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

[Barry Smith]

   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  

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