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

[Matthew Knepley]

On Fri, Mar 12, 2021 at 6:02 AM feng wang <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>
> *Sent:* 11 March 2021 22:15
> *To:* feng wang <snailsoar at hotmail.com>
> *Cc:* petsc-users at mcs.anl.gov <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> 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/>
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