On Fri, Mar 12, 2021 at 9:55 AM feng wang <[email protected]> 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 <[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]> 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...
Thanks,
Matt
Many thanks, Feng
------------------------------ *From:* Barry Smith <[email protected]> *Sent:* 11 March 2021 22:15 *To:* feng wang <[email protected]> *Cc:* [email protected] <[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]> 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/>
-- 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/>