fft of a very large 3D array

Hi guys,

I have a problem on my hands. I am trying to take the fft (using fftn) of a very large 3D array. The size is 4000^3, double precision. That sits at about 242 gb. My problem is memory. I'm allotted 50 gb of free ram on my department's cluster. It still is not enough.

I want to know if there are tricks one can do to circumnavigate this problem. I'm trying to find methods where perhaps one can do fourier transforms piece-wise...no luck yet.

If anyone knows of anything, please let me know. Thanks in advance.