d3_qpgf_d2

This is the calculation program of quasi-periodic Green's function for the Helmholtz equations. The quasi-periodicity is 2-dimensions ( z component is zero ), Green's function is 3-dimensions. This program is used my original method.

Definitions

• quasi-periodic Green's function
  
  
  is quasi-periodic Green's function
  is Green's function of the 3-dimensional Helmholtz equation
  is wave number vector,
  is 1st lattice vector,
  is 2nd lattice vector,
  These lattice vectors must be linearly independent.

• quasi-periodic condition

  

Usage of example code

1. type 'make' command to compile
2. type './example1.out', './example2.out' to run

Please see src/d3_qpgf_d2.h for detail of functions, src/example1.c and src/example2.c for detail of function usages.

References

1. Capolino, Filippo, Donald R. Wilton, and William A. Johnson. "Efficient computation of the 2-D Green's function for 1-D periodic structures using the Ewald method." IEEE Transactions on Antennas and Propagation 53.9 (2005): 2977-2984.  
2. Beylkin, Gregory, Christopher Kurcz, and Lucas Monzón. "Fast algorithms for Helmholtz Green's functions." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 464.2100 (2008): 3301-3326.
3. Abramowitz, Milton, Irene A. Stegun, and Robert H. Romer. "Handbook of mathematical functions with formulas, graphs, and mathematical tables." (1988).
4. Faddeeva Package. http://ab-initio.mit.edu/Faddeeva