Asymptotic expansions of lattice green's functions

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 458, Issue 2027, 2002, Pages 2609-2622

  Martinsson, Per Gunnar ^a   Rodin, Gregory J ^a  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

Cubic lattice; Discrete potential theory; Lattice Green's function

Indexed keywords

EID: 57249087298     PISSN: 13645021     EISSN: None     Source Type: Journal    
DOI: 10.1098/rspa.2002.0985     Document Type: Article

References (17)

1. Babuška, I. 1970 Approximation by Hill functions. Commentat. Math. Univ. Carolinae 11, 787-811.
2. Borwein, J. M. & Zucker, I. J. 1992 Fast evaluation of the gamma function for small rational fractions using complete elliptic integrals of the first kind. IMA J. Numer. Analysis 12, 519-526.
3. Cserti, J. 2000 Application of the lattice Green's function for calculating the resistance of an infinite network of resistors. Am. J. Phys. 68, 896-906.
4. Duffin, R. J. 1953 Discrete potential theory. Duke Math. J. 20, 233-251.
5. Duffin, R. J. & Shelly, E. P. 1958 Difference equations of polyharmonic type. Duke Math. J. 25, 209-238.
6. Fix, G. & Strang, G. 1969 Fourier analysis of the finite element method in Ritz-Galerkin theory. Stud. Appl. Math. 48, 265-273.
7. Fix, G. & Strang, G. 1973 A Fourier analysis of the finite element variational method. In Constructive Aspects of Functional Analysis, pp. 795-840. Rome: Edizioni Cremonese.
8. Gel'fand, I. M. & Shilov, G. E. 1964 Generalized Functions, vol. 1. Academic.
9. Gibson, L. J. & Ashby, M. F. 1988 Cellular Solids, Structure and Properties. Oxford: Pergamon.
10. Glasser, M. L. & Boersma, J. 2000 Exact values for the cubic lattice Green functions. J. Phys. A 33, 5017-5023.
11. Greengard, L. & Rokhlin, V. 1987 A fast algorithm for particle simulations. J. Computat. Phys. 73, 325-348.
12. Joyce, G. S. 1973 On the simple cubic lattice Green function. Phil. Trans. R. Soc. Lond. A 273, 583-610.
13. Joyce, G. S. 1994 On the cubic lattice Green functions. Proc. R. Soc. Lond. A 445, 463-477.
14. Joyce, G. S. 2001 Singular behaviour of the cubic lattice Green functions and associated integrals. J. Phys. A 34, 3831-3839.
15. Maradudin, A. A., Montroll, E. W., Weiss, G. H., Herman, R. & Milnes, H. W. 1960 Green's Functions for Monatomic Simple Cubic Lattices. Brussel: Belgian Royal Academy of Science.
16. Martinsson, P.-G. 2002 Fast Multiscale Methods for Lattice Equations. PhD dissertation, University of Texas at Austin, TX.
17. Noor, A. K. 1988 Continuum modelling for repetitive lattice structures. Appl. Mech. Rev. 41, 285-296.