[petsc-users] Questions on matrix-free GMRES implementation

Fri Mar 12 11:12:53 CST 2021

Hi Matt,

Thanks for your reply. I've checked my math, it is correct. I did not intend to reset the base point within a Newton iteration.   what criteria is used in petsc to decide if it needs to automatically  re-compute the basepoint?

Thanks,
Feng

________________________________
From: Matthew Knepley <knepley at gmail.com>
Sent: 12 March 2021 15:40
To: feng wang <snailsoar at hotmail.com>
Cc: Barry Smith <bsmith at petsc.dev>; petsc-users at mcs.anl.gov <petsc-users at mcs.anl.gov>
Subject: Re: [petsc-users] Questions on matrix-free GMRES implementation

On Fri, Mar 12, 2021 at 10:37 AM feng wang <snailsoar at hotmail.com<mailto:snailsoar at hotmail.com>> wrote:
Hi Matt,

Thanks for your prompt response.

Below are my two versions. one is buggy and the 2nd one is working.  For the first one, I add the diagonal contribution to the true RHS (variable: rhs) and then set the base point, the callback function is somehow called twice afterwards to compute Jacobian.  For the 2nd one, I just call the callback function manually to recompute everything, the callback function is then called once as expected to compute the Jacobian. For me, both versions should do the same things. but I don't know why in the first one the callback function is called twice after I set the base point. what could possibly go wrong?

If you reset the base point, we need to recompute F(b), so you get two function calls. Normally, you do not reset the base point
within a Newton iteration. Maybe you should write out mathematically what you are doing. I cannot understand it right now.

  Thanks,

     Matt

Thanks,
Feng

//This does not work
         fld->cnsv( iqs,iqe, q, aux, csv );
         //add contribution of time-stepping
         for(iv=0; iv<nv; iv++)
        {
            for(iq=0; iq<nq; iq++)
           {
               //use conservative variables here
               rhs[iv][iq] = -rhs[iv][iq] + csv[iv][iq]*lhsa[nlhs-1][iq]/cfl;
           }
        }
         ierr = petsc_setcsv(petsc_csv); CHKERRQ(ierr);
         ierr = petsc_setrhs(petsc_baserhs); CHKERRQ(ierr);
         ierr = MatMFFDSetBase(petsc_A_mf, petsc_csv, petsc_baserhs); CHKERRQ(ierr);

//This works
         fld->cnsv( iqs,iqe, q, aux, csv );
         ierr = petsc_setcsv(petsc_csv); CHKERRQ(ierr);
         ierr = FormFunction_mf(this, petsc_csv, petsc_baserhs); //this is my callback function, now call it manually
         ierr = MatMFFDSetBase(petsc_A_mf, petsc_csv, petsc_baserhs); CHKERRQ(ierr);

________________________________
From: Matthew Knepley <knepley at gmail.com<mailto:knepley at gmail.com>>
Sent: 12 March 2021 15:08
To: feng wang <snailsoar at hotmail.com<mailto:snailsoar at hotmail.com>>
Cc: Barry Smith <bsmith at petsc.dev<mailto:bsmith at petsc.dev>>; petsc-users at mcs.anl.gov<mailto:petsc-users at mcs.anl.gov> <petsc-users at mcs.anl.gov<mailto:petsc-users at mcs.anl.gov>>
Subject: Re: [petsc-users] Questions on matrix-free GMRES implementation

On Fri, Mar 12, 2021 at 9:55 AM feng wang <snailsoar at hotmail.com<mailto:snailsoar at hotmail.com>> wrote:
Hi Mat,

Thanks for your reply. I will try the parallel implementation.

I've got a serial matrix-free GMRES working, but I would like to know why my initial version of matrix-free implementation does not work and there is still something I don't understand. I did some debugging and find that the callback function to compute the RHS for the matrix-free matrix is called twice by Petsc when it computes the finite difference Jacobian, but it should only be called once. I don't know why, could you please give some advice?

F is called once to calculate the base point and once to get the perturbation. The base point is not recalculated, so if you do many iterates, it is amortized.

  Thanks,

     Matt

Thanks,
Feng

________________________________
From: Matthew Knepley <knepley at gmail.com<mailto:knepley at gmail.com>>
Sent: 12 March 2021 12:05
To: feng wang <snailsoar at hotmail.com<mailto:snailsoar at hotmail.com>>
Cc: Barry Smith <bsmith at petsc.dev<mailto:bsmith at petsc.dev>>; petsc-users at mcs.anl.gov<mailto:petsc-users at mcs.anl.gov> <petsc-users at mcs.anl.gov<mailto:petsc-users at mcs.anl.gov>>
Subject: Re: [petsc-users] Questions on matrix-free GMRES implementation

On Fri, Mar 12, 2021 at 6:02 AM feng wang <snailsoar at hotmail.com<mailto:snailsoar at hotmail.com>> wrote:
Hi Barry,

Thanks for your advice.

You are right on this. somehow there is some inconsistency when I compute the right hand side (true RHS + time-stepping contribution to the diagonal matrix) to compute the finite difference Jacobian. If I just use the call back function to recompute my RHS before I call MatMFFDSetBase, then it works like a charm. But now I end up with computing my RHS three times. 1st time is to compute the true RHS, the rest two is for computing finite difference Jacobian.

In my previous buggy version, I only compute RHS twice.  If possible, could you elaborate on your comments "Also be careful about  petsc_baserhs", so I may possibly understand what was going on with my buggy version.

Our FD implementation is simple. It approximates the action of the Jacobian as

  J(b) v = (F(b + h v) - F(b)) / h ||v||

where h is some small parameter and b is the base vector, namely the one that you are linearizing around. In a Newton step, b is the previous solution
and v is the proposed solution update.

Besides, for a parallel implementation, my code already has its own partition method, is it possible to allow petsc read in a user-defined partition?  if not what is a better way to do this?

Sure

  https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/Vec/VecSetSizes.html

  Thanks,

    Matt

Many thanks,
Feng

________________________________
From: Barry Smith <bsmith at petsc.dev<mailto:bsmith at petsc.dev>>
Sent: 11 March 2021 22:15
To: feng wang <snailsoar at hotmail.com<mailto:snailsoar at hotmail.com>>
Cc: petsc-users at mcs.anl.gov<mailto:petsc-users at mcs.anl.gov> <petsc-users at mcs.anl.gov<mailto:petsc-users at mcs.anl.gov>>
Subject: Re: [petsc-users] Questions on matrix-free GMRES implementation

   Feng,

     The first thing to check is that for each linear solve that involves a new operator (values in the base vector) the MFFD matrix knows it is using a new operator.

The easiest way is to call MatMFFDSetBase() before each solve that involves a new operator (new values in the base vector).  Also be careful about  petsc_baserhs, when you change the base vector's values you also need to change the petsc_baserhs values to the function evaluation at that point.

If that is correct I would check with a trivial function evaluator to make sure the infrastructure is all set up correctly. For examples use for the matrix free a 1 4 1 operator applied matrix free.

Barry

On Mar 11, 2021, at 7:35 AM, feng wang <snailsoar at hotmail.com<mailto:snailsoar at hotmail.com>> wrote:

Dear All,

I am new to petsc and trying to implement a matrix-free GMRES. I have assembled an approximate Jacobian matrix just for preconditioning. After reading some previous questions on this topic, my approach is:

the matrix-free matrix is created as:

      ierr = MatCreateMFFD(*A_COMM_WORLD, iqe*blocksize, iqe*blocksize, PETSC_DETERMINE, PETSC_DETERMINE, &petsc_A_mf); CHKERRQ(ierr);
      ierr = MatMFFDSetFunction(petsc_A_mf, FormFunction_mf, this); CHKERRQ(ierr);

KSP linear operator is set up as:

      ierr = KSPSetOperators(petsc_ksp, petsc_A_mf, petsc_A_pre); CHKERRQ(ierr); //petsc_A_pre is my assembled pre-conditioning matrix

Before calling KSPSolve, I do:

         ierr = MatMFFDSetBase(petsc_A_mf, petsc_csv, petsc_baserhs); CHKERRQ(ierr); //petsc_csv is the flow states, petsc_baserhs is the pre-computed right hand side

The call back function is defined as:

   PetscErrorCode cFdDomain::FormFunction_mf(void *ctx, Vec in_vec, Vec out_vec)
  {
      PetscErrorCode ierr;
      cFdDomain *user_ctx;

      cout << "FormFunction_mf called\n";

      //in_vec: flow states
      //out_vec: right hand side + diagonal contributions from CFL number

      user_ctx = (cFdDomain*)ctx;

      //get perturbed conservative variables from petsc
      user_ctx->petsc_getcsv(in_vec);

      //get new right side
      user_ctx->petsc_fd_rhs();

      //set new right hand side to the output vector
      user_ctx->petsc_setrhs(out_vec);

      ierr = 0;
      return ierr;
  }

The linear system I am solving is (J+D)x=RHS. J is the Jacobian matrix.  D is a diagonal matrix and it is used to stabilise the solution at the start but reduced gradually when the solution moves on to recover Newton's method. I add D*x to the true right side when non-linear function is computed to work out finite difference Jacobian, so when finite difference is used, it actually computes (J+D)*dx.

The code runs but diverges in the end. If I don't do matrix-free and use my approximate Jacobian matrix, GMRES  works. So something is wrong with my matrix-free implementation. Have I missed something in my implementation? Besides,  is there a way to check if the finite difference Jacobian matrix is computed correctly in a matrix-free implementation?

Thanks for your help in advance.
Feng

--
What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.
-- Norbert Wiener

https://www.cse.buffalo.edu/~knepley/<http://www.cse.buffalo.edu/~knepley/>

--
What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.
-- Norbert Wiener

https://www.cse.buffalo.edu/~knepley/<http://www.cse.buffalo.edu/~knepley/>

--
What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead.
-- Norbert Wiener

https://www.cse.buffalo.edu/~knepley/<http://www.cse.buffalo.edu/~knepley/>
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