# [petsc-users] [EXTERNAL] Question about SuperLU

Tang, Qi tangqi at msu.edu
Sat Jun 11 12:39:25 CDT 2022

```Thanks for explaining. Let me summarize what we found so far. Barry was correct on the fieldsplit comment.
* Applying superlu_dist to the entire BV block failed (“together factorization”)
* Applying superlu_dist to the selfp version of schur complement for B and the diagonal sub-block for V succeeded (“separate factorization”). The solution looks fine. It is a regularized saddle point problem, so the diagonal blocks are not singular.

There is no implementation to switch between two options on our end, so that should exclude any potential bugs in the solver level.

The original size of BV block is 240K, so we have to use superlu_dist. We also check its precondition number and it looks fine.

Now we downsize the problem so that we can analyze in matlab. The BV size becomes roughly 10K. We checked various things using matlab and it seems the matrix looks fine from matlab. But superlu_dist still runs into zero pivoting error (all default options on superlu_dist). Yes, we should try superlu or mumps, which is a good suggestion. We will also try change the superlu_dist flag as Sherry suggested. Now we know a few detections to do on petsc/matlab. Thanks for all the good suggestions.

Qi

On Jun 11, 2022, at 8:46 AM, Barry Smith <bsmith at petsc.dev> wrote:

﻿

On Jun 10, 2022, at 7:30 PM, Jorti, Zakariae <zjorti at lanl.gov<mailto:zjorti at lanl.gov>> wrote:

Hi,

I have tried your suggestions and here is what I found.
Barry you were right about the first case. But in the second case, I am not using a Schur fieldsplit but a multiplicative fieldsplit : -fieldsplit_TEBV_fieldsplit_EBV_pc_type fieldsplit -fieldsplit_TEBV_fieldsplit_EBV_pc_fieldsplit_type multiplicative

The previous email indicated

b) a Schur-based fieldsplit preconditioner that uses SuperLU for both V and B blocks:
-fieldsplit_TEBV_fieldsplit_EBV_fieldsplit_BV_ksp_type gmres -fieldsplit_TEBV_fieldsplit_EBV_fieldsplit_BV_pc_type fieldsplit -fieldsplit_TEBV_fieldsplit_EBV_fieldsplit_BV_pc_fieldsplit_type schur -

which means there is a Schur complement PC inside the multiplicative so my explanation that the Schur complement "saves" the problem by passing into SuperLU_DIST a non-singular matrix that is some approximation to the Schur complement could be true.

Then I tried this flag -fieldsplit_TEBV_fieldsplit_EBV_fieldsplit_BV_ksp_view_pmat binary:BVmat:binary_matlab and checked the resulting matrix in Matlab.
For Matlab, this is a full rank matrix, and the LU factorization there was carried out without any issues.
I also outputted the BV block directly from the Jacobian matrix.
Once again, according to Matlab, it is a full rank matrix and it computes the LU factorization without any problem.

The BV matrix you saved into Matlab is a "block" matrix where the first block is B and the second block V (presumably both the same size). Can you, in Matlab, extract the two blocks separated and examine them (via say spy) and also have Matlab factor each of them separately? In your failed fieldsplit case SuperLU_DIST is factoring each of these matrices separately which could produce a zero pivot that would not occur when the larger matrix (of both blocks) is factored together. Let's see what happens with Matlab's solver.

It looks like you are running on one rank?  If the above process is not informative this is what you do next.

Use PetscBinaryWrite() from Matlab to save each of the two blocks (one for B and one for V) to two files. Then use a simple standalone PETSc code, say src/ksp/ksp/tutorials/ex10.c to read each of the files and use SuperLU_DIST directly on each of the two linear systems. This will, at least to my understanding, result in the exact same SuperLU_DIST solves that you get with the failed use of PCFIELDSPLIT. If they succeed or fail will be very informative.

Barry

So, there should not be any Schur complement approximation Sp.

When I ran a test with -fieldsplit_TEBV_fieldsplit_EBV_fieldsplit_BV_ksp_view_pre -fieldsplit_TEBV_fieldsplit_EBV_fieldsplit_BV_ksp_error_if_not_converged, I got this error:

0 SNES Function norm 6.368031218939e-02
0 KSP Residual norm 6.368031218939e-02
Linear fieldsplit_ni_ solve converged due to CONVERGED_ATOL iterations 0
Linear fieldsplit_TEBV_fieldsplit_tau_ solve converged due to CONVERGED_RTOL iterations 1
Linear fieldsplit_TEBV_fieldsplit_EBV_fieldsplit_EP_ solve converged due to CONVERGED_RTOL iterations 3
[0]PETSC ERROR: --------------------- Error Message --------------------------------------------------------------
[0]PETSC ERROR: Zero pivot in LU factorization: https://petsc.org/release/faq/#zeropivot<https://urldefense.com/v3/__https://petsc.org/release/faq/*zeropivot__;Iw!!HXCxUKc!1vY5FSHg9a143jpT3lhbQey_sldBBXUDcobIHEM7_pSCNpzEjSMIA-uaq6k_Ov9kiGJ9WBEKSca2QVY\$>
[0]PETSC ERROR: Zero pivot in row 1658
[0]PETSC ERROR: See https://petsc.org/release/faq/<https://urldefense.com/v3/__https://petsc.org/release/faq/__;!!HXCxUKc!1vY5FSHg9a143jpT3lhbQey_sldBBXUDcobIHEM7_pSCNpzEjSMIA-uaq6k_Ov9kiGJ9WBEKSDe1jhs\$> for trouble shooting.
[0]PETSC ERROR: Petsc Development GIT revision: v3.16.3-751-g2f43bd9bc3  GIT Date: 2022-01-26 22:34:02 -0600
[0]PETSC ERROR: ./main on a macx named pn2032683.lanl.gov<https://urldefense.com/v3/__http://pn2032683.lanl.gov/__;!!HXCxUKc!1vY5FSHg9a143jpT3lhbQey_sldBBXUDcobIHEM7_pSCNpzEjSMIA-uaq6k_Ov9kiGJ9WBEKW6FQ13g\$> by zjorti Fri Jun 10 16:17:35 2022

Then I tried this flag -fieldsplit_TEBV_fieldsplit_EBV_fieldsplit_BV_ksp_view_pmat binary:BVmat:binary_matlab and checked the resulting matrix in Matlab.
For Matlab, this is a full rank matrix, and the LU factorization there was carried out without any issues.
I also outputted the BV block directly from the Jacobian matrix.
Once again, according to Matlab, it is a full rank matrix and it computes the LU factorization without any problem.

________________________________
From: Barry Smith <bsmith at petsc.dev<mailto:bsmith at petsc.dev>>
Sent: Friday, June 10, 2022 7:32 AM
To: Jorti, Zakariae
Cc: petsc-users at mcs.anl.gov<mailto:petsc-users at mcs.anl.gov>; Tang, Xianzhu
Subject: [EXTERNAL] Re: [petsc-users] Question about SuperLU

It is difficult to tell exactly how the preconditioner is being formed with the information below it looks like in the

first case: the original B diagonal block and V diagonal block of the matrix are being factored separately with SuperLU_DIST

second case: the B block is factored with SuperLU_DIST and an explicit approximation to a Schur complement of the V block (Schur complement on eliminating the B block) is formed using "Preconditioner for the Schur complement formed from Sp, an assembled approximation to S, which uses A00's %sdiagonal's inverse" (this is the printout from a KSPView() for this part of the preconditioner).

My guess is you have a "Stokes"-like problem where the V block is identically 0 so, of course, the SuperLU_DIST will fail on it. But the approximation of the Schur complement onto that block is not singular so SuperLU_DIST has no trouble. If I am wrong and the V block is not identically 0 then it may be singular (or possibly, but less likely just badly order) so that SuperLU_DIST encounters a zero pivot.

You can run with -ksp_view_pre to have the KSP print the KSP solver algorithm details BEFORE the linear solve (hence they would get printed despite your failed solve). That would be useful to see exactly what your preconditioner is.

You can use -ksp_view_pmat (with appropriate prefix) to display the matrix that is going to be factored. Thus you can quickly verify what V is.

If you run with -ksp_error_if_not_converged then the solver will stop exactly when the zero pivot is encountered; this would include some information from SuperLU_DIST which might include the row number etc.

Notes on PETSc improvements needed.

1) The man page for KSPCheckSolve() is terribly misleading

2) It would be nice to have a view that displayed the nested fieldsplit preconditioners more clearly

On Jun 9, 2022, at 5:19 PM, Jorti, Zakariae via petsc-users <petsc-users at mcs.anl.gov<mailto:petsc-users at mcs.anl.gov>> wrote:

Hi,

I am solving non-linear problem that has 5 unknowns {ni, T, E, B, V}, and for the preconditioning part, I am using a FieldSplit preconditioner. At the last fieldsplit/level, we are left with a {B,V} block that tried to precondition in 2 different ways:
a) SuperLU:
-fieldsplit_TEBV_fieldsplit_EBV_fieldsplit_BV_ksp_type preonly -fieldsplit_TEBV_fieldsplit_EBV_fieldsplit_BV_pc_type lu -fieldsplit_TEBV_fieldsplit_EBV_fieldsplit_BV_pc_factor_mat_solver_type superlu_dist
b) a Schur-based fieldsplit preconditioner that uses SuperLU for both V and B blocks:
-fieldsplit_TEBV_fieldsplit_EBV_fieldsplit_BV_ksp_type gmres -fieldsplit_TEBV_fieldsplit_EBV_fieldsplit_BV_pc_type fieldsplit -fieldsplit_TEBV_fieldsplit_EBV_fieldsplit_BV_pc_fieldsplit_type schur -fieldsplit_TEBV_fieldsplit_EBV_fieldsplit_BV_pc_fieldsplit_schur_precondition selfp -fieldsplit_TEBV_fieldsplit_EBV_fieldsplit_BV_fieldsplit_B_ksp_type preonly -fieldsplit_TEBV_fieldsplit_EBV_fieldsplit_BV_fieldsplit_B_pc_type lu -fieldsplit_TEBV_fieldsplit_EBV_fieldsplit_BV_fieldsplit_B_pc_factor_mat_solver_type superlu_dist -fieldsplit_TEBV_fieldsplit_EBV_fieldsplit_BV_fieldsplit_V_ksp_type preonly -fieldsplit_TEBV_fieldsplit_EBV_fieldsplit_BV_fieldsplit_V_pc_type lu -fieldsplit_TEBV_fieldsplit_EBV_fieldsplit_BV_fieldsplit_V_pc_factor_mat_solver_type superlu_dist

Option a) yields the following error:
"     Linear fieldsplit_ni_ solve converged due to CONVERGED_ATOL iterations 0
Linear fieldsplit_TEBV_fieldsplit_tau_ solve converged due to CONVERGED_RTOL iterations 1
Linear fieldsplit_TEBV_fieldsplit_EBV_fieldsplit_EP_ solve converged due to CONVERGED_RTOL iterations 5
Linear fieldsplit_TEBV_fieldsplit_EBV_fieldsplit_BV_ solve did not converge due to DIVERGED_PC_FAILED iterations 0
PC failed due to FACTOR_NUMERIC_ZEROPIVOT "
whereas options b) seems to be working well.
Is it possible that the SuperLU on the {V,B} block uses a reordering that introduces a zero pivot or could there be another explanation for this error?

Many thanks.
Best,

Zakariae

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