Parallel mesh refinement of higher order finite elements for electronic structure calculations

Communications in Computational Physics

Volumn 4, Issue 5, 2008, Pages 1086-1105

  Zhang, Dier ^a   Zhou, Aihui ^b   Gong, Xin Gao ^a  

^a FUDAN UNIVERSITY   (China)

^b INSTITUTE OF COMPUTATIONAL MATHEMATICS AND SCIENTIFIC ENGINEERING COMPUTING   (China)

Author keywords

Adaptive mesh refinement; Electronic structure calculations; Parallel algorithms; Tetrahedral mesh

Indexed keywords

EID: 57849105507     PISSN: 18152406     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (26)

1. R. M. Martin, Electronic Structure Basic Theory and Practical Methods, Cambridge University Press, 2004, 236.
2. E. Tsuchida and M. Tsuukada, Electronic-structure calculations based on the finite-element method, Phys. Rev. B, 52 (1995), 5573-5578.
3. E. Tsuchida and M. Tsuukada, Adaptive finite-element method for electronic-structure calculations, Phys. Rev. B, 54 (1996), 7602-7605.
4. E. Tsuchida and M. Tesukada, Large-scale electronic-structure calculations based on the adaptive finite element methods, J. Phy. Soc. Jpn., 67 (1998), 3844-3858.
5. T. L. Beck, Real-space mesh techniques in density-function theory, Rev. Modern Phys., 72 (2000), 1041-1080.
6. J. E. Pask, B. M. Klein, P.A. Sterne and C.Y. Fong, Finite-element methods in electronic-structure theory, Comput. Phys. Commun., 135 (2001), 1-34.
7. E. Tsuchida, Ab initio molecular-dynamics study of liquid formamide, J. Chem. Phys., 121 (2004), 4740-4746.
8. J. E. Pask and P. A. Sterne, Finite element methods in ab initio electronic structure calculations, Modelling Simul. Mater. Sci. Eng., 13 (2005), R7-R96.
9. T. Torsti, T. Eirola, J. Enkovaaral, T. Hakala, P. Havu, V. Havu, T. Höynälänmaa, J. Ignatius, M. Lyly, I. Makkonen, T. T. Rantala, J. Ruokolainen, K. Ruotsalainen, E. Räsänen, H. Saarikoski and M. J. Puska, Three real-space discretization techniques in electronic structure calculations, Phys. Stat. Sol., B243 (2006), 1016-1053.
10. S. R. White, J.W. Wilkinsand and M.P. Teter, Finite-element method for electronic structure, Phys. Rev. B, 39 (1989), 5819-5833.
11. T. L. Beck, Multigrid high-order mesh refinement techniques for composite grid electrostatics calculations, J. Comput. Chem., 20 (1999), 1731-1739.
12. D. Zhang, L. Shen, A. Zhou and X. G. Gong, Finite element method for solving Kohn-Sham equations based on self-adaptive simplex mesh, Phys. Lett. A., to appear.
13. D. Mao, L. Shen and A. Zhou, Adaptive finite element algorithms for eigenvalue problems based on local averaging type a posteriori error estimates, Adv. Comp. Math., 25, (2006), 135-160.
14. M. T. Jones and P.E. Plassmann, Parallel algorithms for adaptive mesh refinement, SIAM J. Sci. Comput., 18 (1997), 686-708.
15. J. G. Castaños and J.E. Savage, Parallel refinement of unstructured meshes, Proceedings of the IASTED International Conference on Parallel and Distributed Computing and Systems, November 3-6, (1999), MIT, Boston, USA.
16. L. Zhang, A parallel algorithm for adaptive local refinement of tetrahedral meshes using bisection, Preprint ICM-05-09, (2005).
17. E. Bänsch, An adaptive finite-element strategy for the three dimensional time dependent Navier-Stokes equations, J. Comput. Appl. Math., 36 (1991), 3-28.
18. J. M. Maubach, Local bisection refinement for N-simplicial grids generated by reflection, SIAM J. Sci. Comput., 16 (1995), 210-227.
19. R. Horst, On generalized bisection of n-simplices, Math. Comp., 66 (1997), 691-698.
20. I. Kossaczky, A recursive approach to local mesh refinement in two and three dimensions, J. Comput. Appl. Math., 55 (1994), 275-288.
21. A. Liu and B. Joe, Quality local refinement of tetrahedral meshes based on bisection, SIAM J. Sci. Comput., 16 (1995), 1269-1291.
22. D. N. Arnold, A. Mukherjee and L. Pouly, Locally adapted tetrahedral meshes using bisection, SIAM J. Sci. Comput., 22 (2000), 431-448.
23. A. Khamayseh and G. Hansen, Use of the spatial kD-tree in computational physics applications, Commun. Comput. Phys., 2 (2007), 545-576.
24. W. Kohn, Noble lecture: electronic structure of matter wave functions and density functionals, Rev. Mod. Phys., 71 (1999) 1253.
25. R. O. Jones and O. Gunnarsson, Density-functional formalism: Sources of error in local-density approximations, Phys. Rev. Lett. 55 (1985) 107.
26. X. G. Gong, L. Shen, D. Zhang and A. Zhou, Finit element approximations for schrodinger equations with applications to electronic structure computations, J. Comput. Math., 26 (2008), 310-323.