MATLAB Periodic Operators use non-standard grid size. #304
Description
The grad and div operators in the MATLAB source code have non-standard sizes for the periodic operators. This non-standard size operator is confusing for new users and makes multi-dimension operators harder to implement.
The standard grad and div have sizes (m+1,m+2) and (m+2, m+1) respectively in 1D. The same pattern goes for two and three dimensions, as well as the Laplacian which will have size (m+1, m+1).
The periodic grad and div have sizes (m,m+2) and (m+2, m), respectively. This cascades for two and three dimensions, as well as the Laplacian, which will have size (m,m).
Examples using periodic operators have non-mimetic grid sizes, with no explanation why. Here is an example where the boundary conditions are periodic in X and Dirichlet in Y. The grids have different constructions for the different dimensions.
I think the use of different grids for different boundary conditions is very confusing, especially considering the already complicated nature of the mimetic grid.
I think this particular aspect was missed in the previous commit for the scalarBCs. But that's why there is GitHub. I know @mdumett did a lot of work to get the addScalarBC code initially merged, but I think the periodic operators should be the same size as the regular operators. While not ideal, it is the easiest for the user and maintains consistency.
That means a lot of the previous EXTRA code written for the different sizes will have to be redone or removed. There would no longer be a need for the divPeriodic and divNonPeriodic, and the grids would need to be redone for the affected examples.