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Dear All,</div>
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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:</div>
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the matrix-free matrix is created as:</div>
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ierr = MatCreateMFFD(*A_COMM_WORLD, iqe*blocksize, iqe*blocksize, PETSC_DETERMINE, PETSC_DETERMINE, &petsc_A_mf); CHKERRQ(ierr);
<div> ierr = MatMFFDSetFunction(petsc_A_mf, FormFunction_mf, this); CHKERRQ(ierr);</div>
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<div>KSP linear operator is set up as:</div>
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<div> ierr = KSPSetOperators(petsc_ksp, petsc_A_mf, petsc_A_pre); CHKERRQ(ierr); //petsc_A_pre is my assembled pre-conditioning matrix<br>
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<div>Before calling KSPSolve, I do:</div>
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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</div>
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The call back function is defined as:</div>
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PetscErrorCode cFdDomain::FormFunction_mf(void *ctx, Vec in_vec, Vec out_vec)
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<div> PetscErrorCode ierr;</div>
<div> cFdDomain *user_ctx;</div>
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<div> cout << "FormFunction_mf called\n";</div>
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<div> //in_vec: flow states</div>
<div> //out_vec: right hand side + diagonal contributions from CFL number</div>
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<div> user_ctx = (cFdDomain*)ctx;</div>
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<div> //get perturbed conservative variables from petsc</div>
<div> user_ctx->petsc_getcsv(in_vec);</div>
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<div> //get new right side</div>
<div> user_ctx->petsc_fd_rhs();</div>
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<div> //set new right hand side to the output vector</div>
<div> user_ctx->petsc_setrhs(out_vec);</div>
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<div> ierr = 0;</div>
<div> return ierr;</div>
<div> }</div>
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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.
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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?</div>
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Thanks for your help in advance.</div>
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Feng <br>
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