# Use of restriction on a meshL and matrix free operator
**URL:** https://community.freefem.org/t/use-of-restriction-on-a-meshl-and-matrix-free-operator/862
**Category:** General Discussion
**Created:** [March 18, 2021, 3:34pm UTC](https://community.freefem.org/t/use-of-restriction-on-a-meshl-and-matrix-free-operator/862 "2021-03-18T15:34:26Z")
**Posts on this page:** 6
**Page:** 1
### Author:  [@LucasPa](https://community.freefem.org/u/LucasPa)
#### Post date: [March 18, 2021, 3:34pm UTC](https://community.freefem.org/t/use-of-restriction-on-a-meshl-and-matrix-free-operator/862/1 "2021-03-18T15:34:26Z")
Hi,
I would like to define a square matrix-free operator which dimension corresponds to the size of the restricted space that corresponds to the left boundary of the 2d domain. So basically the operator behaves as:
another\_vector\_on\_1D\_space = matrix\_on\_1D\_space \* input\_vector\_on\_1D\_space
vector\_on\_2D\_space = prolongation\_matrix \* another\_vector\_on\_1D\_space
another\_vector\_on\_2D\_space = matrix\_on\_2D\_space \* vector\_on\_2D\_space
return\_vector\_on\_1D\_space = restrictionMatrix \* another\_vector\_on\_2D\_space
I started to implement this in the following script: [meshL\_2d\_SLEPc.edp](https://community.freefem.org/uploads/short-url/hG2uHfHnyEizbSULoN2xPlDdGUC.edp) (1.5 KB)
Obviously there is something I do not understand, I guess I have non consistent operator sizes.
Could someone please help me here ?
Best,
Lucas
PS: It is not clear to me why A.n is different from Vh.ndof. Could someone please explain me why?
---
### Author:  [@prj](https://community.freefem.org/u/prj)
#### Post date: [March 18, 2021, 4:14pm UTC](https://community.freefem.org/t/use-of-restriction-on-a-meshl-and-matrix-free-operator/862/2 "2021-03-18T16:14:41Z")
I’ll look into your script, but first.
> PS: It is not clear to me why A.n is different from Vh.ndof. Could someone please explain me why?
`A.n` is the local size of the PETSc `Mat` (without overlapping unknown), while `Vh.ndof` is the local size of the FreeFEM `fespace) (with overlapping unknowns).
---
### Author:  [@LucasPa](https://community.freefem.org/u/LucasPa)
#### Post date: [March 18, 2021, 4:36pm UTC](https://community.freefem.org/t/use-of-restriction-on-a-meshl-and-matrix-free-operator/862/3 "2021-03-18T16:36:59Z")
Thanks for this explanation.
Knowing this I may be able to correct something in the script, I will do that tomorrow.
---
### Author:  [@prj](https://community.freefem.org/u/prj)
#### Post date: [March 18, 2021, 4:46pm UTC](https://community.freefem.org/t/use-of-restriction-on-a-meshl-and-matrix-free-operator/862/4 "2021-03-18T16:46:32Z")
In fact, your script is correct, just the sizes are wrong. You are using FreeFEM notation (`*`) instead of `MatMult`, so you need to use FreeFEM lengths, like this:
```auto
real[int] u(VhL.ndof), v(VhL.ndof), w(Vh.ndof), vv(Vh.ndof);
```
I now get a consistent result with an increasing number of processes.
```auto
$ mpirun -n 1 FreeFem++-mpi meshL_2d_SLEPc.edp -eps_view_values -v 0
Mat Object: 1 MPI processes
type: shell
rows=41, cols=41
Eigenvalues =
0.02498
$ mpirun -n 4 FreeFem++-mpi meshL_2d_SLEPc.edp -eps_view_values -v 0
Mat Object: 4 MPI processes
type: shell
rows=41, cols=41
Eigenvalues =
0.02498
```
---
### Author:  [@LucasPa](https://community.freefem.org/u/LucasPa)
#### Post date: [March 23, 2021, 1:43pm UTC](https://community.freefem.org/t/use-of-restriction-on-a-meshl-and-matrix-free-operator/862/5 "2021-03-23T13:43:41Z")
And one additional question on that point: what does happen if the boundary labelled 1 is partitioned on multiple procs? Do I have something to do then ? Communicating the ghost values ?
Best,
Lucas
---
### Author:  [@prj](https://community.freefem.org/u/prj)
#### Post date: [March 23, 2021, 2:01pm UTC](https://community.freefem.org/t/use-of-restriction-on-a-meshl-and-matrix-free-operator/862/6 "2021-03-23T14:01:17Z")
It should be done for you, unless something else is broken.