Hi Barry,

Thanks for your help, I really appreciate it.

In the end I used a shell matrix to compute the matrix-vector product, it is clearer to me and there are more things under my control.  I am now trying to do a parallel implementation, I have some questions on setting up parallel matrices and vectors for a user-defined partition, could you please provide some advice? Suppose I have already got a partition for 2 CPUs. Each cpu is assigned a list of elements and also their halo elements.
  1. The global element index for each partition is not necessarily continuous, do I have to I re-order them to make them continuous?
  2. When I set up the size of the matrix and vectors for each cpu, should I take into account the halo elements? 
  3. In my serial version, when I initialize my RHS vector, I am not using VecSetValues, Instead I use VecGetArray/VecRestoreArray to assign the values.  VecAssemblyBegin()/VecAssemblyEnd() is never used. would this still work for a parallel version?
Thanks,
Feng

From: Barry Smith <bsmith@petsc.dev>
Sent: 12 March 2021 23:40
To: feng wang <snailsoar@hotmail.com>
Cc: petsc-users@mcs.anl.gov <petsc-users@mcs.anl.gov>
Subject: Re: [petsc-users] Questions on matrix-free GMRES implementation
 


On Mar 12, 2021, at 9:37 AM, feng wang <snailsoar@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. 

    Do you mean "to compute the Jacobian matrix-vector product?"

    Is it only in the first computation of the product (for the given base vector) that it calls it twice or every matrix-vector product?

    It is possible there is a bug in our logic; run in the debugger with a break point in FormFunction_mf and each time the function is hit in the debugger type where or bt to get the stack frames from the calls. Send this. From this we can all see if it is being called excessively and why.

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?

   The logic of how it is suppose to work is shown below.

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);


    Since you provide petsc_baserhs MatMFFD assumes (naturally) that you will keep the correct values in it. Hence for each new base value YOU need to compute the new values in petsc_baserhs. This approach gives you a bit more control over reusing the information in petsc_baserhs. 

    If you would prefer that MatMFFD recomputes the base values, as needed, then you call FormFunction_mf(this, petsc_csv, NULL); and PETSc will allocate a vector and fill it up as needed by calling your FormFunction_mf() But you need to call MatAssemblyBegin/End each time you the base input vector  this, petsc_csv values change. For example

    MatAssemblyBegin(petsc_A_mf,...)
    MatAssemblyEnd(petsc_A_mf,...)
    KSPSolve()





From: Matthew Knepley <knepley@gmail.com>
Sent: 12 March 2021 15:08
To: feng wang <snailsoar@hotmail.com>
Cc: Barry Smith <bsmith@petsc.dev>; petsc-users@mcs.anl.gov <petsc-users@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@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@gmail.com>
Sent: 12 March 2021 12:05
To: feng wang <snailsoar@hotmail.com>
Cc: Barry Smith <bsmith@petsc.dev>; petsc-users@mcs.anl.gov <petsc-users@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@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


  Thanks,

    Matt
 
Many thanks,
Feng

From: Barry Smith <bsmith@petsc.dev>
Sent: 11 March 2021 22:15
To: feng wang <snailsoar@hotmail.com>
Cc: petsc-users@mcs.anl.gov <petsc-users@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@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



--
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