AMReX Hypre supported boundary conditions

[ankithadas]

Hey AMReX team,

I just wanted to confirm my finding after going through the HYPRE wrapper and make sure I haven't missed anything. To my understanding, does the Hypre Wrapper only support zero Dirichlet and zero gradient Nuemann boundary conditions.

Kind regards,
Ankith

[WeiqunZhang]

It's true that the Hypre wrapper at Src/Extern/HYPRE only supports homogeneous Dirichlet and Neumann BCs. However, this does not mean it cannot be used to solve problems with inhomogeneous Dirichlet and Neumann BCs. The inhomogeneous part is handled in src/LinearSolvers/MLMG.

[ankithadas]

Could you please direct me where the inhomogeneous Dirichlet and Neumann BC components are added to the RHS in MLMG solver? I am attempting to write a linear solver that can handle advection as well

[WeiqunZhang]

amrex/Src/LinearSolvers/MLMG/AMReX_MLCellABecLap.H

Line 275 in d4d0e90

MLCellABecLapT<MF>::applyInhomogNeumannTerm (int amrlev, MF& rhs) const

Here is an example of modifying RHS for inhomogeneous Neumann.

amrex/Src/LinearSolvers/MLMG/AMReX_MLABecLaplacian.H

Line 451 in d4d0e90

// Suppose we are solving `alpha u - del (beta grad u) = rhs` (Scalar

Here is how we handle Robin BC.

As for inhomogeneous Dirichlet, it does not change RHS. It's handled here.

amrex/Src/LinearSolvers/MLMG/AMReX_MLCellLinOp.H

Line 652 in d4d0e90

template <typename MF>

Note that given a linear system L(phi) = f, we compute res = f - L(phi_initial_guess). Then we solve L(dphi) = res, for which Dirichlet BC becomes homogenous. When we use Hypre, what it solves is actually L(dphi) = res and the final solution is then phi_initial_guess + dphi.

[WeiqunZhang]

Also note that there are a number of classes in Src/Extern/HYPRE. For the HypreSolver class, there is no concept of BC. It's algebraic. It's up to the user to set up the matrix.