Multicomponent Linear Solve

[alahyari]

Hello AMReX folks,

I have a question wrt the MC linear solve feature. I need to solve three Poisson equations in the form of $$\Delta u_i = f_i$$ one for each velocity component in three dimensions. All components are cell-centered.

What I do now is that I solve one Poisson equation independently for each component in a for loop. I was thinking to use the MC feature. My first question is that is there going to be any saving in computational time if I use the MC feature compared to what I have now? And my second question is that is there any sample implementation of MC linear solve for cell-centered data that I can refer to?

Thank you.

[WeiqunZhang]

Yes, I believe there will be saving if all three components are solved together. Although our cell-centered Poisson only supports one component, we do have another solver that can be used for this. In Src/LinearSolvers/MLMG/, there is amrex::MLALaplacian that can be used to solve $a A u - b \nabla u = f$. Here $a$ and $b$ are scalars (i.e., amrex::Real) and $A$ is a cell-centered MultiFab. If you use a_ncomp=3 in the constructor of MLALaplacian and call MLALaplacian::setScalars(0.0, -1.0), the system will become three Poisson equations. Note that you don't need to call MLALaplacian::setACoeffs because $a$ is zero. Alternatively, you can extend amrex::MLPoisson to support multiple components. It should be straightforward and it should have better performance than using MLALaplacian, but my guess is probably not that much.