[petsc-users] Matrix Free Method questions

[Jed Brown]

"Blondel, Sophie via petsc-users" <petsc-users at mcs.anl.gov> writes:

> Hi everyone,
>
> I have been using PETSc for a few years with a fully implicit TS ARKIMEX method and am now exploring the matrix free method option. Here is the list of PETSc options I typically use: -ts_dt 1.0e-12 -ts_adapt_time_step_increase_delay 5 -snes_force_iteration -ts_max_time 1000.0 -ts_adapt_dt_max 2.0e-3 -ts_adapt_wnormtype INFINITY -ts_exact_final_time stepover -fieldsplit_0_pc_type sor -ts_max_snes_failures -1 -pc_fieldsplit_detect_coupling -ts_monitor -pc_type fieldsplit -fieldsplit_1_pc_type redundant -ts_max_steps 100
>
> I started to compare the performance of the code without changing anything of the executable and simply adding "-snes_mf", I see a reduction of memory usage as expected and a benchmark that would usually take ~5min to run now takes ~50min. Reading the documentation I saw that there are a few option to play with the matrix free method like -snes_mf_err, -snes_mf_umin, or switching to -snes_mf_type wp. I used and modified the values of each of these options separately but never saw a sizable change in runtime, is it expected?

Totally normal.  Changing the MF method mainly just affects stability of the algorithm (with small consequences in vector work required to determine the differencing parameter).

> And are there other ways to make the matrix free method faster? I saw in the documentation that you can define your own per-conditioner for instance. Let me know if you need additional information about the PETSc setup in the application I use.

Could you share -log_view output for your standard method and the MF variant?