Articles:
Diffraction on the Two-Dimensional Square Lattice
H. S. Bhat; Braxton Osting
Downloads:
- Title:
- Diffraction on the Two-Dimensional Square Lattice
- Author(s):
-
Bhat, H. S.
Osting, Braxton - Date:
- 2009
- Type:
- Articles
- Department:
- Applied Physics and Applied Mathematics
- Volume:
- 70
- Permanent URL:
- http://hdl.handle.net/10022/AC:P:10563
- Book/Journal Title:
- SIAM Journal on Applied Mathematics
- Abstract:
- We solve the thin-slit diffraction problem for two-dimensional lattice waves. More precisely, for the discrete Helmholtz equation on the semi-infinite square lattice with data prescribed on the left boundary (the aperture), we use lattice Green's functions and a discrete Sommerfeld outgoing radiation condition to derive the exact solution everywhere in the lattice. The solution is a discrete convolution that can be evaluated in closed form for the wave number $k=2$. For other wave numbers, we give a recursive algorithm for computing the convolution kernel.
- Subject(s):
- Applied mathematics
- DOI:
- 10.1137/080735345
- Item views:
- 367