An introduction to lattice Green functions in pdf format can be found here.

This is still a work in progress. Any comments, suggestions or questions are welcome.

Some examples of using the LGF to solve problems in electrostatics can be found here.

Maxima code for calculating the LGF matrix elements can be found here. The function g(n,m) in this file will calculate the matrix elements. To run this code you will need Maxima which is a free and open source computer algebra system.

A C program for calculating the LGF matrix elements can be found here. This program, gnm.c, generates the g(n,m) lattice Green function term, and outputs the result both symbolically and as a double. To compile this program, you need to have a C compiler, the GMP library (GNU Multiple Precision arithmetic) and the MPFR library (Multiple-Precision Floating-point computations with exact Rounding). The compiler that we use is gcc. Other compilers may or may not work. The program is compiled with the following command line:

gcc -o gnm gnm.c -I/usr/local/include -L/usr/local/lib -lmpfr -lgmp

For details on using the program, run it with no parameters.

A table of values of the LGF matrix elements g(n,m) in the wedge m <= n <= 20 is here.

A C program for reading a lattice Green function binary file containing values of the LGF matrix elements 2*g(n,m) in the wedge m <= n <= 1001, and returning the specified value of 2*g(n,m) as a 16 significant figure floating point number, can be found here. The binary wedge file is here (4.0 MB).

A bibtex file with some Green function references can be found here.

Some links to our recent work on lattice Green functions:

- Capacitance Calculations Using the Lattice Green Function in Two Dimensions.
- The Lattice Green Function for the Poisson Equation on an Infinite Square Lattice.
- Some Square Lattice Green Function Formulas.

Last modified Mar 20, 2006.

For more information contact:

*Stefan Hollos
stefan[AT]exstrom DOT com
(303) 678-1487*

Copyright 2006 by Exstrom Laboratories LLC | email:info[AT]exstrom DOT com |
Exstrom Labs Home |