How to solve large sparse system without storing the entire matrix in memory?

Hi, I need to solve a coupled 3D Schrodinger-Poisson equation, with 200,200,320 grid points in x,y and z directions respectively. I am using the same mesh grid for both schrodinger and Poisson equations.

Taking a standard 7 point stencil for 3D FDM, I will have approx. 200*200*320=1.28X10^7 unknowns and roughly 8.96X10^7 non-zero entries in my FDM matrix (say A).

Storing A even in sparse format is giving me out of memory errors. Is there a way to get the eigenvalues of this matrix without storing the entire matrix in memory for solving the Schrodinger equation. I just need say 10-15 smallest Eigenvalues at this point.

Also how do I solve the Poisson equation in such a scenario because I need to store old and updated potentials at 1.28X10^7 nodes along with the Jacobian for solving the Poisson equation. How do I solve without getting a out of memory errors?

Will splitting up the matrix help or is there some other better way to do this.

Thanks.