. Phys. Rev. B 71: 035109-103510911
27. Ono T. and Hirose K. (1999). Timesaving double-grid method for real-space electronic-structure calculations. Phys. Rev. Lett. 81: 5016-5019
28. Parrinello M. and Car R. (1985). Unified approach for molecular dynamics and density-functional theory. Phys. Rev. Lett. 55: 2471-2474
29. Perdew J.P. and Zunger A. (1981). Self-interaction correction to density-functional approximations for many-electron systems. Phys. Rev. B 23: 5048-5079
30. Richardson L. (1927). The deferred approach to the limit. I. Single lattice. Philos. Trans. R. Soc. Lond. A 226: 229-349
31. Rüde, U.: Multiple τ-extrapolation for multigrid methods. Tech. Rep. I-8701, Technische Universität München (1987)
32. Schmid R. (2004). Car-Parrinello molecular-dynamics simulations with real space methods. J. Comput. Chem. 25: 799-812
33. Schmid R., Tafipolsky M., König P.H. and Köstler H. (2006). Car-Parrinello molecular dynamics using real space wavefunctions. Phys. Status solidi b 243: 1001-1015
34. Shimojo F., Kalia R.K., Nakano A. and Vashishta P. (2001). Linear-scaling density-functional-theory calculations of electronic structure based on real-space grids: design, analysis, and scalability test of parallel algorithms. Comput. Phys. Commun. 140: 303-314
35. Sterk M. and Trobec R. (2003). Parallel performances of a multigrid poisson solver. ISPDC 00: 238
36. Tafipolsky, M., Schmid, R.: A general and efficient pseudopotential fourier filtering scheme for real space methods using mask functions. J. Chem. Phys. 243(5) (2005)
37. Torsti T., Heiskanen M., Puska M.J. and Nieminen R.M. (2003). Mika: multigrid-based program package for electronic structure calculations. Int. J. Quantum Chem. 91: 171-176
38. Trottenberg U., Oosterlee C. and Schüller A. (2001). Multigrid. Academic, New York
39. Waghmare U.V., Kim H., Park I.J., Modine N., Maragakis P. and Kaxiras E. (2001). Hares: an efficient method for first-principles electronic structure calculations of complex systems. Comput. Phys. Commun. 137: 341-360
40. Wang J. and Beck T.L. (2000). Efficient real-space solution of the Kohn-Sham equations with multiscale techniques. J. Chem. Phys. 112: 9223-9228
41. Wang J., Wang Y., Yu S. and Kolb D. (2005). Nonlinear algorithm for the solution of the Kohn-Sham equations in solids. J. Phys. Cond. Mat. 17: 3701-3715