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 <[email protected]> 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