# Several Lagrange mutiplier using fieldsplit **URL:** \ **Category:** General Discussion\ **Created:** [November 10, 2025, 1:28pm UTC](https://community.freefem.org/t/several-lagrange-mutiplier-using-fieldsplit/4130 "2025-11-10T13:28:53Z")\ **Posts on this page:** 19\ **Page:** 1
**Author:** ![smori](https://avatars.discourse-cdn.com/v4/letter/s/a8b319/32.png) [@smori](https://community.freefem.org/u/smori)\ **Post date:** [November 10, 2025, 1:28pm UTC](https://community.freefem.org/t/several-lagrange-mutiplier-using-fieldsplit/4130/1 "2025-11-10T13:28:53Z")
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, ---
**Author:** ![prj](https://avatars.discourse-cdn.com/v4/letter/p/ecae2f/32.png) [@prj](https://community.freefem.org/u/prj)\ **Post date:** [November 10, 2025, 1:36pm UTC](https://community.freefem.org/t/several-lagrange-mutiplier-using-fieldsplit/4130/2 "2025-11-10T13:36:24Z")
What is `splitfield`? Please share a running code, that should work seamlessly. ---
**Author:** ![smori](https://avatars.discourse-cdn.com/v4/letter/s/a8b319/32.png) [@smori](https://community.freefem.org/u/smori)\ **Post date:** [November 10, 2025, 2:23pm UTC](https://community.freefem.org/t/several-lagrange-mutiplier-using-fieldsplit/4130/3 "2025-11-10T14:23:28Z")
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](https://community.freefem.org/uploads/short-url/cudXpcygvmGqnBiMJgCcXAS4pnT.edp) (4.9 KB) and the associated mesh : [Mod1.zip](https://community.freefem.org/uploads/short-url/auUY47dePRmbPyB5hSJ103iLhOj.zip) (967.2 KB) ---
**Author:** ![prj](https://avatars.discourse-cdn.com/v4/letter/p/ecae2f/32.png) [@prj](https://community.freefem.org/u/prj)\ **Post date:** [November 10, 2025, 2:24pm UTC](https://community.freefem.org/t/several-lagrange-mutiplier-using-fieldsplit/4130/4 "2025-11-10T14:24:38Z")
What is `-fieldsplit_0_indices` and `-fieldsplit_1_indices`? ---
**Author:** ![smori](https://avatars.discourse-cdn.com/v4/letter/s/a8b319/32.png) [@smori](https://community.freefem.org/u/smori)\ **Post date:** [November 10, 2025, 3:01pm UTC](https://community.freefem.org/t/several-lagrange-mutiplier-using-fieldsplit/4130/5 "2025-11-10T15:01:08Z")
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? ---
**Author:** ![prj](https://avatars.discourse-cdn.com/v4/letter/p/ecae2f/32.png) [@prj](https://community.freefem.org/u/prj)\ **Post date:** [November 10, 2025, 3:07pm UTC](https://community.freefem.org/t/several-lagrange-mutiplier-using-fieldsplit/4130/6 "2025-11-10T15:07:47Z")
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. ---
**Author:** ![smori](https://avatars.discourse-cdn.com/v4/letter/s/a8b319/32.png) [@smori](https://community.freefem.org/u/smori)\ **Post date:** [November 10, 2025, 3:44pm UTC](https://community.freefem.org/t/several-lagrange-mutiplier-using-fieldsplit/4130/7 "2025-11-10T15:44:31Z")
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 ! ---
**Author:** ![prj](https://avatars.discourse-cdn.com/v4/letter/p/ecae2f/32.png) [@prj](https://community.freefem.org/u/prj)\ **Post date:** [November 10, 2025, 3:52pm UTC](https://community.freefem.org/t/several-lagrange-mutiplier-using-fieldsplit/4130/8 "2025-11-10T15:52:00Z")
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`. ---
**Author:** ![smori](https://avatars.discourse-cdn.com/v4/letter/s/a8b319/32.png) [@smori](https://community.freefem.org/u/smori)\ **Post date:** [November 10, 2025, 4:12pm UTC](https://community.freefem.org/t/several-lagrange-mutiplier-using-fieldsplit/4130/9 "2025-11-10T16:12:55Z")
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 ---
**Author:** ![prj](https://avatars.discourse-cdn.com/v4/letter/p/ecae2f/32.png) [@prj](https://community.freefem.org/u/prj)\ **Post date:** [November 10, 2025, 4:51pm UTC](https://community.freefem.org/t/several-lagrange-mutiplier-using-fieldsplit/4130/10 "2025-11-10T16:51:56Z")
What are your FreeFEM and PETSc versions? ---
**Author:** ![smori](https://avatars.discourse-cdn.com/v4/letter/s/a8b319/32.png) [@smori](https://community.freefem.org/u/smori)\ **Post date:** [November 10, 2025, 8:09pm UTC](https://community.freefem.org/t/several-lagrange-mutiplier-using-fieldsplit/4130/11 "2025-11-10T20:09:43Z")
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. ---
**Author:** ![prj](https://avatars.discourse-cdn.com/v4/letter/p/ecae2f/32.png) [@prj](https://community.freefem.org/u/prj)\ **Post date:** [November 10, 2025, 8:11pm UTC](https://community.freefem.org/t/several-lagrange-mutiplier-using-fieldsplit/4130/12 "2025-11-10T20:11:18Z")
Just use FreeFEM `develop` branch, there is no error there and the code runs fine. ```auto $ 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 [...] ``` ---
**Author:** ![smori](https://avatars.discourse-cdn.com/v4/letter/s/a8b319/32.png) [@smori](https://community.freefem.org/u/smori)\ **Post date:** [November 10, 2025, 8:35pm UTC](https://community.freefem.org/t/several-lagrange-mutiplier-using-fieldsplit/4130/13 "2025-11-10T20:35:29Z")
By `develop` branch, you mean [Release FreeFEM v4.14 · FreeFem/FreeFem-sources · GitHub](https://github.com/FreeFem/FreeFem-sources/releases/tag/v4.14) ? 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](https://github.com/FreeFem/FreeFem-sources/releases/tag/v4.14-testActions)) I see here [Release FreeFEM v4.14 · FreeFem/FreeFem-sources · GitHub](https://github.com/FreeFem/FreeFem-sources/releases/tag/v4.14) 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) ---
**Author:** ![smori](https://avatars.discourse-cdn.com/v4/letter/s/a8b319/32.png) [@smori](https://community.freefem.org/u/smori)\ **Post date:** [November 16, 2025, 12:19pm UTC](https://community.freefem.org/t/several-lagrange-mutiplier-using-fieldsplit/4130/14 "2025-11-16T12:19:07Z")
Hello again, I’m still struggling with my problem because I’ve different results using fieldsplit or not. My physical case is simple and I can find an analitycal solution and easily discriminate if a numerical solution is correct or not. ![image](https://canada1.discourse-cdn.com/flex030/uploads/freefem/original/2X/5/58afb075cd4b8a637c55d868145f894c0f5d64d8.png) Here the Lagrange multipliers represent the forces and moment apllied by the spring. If i solve the problem using a global LU for elasticity and lagrange multipliers set(NN, sparams=“-pc\_type lu -ksp\_view -ksp\_monitor”); I got correct values for the mean displacements/forces and for the Lagrange multipliers. However, if I try to solve it using fieldsplit with 2 LU, one for elasticity and one for Lagrange multipliers set(NN, sparams = “-ksp\_type gmres -pc\_type fieldsplit " +” -pc\_fieldsplit\_0\_fields 0 -pc\_fieldsplit\_1\_fields 1,2 " +" -fieldsplit\_0\_pc\_type lu -fieldsplit\_1\_pc\_type lu " +" -ksp\_view -ksp\_monitor -ksp\_converged\_reason" ); I got wrong values for the mean displacements/forces, but surprisingly, the Lagrange multipliers values are correct ! From a physical point of view, I would guess that having correct Lagrange multipliers (ie correct forces applyied by the spring) means that I’m solving correctly my problem. But afterwards I am handling incorrect u fields when I postprocess them to extract mean displacements/forces, as if there was a index issue. But it is hard to believe as i am just changing the set(NN, sparams = “ … between the two cases, not the construction of NN nor the postprocess part. (I check with IT team, v4.14 is the really the developp version and is used with petsc 3.20. I made a confusion between the version available using “module load petsc” and the one actualy called using ff-mpirun.) ---
**Author:** ![prj](https://avatars.discourse-cdn.com/v4/letter/p/ecae2f/32.png) [@prj](https://community.freefem.org/u/prj)\ **Post date:** [November 16, 2025, 1:53pm UTC](https://community.freefem.org/t/several-lagrange-mutiplier-using-fieldsplit/4130/15 "2025-11-16T13:53:36Z")
Without a code to run, I can’t help you. And again, you should update your FreeFEM version to use the `develop` branch, without having to resort to installs from the IT team which is lagging behind. ---
**Author:** ![smori](https://avatars.discourse-cdn.com/v4/letter/s/a8b319/32.png) [@smori](https://community.freefem.org/u/smori)\ **Post date:** [November 16, 2025, 4:14pm UTC](https://community.freefem.org/t/several-lagrange-mutiplier-using-fieldsplit/4130/16 "2025-11-16T16:14:00Z")
Thank you prj. Please find here an .edp to reproduce the two behaviors (global LU vs fieldsplit). It is a simplified version, just 2 Lagrange multipliers [Mod2.edp](https://community.freefem.org/uploads/short-url/zOPMsgOcgOPaoxk4m3BKKb7HEy.edp) (9.6 KB) The mesh used is the same [Mod1.zip](https://community.freefem.org/uploads/short-url/auUY47dePRmbPyB5hSJ103iLhOj.zip) (967.2 KB) I can also give you the cout files in order to check that we have the same results. Both were obtained using ff-mpirun -n 4 and freefem v4.15 : [Cout.zip](https://community.freefem.org/uploads/short-url/6H63y3b1mUbb1RRoFGjTH36AW7v.zip) (1.1 KB) What does matter in here are the values of Lagrange multipliers, the mean efforts/moments/displacements and rotations in Z. The different values correspond to the means over the surfaces defined bellow : ![image](https://canada1.discourse-cdn.com/flex030/uploads/freefem/original/2X/f/f228115442d9d72a8efd190f1167f5d64fd32385.png) I’ll check how to launch Freefem using directcly the developp branch. ---
**Author:** ![prj](https://avatars.discourse-cdn.com/v4/letter/p/ecae2f/32.png) [@prj](https://community.freefem.org/u/prj)\ **Post date:** [November 16, 2025, 5:05pm UTC](https://community.freefem.org/t/several-lagrange-mutiplier-using-fieldsplit/4130/17 "2025-11-16T17:05:00Z")
There are at least two issues in the code: 1. you are not using a Schur complement approach, though you should given the small number of Lagrange multipliers 2. the vectors you are putting in the block matrix are not consistent with the BC. You should use `tgv = -10` for the blocks on the first row (except for the diagonal block), you should use linear forms without Dirichlet BC on the first row (except for the diagonal block). This gives slightly better results, see attached. [schur.txt.zip](https://community.freefem.org/uploads/short-url/u3LxHdun5cXEWsMJQdGg0uOsxXf.zip) (3.1 KB) ---
**Author:** ![smori](https://avatars.discourse-cdn.com/v4/letter/s/a8b319/32.png) [@smori](https://community.freefem.org/u/smori)\ **Post date:** [November 16, 2025, 6:19pm UTC](https://community.freefem.org/t/several-lagrange-mutiplier-using-fieldsplit/4130/18 "2025-11-16T18:19:15Z")
Thanks for the advice ! Could you share your modified edp file ? ---
**Author:** ![prj](https://avatars.discourse-cdn.com/v4/letter/p/ecae2f/32.png) [@prj](https://community.freefem.org/u/prj)\ **Post date:** [November 17, 2025, 2:30pm UTC](https://community.freefem.org/t/several-lagrange-mutiplier-using-fieldsplit/4130/19 "2025-11-17T14:30:27Z")
I don’t think it will run until you have an up-to-date FreeFEM version (as it rely on some new PETSc features). [Mod2.edp](https://community.freefem.org/uploads/short-url/dnbboiVnumi3O3lLesAA6ffUEKh.edp) (10.2 KB)