Pole-Based Approximation of the Fermi-Dirac Function
Pole-Based Approximation of the Fermi-Dirac Function
摘要
Two approaches for the efficient rational approximation of the Fermi-Dirac function are discussed： one uses the contour integral representation and conformal real〉 ping, and the other is based on a version of the multipole representation of the Fermi-Dirac function that uses only simple poles. Both representations have logarithmic computational complexity. They are of great interest for electronic structure calculations.
基金
supported by the Department of Energy (No.DE-FG02-03ER25587)
the Office of Naval Research(No.N00014-01-1-0674)
an Alfred P.Sloan Research Fellowship and a startup grant from University of Texas at Austin
参考文献15
-
1Baroni, S. and Giannozzi, P., Towards very large-scale electronic-structure calculations, Europhys. Lett., 17(6), 1992, 547-552.
-
2Ceriotti, M., Kuhne, T. D. and Parrinello, M., A hybrid approach to Fermi operator expansion, 2008, preprint, arXiv:0809.2232v1.
-
3Ceriotti, M., Kuhne, T. D. and Parrinello, M., An effcient and accurate decomposition of the Fermi operator, J. Chem. Phys., 129(2), 2008, 024707.
-
4Goedecker, S. and Colombo, L., Efficient linear scaling algorithm for tight-binding molecular dynamics, Phys. Rev. Lett., 73(1), 1994, 122-125.
-
5Goedecker, S. and Teter, M., Tight-binding electronic-structure calculations and tight-binding molecular dynamics with localized orbitals, Phys. Rev. B, 51(15), 1995, 9455-9464.
-
6Goedecker, S., Linear scaling electronic structure methods, Rev. Mod. Phys., 71(4), 1999, 1085- 1123.
-
7Greengard, L. and Rokhlin, V., A fast algorithm for particle simulations, J. Comput. Phys., 73(2), 1987, 325-348.
-
8Hale, N., Higham, N. J. and Trefethen, L. N., Computing A^α, log(A), and related matrix functions by contour integrals, SIAM J. Numer. Anal., 46(5), 2008, 2505- 2523.
-
9Krajewski, F. R. and Parrinello, M., Stochastic linear scaling for metals and nonmetals, Phys. Rev. B, 71(23), 2005, 233105.
-
10Liang, W. Z., Baer, R., Saravanan, C., et al, Fast methods for resumming matrix polynomials and Chebyshev matrix polynomials, J. Comput. Phys., 194(2), 2004, 575-587.
-
1王荣华,王宗谟.δ-函数及有关中学物理问题[J].物理教师,2013,34(11):55-55.
-
2刘萍.关于狄拉克函数的一点注记[J].武汉食品工业学院学报,1995(3):71-73. 被引量：2
-
3I.I.Guseinov,B.A.Mamedov.Unified treatment for accurate and fast evaluation of the Fermi-Dirac functions[J].Chinese Physics B,2010,19(5):72-77.
-
4甘筱青.在有限差分法下一类抛物型方程的离散化[J].大学数学,1995,16(3):5-8.
-
5叶云志.狄拉克函数及其应用[J].北方文学（中）,2012(6):245-245.
-
6陈端.狄拉克(Dirac)函数及其应用[J].林区教学,2003,0(5):31-32. 被引量：1
-
7Huashui ZHAN.Solution to Nonlinear Parabolic Equations Related to P-Laplacian[J].Chinese Annals of Mathematics,Series B,2012,33(5):767-782. 被引量：5
-
8陈兴翠.探究式教学在小学数学课堂教学中的运用[J].新课程学习（下）,2013(9):8-9.
-
9孙孟乐,郭向阳.运用狄拉克函数求静电场的散度和旋度[J].兰州石化职业技术学院学报,2005,5(4):47-48. 被引量：1
-
10汤志浩,王荣乾.狄拉克函数的定义和性质的研究[J].柳州职业技术学院学报,2009,9(2):76-78. 被引量：2
