Null space of a sparse large matrix

[Trinath Gaduparthi]

Hi all

Over the course of finite difference discretization of an elliptic equation and application of Neumann BCs on all sides of the 2D domain I have a large sparse matrix. I need to find null space of its transpose to enforce consistency condition on either side. For a computational domain of 50X50 and 100X100 I am able to do this with the available RAM of 32 GB in Mathematica and MATLAB. If the computational domain is 500X250 (which is of the order of what I would have) the RAM required for the storage of the matrix of size  (500X250)X(500X250) is 125 GB and is highly prohibitive. Could you please suggest me some low storage methods to compute this? 

Thanks a lot. 

Best

Trinath