I am working on a problem with very large sparse matrices. I'd like to compute $A^{-1} B$, that is a crucial part of converting DAE to ODE (and there is no workaround). Here size of $A$ is 2E+5 x 2E+5 with 0.7% density (especially all diagonal entries are non-zeros). And $B$ is 2E+5 x 1E+6 whose density is only 1E-6.
I tried to solve this problem in python by scipy.sparse.spsolve
, which eventually gave me a memory issue. The same issue happened while using an iterative solver. Unless I save each column to the disk and free the memory before computing the next column in the solution, the memory issue will persist.
So does anybody know a memory-efficient sparse solver or suggest a better way to solve this problem?