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A Scaling And Reordering of Jacobian Free GMRES

  1. Aug 15, 2016 #1
    Hello guys,

    I have to code Jacobian Free version of GMRES with scaling and reordering algorithms separately. But I have serious problems about the convergence of inner gmres iterations and I have doubts on my formulation about jacobian-vector product for scaled equations since its bookkeeping gets harder.
    Please notice me if the following is wrong; (For simplicity lets forget reordering now)
    For row(S1) and column(S2) scalings of right preconditioned jacobian-vector product;

    (1) (S1*A*S2) * (S1*M*S2)^-1 * (S1*v) = S1 * [F(Q+eps*(S1*M*S2)^-1 * (S1*v)) - F(Q)]/eps

    where eps is perturbation epsilon, v is search direction, F(Q) is the function, M is right preconditioner matrix and A is jacobian matrix. Notation is similar to Yousef Saad's notation. I'm pretty sure about my formulation and application on code is right. But I'm not sure if I have to scale my residual vector. If answer is yes, how? Can someone share good references,

    Thank you all.
  2. jcsd
  3. Aug 20, 2016 #2
    Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.
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