## MueLu: removing BCs from piece-wise constant structured aggregates

*Created by: lucbv*

## Enhancement

@trilinos/muelu

At the moment BCs are simply aggregated without special treatment. This usually leads to a degraded convergence rate in MG.
The idea is to propose a better treatment of BC using structured aggregation at least in the case of piece-wise constant aggregation (piece-wise linear might be trickier...).
One option to implement this is to check whether a given row of `A`

has a single diagonal entry equal to `1`

which indicates a Dirichlet BC. Once this is detected, the corresponding row in `P`

is set to zero thus preventing the fine degree of freedom from contributing to the coarse problem.
One particular issue to address with the above implementation is the case when a column of `P`

becomes full of zeros which means that a whole aggregate has been eliminated. In that case the aggregate has to be eliminated and to keep a structured matrix we also need to adjust the number of coarse nodes per direction.