d2_qpgf_d1

This is the calculation program of quasi-periodic Green's function for the Helmholtz equations. The quasi-periodicity is 1-dimension ( x component only ), Green's function is 2-dimensions.

Definitions

• quasi-periodic Green's function
  
  
  is quasi-peridic Green's function
  is Green's function of the 2-dimensional Helmholtz equation
  is wave number vector,
  is lattice vector,

• quasi-periodic condition

  ,

Usage of example code

1. type 'make' command to compile
2. type './example.out' to run

Please see src/d2_qpgf_d1.h for detail of functions, src/example.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. Linton, Chris M. "Lattice sums for the Helmholtz equation." SIAM review 52.4 (2010): 630-674.
4. Abramowitz, Milton, Irene A. Stegun, and Robert H. Romer. "Handbook of mathematical functions with formulas, graphs, and mathematical tables." (1988).
5. Faddeeva Package. http://ab-initio.mit.edu/Faddeeva