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? Thanks, Feng ________________________________ From: Matthew Knepley <[email protected]> Sent: 12 March 2021 12:05 To: feng wang <[email protected]> Cc: Barry Smith <[email protected]>; [email protected] <[email protected]> Subject: Re: [petsc-users] Questions on matrix-free GMRES implementation On Fri, Mar 12, 2021 at 6:02 AM feng wang <[email protected]<mailto:[email protected]>> 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 <[email protected]<mailto:[email protected]>> Sent: 11 March 2021 22:15 To: feng wang <[email protected]<mailto:[email protected]>> Cc: [email protected]<mailto:[email protected]> <[email protected]<mailto:[email protected]>> 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 <[email protected]<mailto:[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 -- 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/>
