# Efficient solver and preconditionner for 3D Stokes Problem **URL:** \ **Category:** General Discussion\ **Created:** [March 7, 2023, 7:51am UTC](https://community.freefem.org/t/efficient-solver-and-preconditionner-for-3d-stokes-problem/2318 "2023-03-07T07:51:40Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![Loic](https://avatars.discourse-cdn.com/v4/letter/l/e9c0ed/32.png) [@Loic](https://community.freefem.org/u/Loic)\ **Post date:** [March 7, 2023, 7:51am UTC](https://community.freefem.org/t/efficient-solver-and-preconditionner-for-3d-stokes-problem/2318/1 "2023-03-07T07:51:40Z")
Dear all, I am solving a 3D Stokes problem with PETSc in parallel, with this variationnal formulation `grad(u)' * grad(v) + grad(uB)' * grad(vB) + grad(uC)' * grad(vC) - div(u) * q - div(v) * p + epsq * p * q ` To solve this I am currently using the solver `gmres` with the `LU` preconditionning ` -ksp_type gmres -pc_type lu -pc_factor_mat_solver_type mumps`. However this method, is memory and time consuming due to the `LU` factorization (so I can only run small case even on HPC). I have also try the solver `block jacobi` with a `ILU` preconditionning, but the the linear solver does not converge. Could someone know a solver and a preconditionner to solve efficiently such a problem ? Thank you in advance for your help, Best regards, Loïc, ---
**Author:** ![prj](https://avatars.discourse-cdn.com/v4/letter/p/ecae2f/32.png) [@prj](https://community.freefem.org/u/prj)\ **Post date:** [March 7, 2023, 8:06am UTC](https://community.freefem.org/t/efficient-solver-and-preconditionner-for-3d-stokes-problem/2318/2 "2023-03-07T08:06:51Z")
Use fieldsplit and look at the literature. ---
**Author:** ![Loic](https://avatars.discourse-cdn.com/v4/letter/l/e9c0ed/32.png) [@Loic](https://community.freefem.org/u/Loic)\ **Post date:** [March 7, 2023, 8:29am UTC](https://community.freefem.org/t/efficient-solver-and-preconditionner-for-3d-stokes-problem/2318/3 "2023-03-07T08:29:32Z")
Thanks ! I will have a look on this. Loïc, ---
**Author:** ![Loic](https://avatars.discourse-cdn.com/v4/letter/l/e9c0ed/32.png) [@Loic](https://community.freefem.org/u/Loic)\ **Post date:** [March 7, 2023, 10:24am UTC](https://community.freefem.org/t/efficient-solver-and-preconditionner-for-3d-stokes-problem/2318/4 "2023-03-07T10:24:32Z")
I have tried the solver proposed on the FreeFEM git: `https://github.com/FreeFem/FreeFem-sources/blob/develop/examples/hpddm/stokes-fieldsplit-3d-PETSc.edp` ```auto set(A, sparams = " -ksp_type fgmres -pc_type fieldsplit -pc_fieldsplit_type schur -pc_fieldsplit_schur_fact_type lower -pc_fieldsplit_detect_saddle_point -fieldsplit_velocity_sub_pc_type lu " + " -fieldsplit_pressure_sub_pc_type lu -fieldsplit_velocity_sub_pc_factor_mat_solver_type mumps -fieldsplit_pressure_sub_pc_factor_mat_solver_type mumps -ksp_monitor -ksp_view " + " -fieldsplit_velocity_ksp_type gmres -fieldsplit_velocity_ksp_max_it 5 -fieldsplit_pressure_ksp_type gmres -fieldsplit_pressure_ksp_max_it 5 -ksp_rtol 1e-6"); ``` However, this solver is slower that my previous solver and gives me an incorrect result. Do you know what might be the cause ? or how could I adapt it ? Thank you in advance, Best regards, Loïc, ---
**Author:** ![prj](https://avatars.discourse-cdn.com/v4/letter/p/ecae2f/32.png) [@prj](https://community.freefem.org/u/prj)\ **Post date:** [March 7, 2023, 12:37pm UTC](https://community.freefem.org/t/efficient-solver-and-preconditionner-for-3d-stokes-problem/2318/5 "2023-03-07T12:37:18Z")
What does -ksp\_converged\_reason return? ---
**Author:** ![Loic](https://avatars.discourse-cdn.com/v4/letter/l/e9c0ed/32.png) [@Loic](https://community.freefem.org/u/Loic)\ **Post date:** [March 7, 2023, 12:50pm UTC](https://community.freefem.org/t/efficient-solver-and-preconditionner-for-3d-stokes-problem/2318/6 "2023-03-07T12:50:53Z")
It returns ```auto 0 KSP Residual norm 4.595362033965e+31 1 KSP Residual norm 3.698028393291e+16 Linear solve converged due to CONVERGED_RTOL iterations 1 ``` Loïc, ---
**Author:** ![prj](https://avatars.discourse-cdn.com/v4/letter/p/ecae2f/32.png) [@prj](https://community.freefem.org/u/prj)\ **Post date:** [March 7, 2023, 12:52pm UTC](https://community.freefem.org/t/efficient-solver-and-preconditionner-for-3d-stokes-problem/2318/7 "2023-03-07T12:52:51Z")
Are you using the default `tgv` value of 10^{30}? ---
**Author:** ![Loic](https://avatars.discourse-cdn.com/v4/letter/l/e9c0ed/32.png) [@Loic](https://community.freefem.org/u/Loic)\ **Post date:** [March 7, 2023, 12:54pm UTC](https://community.freefem.org/t/efficient-solver-and-preconditionner-for-3d-stokes-problem/2318/8 "2023-03-07T12:54:33Z")
Yes I am using the default one. ---
**Author:** ![prj](https://avatars.discourse-cdn.com/v4/letter/p/ecae2f/32.png) [@prj](https://community.freefem.org/u/prj)\ **Post date:** [March 7, 2023, 1:01pm UTC](https://community.freefem.org/t/efficient-solver-and-preconditionner-for-3d-stokes-problem/2318/9 "2023-03-07T13:01:28Z")
Then switch to something else first. ---
**Author:** ![Loic](https://avatars.discourse-cdn.com/v4/letter/l/e9c0ed/32.png) [@Loic](https://community.freefem.org/u/Loic)\ **Post date:** [March 7, 2023, 1:10pm UTC](https://community.freefem.org/t/efficient-solver-and-preconditionner-for-3d-stokes-problem/2318/10 "2023-03-07T13:10:58Z")
I have tried different value of `tgv` but the result remain not correct and the residuals remain big. ---
**Author:** ![prj](https://avatars.discourse-cdn.com/v4/letter/p/ecae2f/32.png) [@prj](https://community.freefem.org/u/prj)\ **Post date:** [March 7, 2023, 1:12pm UTC](https://community.freefem.org/t/efficient-solver-and-preconditionner-for-3d-stokes-problem/2318/11 "2023-03-07T13:12:50Z")
What do you get with `tgv = -1` + `-ksp_monitor_true_residual -pc_type lu`? ---
**Author:** ![Loic](https://avatars.discourse-cdn.com/v4/letter/l/e9c0ed/32.png) [@Loic](https://community.freefem.org/u/Loic)\ **Post date:** [March 7, 2023, 1:19pm UTC](https://community.freefem.org/t/efficient-solver-and-preconditionner-for-3d-stokes-problem/2318/12 "2023-03-07T13:19:08Z")
By doing this, I get the right result: ```auto -->Solving with PETSc began.... 0 KSP preconditioned resid norm 2.720997719081e+02 true resid norm 4.595728221659e+01 ||r(i)||/||b|| 1.000000000000e+00 1 KSP preconditioned resid norm 1.879238360449e-04 true resid norm 1.609760664389e-10 ||r(i)||/||b|| 3.502732508859e-12 ``` and it is much faster. Loïc, ---
**Author:** ![prj](https://avatars.discourse-cdn.com/v4/letter/p/ecae2f/32.png) [@prj](https://community.freefem.org/u/prj)\ **Post date:** [March 7, 2023, 1:22pm UTC](https://community.freefem.org/t/efficient-solver-and-preconditionner-for-3d-stokes-problem/2318/13 "2023-03-07T13:22:05Z")
For the largest problem you tried with this, what was the performance of the method? Also, if the problem is symmetric with homogeneous Dirichlet boundary conditions (`tgv = -2`), you should consider switching to `-pc_type cholesky`. ---
**Author:** ![Loic](https://avatars.discourse-cdn.com/v4/letter/l/e9c0ed/32.png) [@Loic](https://community.freefem.org/u/Loic)\ **Post date:** [March 7, 2023, 1:33pm UTC](https://community.freefem.org/t/efficient-solver-and-preconditionner-for-3d-stokes-problem/2318/14 "2023-03-07T13:33:42Z")
With `-ksp_type gmres -pc_type lu -pc_factor_mat_solver_type mumps` I have been able to run a case with about 384 000 tetras (`mesh3 cube(40, 40, 40)`) on 144 CPUs and it takes 53 min. I have not succeeded to run larger case with this method, Loïc, ---
**Author:** ![Loic](https://avatars.discourse-cdn.com/v4/letter/l/e9c0ed/32.png) [@Loic](https://community.freefem.org/u/Loic)\ **Post date:** [March 7, 2023, 1:41pm UTC](https://community.freefem.org/t/efficient-solver-and-preconditionner-for-3d-stokes-problem/2318/15 "2023-03-07T13:41:09Z")
I have try `tgv=-2` with `-pc_type cholesky`. The code converges, but the results are not correct. ---
**Author:** ![prj](https://avatars.discourse-cdn.com/v4/letter/p/ecae2f/32.png) [@prj](https://community.freefem.org/u/prj)\ **Post date:** [March 7, 2023, 1:42pm UTC](https://community.freefem.org/t/efficient-solver-and-preconditionner-for-3d-stokes-problem/2318/16 "2023-03-07T13:42:15Z")
Is your problem symmetric with homogeneous Dirichlet boundary conditions? ---
**Author:** ![Loic](https://avatars.discourse-cdn.com/v4/letter/l/e9c0ed/32.png) [@Loic](https://community.freefem.org/u/Loic)\ **Post date:** [March 7, 2023, 1:45pm UTC](https://community.freefem.org/t/efficient-solver-and-preconditionner-for-3d-stokes-problem/2318/17 "2023-03-07T13:45:46Z")
Sorry for my misunderstanding, I don’t have homogeneous Dirichlet boundary conditions. And my problem I think is not symmetric due to the extra term `-eps*p*q`. ---
**Author:** ![prj](https://avatars.discourse-cdn.com/v4/letter/p/ecae2f/32.png) [@prj](https://community.freefem.org/u/prj)\ **Post date:** [March 7, 2023, 1:47pm UTC](https://community.freefem.org/t/efficient-solver-and-preconditionner-for-3d-stokes-problem/2318/18 "2023-03-07T13:47:09Z")
The term `-eps*p*q` is symmetric, but if you don’t have homogeneous Dirichlet BC, `tgv=-2` is useless indeed. 53 minutes for the above problem suggest that something is wrong on your machine. ---
**Author:** ![Loic](https://avatars.discourse-cdn.com/v4/letter/l/e9c0ed/32.png) [@Loic](https://community.freefem.org/u/Loic)\ **Post date:** [March 7, 2023, 1:55pm UTC](https://community.freefem.org/t/efficient-solver-and-preconditionner-for-3d-stokes-problem/2318/19 "2023-03-07T13:55:16Z")
Considering a case with 750 000 tetras (`cube(50, 50, 50)`) I have not been able to run it even using more that 200 CPUs. The PETSc iterations don’t even start. This suggests that there is indeed a problem on the machine. But in the other hand it is known that LU factorization is time and memory consuming. So I don’t know what is exactly the problem Loïc, ---
**Author:** ![prj](https://avatars.discourse-cdn.com/v4/letter/p/ecae2f/32.png) [@prj](https://community.freefem.org/u/prj)\ **Post date:** [March 7, 2023, 2:00pm UTC](https://community.freefem.org/t/efficient-solver-and-preconditionner-for-3d-stokes-problem/2318/20 "2023-03-07T14:00:23Z")
Share the test case, I will let you know how much time it takes on a properly configured machine. [Next page](https://community.freefem.org/t/efficient-solver-and-preconditionner-for-3d-stokes-problem/2318.md?page=2)