MLMG solver failed to converge

[solarmaterial]

Hi amrex team,

I am using the MLMG linear solver (MLABecLaplacian) to solve a discretized heat conduction equation in a 2D domain in single level (uniform grid) with 2400 grids in the x-direction and 200 grids in the y-direction. An external heat source q is applied along the x-direction (q=q(x,t). When the magnitude of the heat source is relatively small, the solver performs well and converges quickly. However, when I increase the magnitude of the heat source by two orders of magnitude, the solver fails to achieve the required precision even after thousands of iterations.

I have tried several approaches to address this issue, including reducing the precision requirements, increasing the maximum number of iterations, and switching solvers (e.g., BiCGSTAB, smoother, and Hypre with preconditioners). Unfortunately, as the simulation progresses in time, the solver eventually fails because it cannot meet the required precision.

Interestingly, when I reduce the number of grids in the y-direction to 5 or 50 (while keeping the x-direction resolution unchanged), the solver is able to proceed, albeit requiring multiple iterations to converge. However, when the number of grids in the y-direction increases to 100 or 200, the solver fails.

Could you please provide suggestions or insights on how to address this issue? I greatly appreciate your help and look forward to your reply.

Yours sincerely,
solar

PS：The result is shown in the figure below.

[WeiqunZhang]

MLMG is a geometric multigrid method. It's most effective when (1) the cell size is uniform, (2) the domain is a cube, and (3) the number of cells in each direction is power of 2. What is the cell size in your problem? If you can, could you try to adjust your problem settings toward the three conditions above.

When you use hypre, did you set max_coarsening_level? If not, you should try to set LPInfo's max coarsening level to 0 when using hypre so that the entire problem is solved by hypre.

You could also try GMRES. See amrex/Tests/LinearSolvers/ABecLaplacian_C/ for an example.

[solarmaterial]

So, you mean that instead of using the GMRES bottom solver in hypre, I should use the GMRES solver in MLMG, right?Anyway, thank you so much for your help! :) I will give it a try. Also the max_coarsening_level = 0.
I will compile a test code later. Thanks again for your suggestions!!

[solarmaterial]

Hi, Weiqun
The code link is here https://github.com/solarmaterial/amrex-heat-equation).

[WeiqunZhang]

The code you shared above contains a single function without any other functions (including main) or input data. I am not sure how I could help you. By "providing a test code", I meant a complete code that I could make and then run.

void heatConduction (MultiFab& phi_old,
              MultiFab& phi_new,
              MultiFab& Laser_rhs,
              MultiFab& temp_new,
              Real dt,
              const Geometry& geom,
              const BoxArray& grids,
              const DistributionMapping& dmap,
              const Vector<BCRec>& bc,
              Real time,
              int ny_cell,
              //amrex::Vector<int>& HeatSource,
              amrex::Vector<amrex::Real>& First_phy_HeatSource)
{ ... }

[solarmaterial]

Hi, Weiqun
The complete code was uploaded.
The code link is here https://github.com/solarmaterial/amrex-heat-equation).

[solarmaterial]

Hi, Weiqun
Could you please let me know if you’ve identified any issues in the code I provided? I’d greatly appreciate any insights or advice you could share. Unfortunately, I’m still struggling to resolve the problem.

Thank you for your time and guidance!