here is some comment from the expert, wouldthat be helpful to solve the problem:
PARDISO now supports sparse RHS and solution vectors (iparm(31)). Using this switch it might be possible to get a block of an inverse matrix faster than a complete inverse matrix. The idea is the same as mentioned below we solve a system AX=B. If B is an identity matrix, then X=inverse(A). If the customer wants to have partial inverse, she should use sub-matrix of an identity matrix and indicate that only partial solution is needed through iparm(31) and proper perm settings as described in MKL Manual.