Backward problem to the 2D wave eqaution


I am solving the 2D wave equation on a square with a hole with uniform mesh, where the number of partitions in each direction is 128. Since I used “trunc” command in my code the (Degrees of Freedom) DOF in this domain is 16016. I save the solution at each point using the “ifsream” command.
Then I solve a backward problem to the wave equation where the saved solution at each time is given to the numerical scheme.
The problem is that the domain in the backward problem has a larger hole and thus this domain and the finite element space (defined in the backward problem) have lower DOF so FF++ can’t read the saved solution at each time since the DOF in the backward problem is lower.
(I have to take a larger hole in the backward problem because it is a stage in a method to identify a scatterer).

Please, how can I resolve this problem?

Thank you,