# Which fourier series is needed to solve a 2D poisson problem with mixed boundary conditions using Fast Fourier Transform?

I have heard that a fast fourier transform can be used to solve the poisson problem when the boundary conditions are all one type... Sine series for dirichlet, cosine for neumann, and both for periodic. Considering a 2D rectangular domain, suppose two opposite sides have periodic boundary conditions, and the other two have dirichlet conditions. Can a fast fourier transform be applied to solve this problem efficiently? If so, wouldn't the exponential form be sufficient? If not, what solver would you recommend for this situation?

• Have you seen this? – J. M. Jan 19 '12 at 17:18
• @J.M.: Could you elaborate on this paper in an answer form? – Paul Apr 11 '12 at 19:11
• I sorta kinda have my hands full on RL stuff, so it might take a while. But, if you've taken a glimpse at the paper, you'll see how the various DCTs/DSTs are suitably modified to suit boundary conditions... – J. M. Apr 14 '12 at 2:42