# Backward problem to the 2D wave eqaution

**URL:** https://community.freefem.org/t/backward-problem-to-the-2d-wave-eqaution/618
**Category:** General Discussion
**Created:** [October 17, 2020, 7:20pm UTC](https://community.freefem.org/t/backward-problem-to-the-2d-wave-eqaution/618 "2020-10-17T19:20:10Z")
**Posts on this page:** 1
**Page:** 1

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### Author: ![mordechaiy](https://avatars.discourse-cdn.com/v4/letter/m/cc9497/32.png) [@mordechaiy](https://community.freefem.org/u/mordechaiy)
#### Post date: [October 17, 2020, 7:20pm UTC](https://community.freefem.org/t/backward-problem-to-the-2d-wave-eqaution/618/1 "2020-10-17T19:20:11Z")

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Hi,

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,

Mordechai.