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# MatGalerkin
Constructs the coarse grid problem matrix via Galerkin projection. 
## Synopsis
```
#include "petscmat.h" 
PetscErrorCode MatGalerkin(Mat restrct, Mat dA, Mat interpolate, MatReuse reuse, PetscReal fill, Mat *A)
```
If the interpolation and restriction operators are the same, uses `MatPtAP()`.
If they are not the same, uses `MatMatMatMult()`.

Once the coarse grid problem is constructed, correct for interpolation operators
that are not of full rank, which can legitimately happen in the case of non-nested
geometric multigrid.


## Input Parameters

- ***restrct -*** restriction operator
- ***dA -*** fine grid matrix
- ***interpolate -*** interpolation operator
- ***reuse -*** either `MAT_INITIAL_MATRIX` or `MAT_REUSE_MATRIX`
- ***fill -*** expected fill, use `PETSC_DEFAULT` if you do not have a good estimate



## Output Parameter

- ***A -*** the Galerkin coarse matrix



## Options Database Key

- ***-pc_mg_galerkin <both,pmat,mat,none> -*** for what matrices the Galerkin process should be used





## See Also
 [](ch_matrices), `Mat`, `MatPtAP()`, `MatMatMatMult()`

## Level
developer

## Location
<A HREF="PETSC_DOC_OUT_ROOT_PLACEHOLDER/src/mat/interface/matrix.c.html#MatGalerkin">src/mat/interface/matrix.c</A>


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[Edit on GitLab](https://gitlab.com/petsc/petsc/-/edit/release/src/mat/interface/matrix.c)


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