Several Lagrange mutiplier using fieldsplit

General Discussion
1

Hello Freefem user,

I’m studying the following system :

Mat NN = [[ A , pBEx,pBEy,pBEz,pBMx,pBMy,pBMz ],
[ pBEx’,-1/kt,0,0,0,0,0 ],
[ pBEy’,0,-1/kt,0,0,0,0 ],
[ pBEz’,0,0,-1/ka,0,0,0 ],
[ pBMx’,0,0,0,-1/kf,0,0 ],
[ pBMy’,0,0,0,0,-1/kf,0 ],
[ pBMz’,0,0,0,0,0,-1/kth ]];

Here, A is a large matrix coming from 3D elasticity varf, and the pBxxx are linear forms used to enforce boundary conditions via six Lagrange multipliers. More precisely, the goal is to create a mean spring effect between two surfaces of the solid, where the kxx are the stiffnesses of these springs.

I managed to solve this problem on a small mesh using PETSc + LU and obtained correct results.

I now want to increase the mesh size and use Hypre preconditioning. Even on small meshes, the system does not converge with six springs, but it works with just one.

Correct me if I’m wrong, but a good way to handle this problem could be to use splitfield:

  • Solve A using Hypre.

  • Solve the rest using LU.

I’m struggling with implementing this using set(NN, sparams=" ") and specifying the block sizes.

I also haven’t found a way to rewrite the problem in a more compact form like NN = [A B; B' S], which would be more convenient if I want to handle more springs in the future.

Do you have any suggestions on how to do this?

Thanks,

2

What is splitfield? Please share a running code, that should work seamlessly.

3

My mistake, I swept splitfield and fieldsplit (like in -pc_type fieldsplit) ! It was correct in my .edp though

Please find a working exemple with
set(NN, sparams=“-pc_type lu -ksp_view -ksp_monitor -ksp_converged_reason”);

(and not working with)
set(NN, sparams = “-ksp_type gmres -pc_type fieldsplit "
+” -fieldsplit_0_indices 0:nA -fieldsplit_1_indices nA+1:nA+6 "
+" -fieldsplit_0_pc_type hypre -fieldsplit_1_pc_type lu "
+" -ksp_view -ksp_monitor -ksp_converged_reason");

ex0.edp (4.9 KB)

and the associated mesh :

Mod1.zip (967.2 KB)

4

What is -fieldsplit_0_indices and -fieldsplit_1_indices?

5

In my understanding these indices are used to delimit the blocks solved with the various conditioners, but they seem to have absolutely no effect.

Did I get the keyword wrong for specifying the separation, or is this not the correct approach for this type of problem at all?

6

Where did you get this keyword from? It is definitely the correct approach, I have the fix, I’m trying to figure out how you got to the point of using the indices option that I cannot find anywhere.

7

Finding no clues of how solve my problem in this forum or in the git exemples, I tried IA. Sometimes it works and sometimes it creates unknown keywords !

8

Oh, of course it’s AI producing nonsense, I should have known better. This will work -pc_fieldsplit_0_fields 0 -pc_fieldsplit_1_fields 1,2,3,4,5,6 instead of the nonsensical indices.

9

Using

set(NN, sparams = “-ksp_type gmres -pc_type fieldsplit "
+” -pc_fieldsplit_0_fields 0 -pc_fieldsplit_1_fields 1,2,3,4,5,6 "
+" -fieldsplit_0_pc_type hypre -fieldsplit_1_pc_type lu "
+" -ksp_view -ksp_monitor -ksp_converged_reason");

It reacts, but maybe not in the expected way :

[6]PETSC ERROR: --------------------- Error Message --------------------------------------------------------------
[6]PETSC ERROR: Argument out of range
[6]PETSC ERROR: Field 1 requested but only 1 exist

10

What are your FreeFEM and PETSc versions?

11

I’m currently using petsc/3.14.2 and freefem/4.14

freefem/4.15 is available on my machine. With this version, there are no Petsc errors anymore and it does iterate.

However, I’m suprised by the results obtained -pc_type fieldsplit. Trying various parameter i’ve got “Linear solve did not converge due to DIVERGED_BREAKDOWN” I failed to reproduce the results obtained by using -pc_type lu alone on the global system.

12

Just use FreeFEM develop branch, there is no error there and the code runs fine.

$ ff-mpirun -n 4 ex0.edp -v 0
  0 KSP Residual norm 9.454872682505e+13
  1 KSP Residual norm 4.725899220351e-03
  Linear solve converged due to CONVERGED_RTOL iterations 1
[...]
13

By develop branch, you mean Release FreeFEM v4.14 · FreeFem/FreeFem-sources · GitHub ?

I’ll check with the IT team that it is actually the version installed on our machine and not (Release FreeFEM v4.14 · FreeFem/FreeFem-sources · GitHub)

I see here Release FreeFEM v4.14 · FreeFem/FreeFem-sources · GitHub that the version of Petsc recquired is PETSc 3.20.2 which is quite far from the one I’m using (3.14.2). Could it be the explanation why we don’t have the same results with the same edp file ?

(3.14.2 is the latest available on my machine, I’ll ask for an update)