> My aim is to implement the jacobian approximation, i.e. (if F(u) = 0 is
> the function to solve) I wanted to implement
> dst = (F(current_solution + epsilon * src) - F(current_solution))/epsilon.
> In my LinearOperator, my code is
> LinearOperator<LinearAlgebraTrilinos::MPI::Vector> jacobian_operator;
> jacobian_operator.vmult = [&](LinearAlgebraTrilinos::MPI::Vector &dst,
> const LinearAlgebraTrilinos::MPI::Vector &src){
> local_src = src;
> extended_src = src;
> local_solution = present_solution;
>
> double epsilon = 1e-6;
> if(local_src.l2_norm() != 0){
> epsilon = sqrt((1 + local_solution.l2_norm()) * 1e-16) / local_src
> .l2_norm();
> };
> forward_eps_solution = present_solution;
> backward_eps_solution = present_solution;
>
> extended_src *= epsilon;
> forward_eps_solution += extended_src;
> backward_eps_solution -= extended_src;
>
> compute_residual(backward_eps_solution, cur_residual);
> compute_residual(forward_eps_solution, eps_residual);
> eps_residual -= cur_residual;
> eps_residual /= (2 * epsilon);
> dst.reinit(locally_owned_dofs,
> mpi_communicator);
> dst = eps_residual;
> };
>
> Is the same/similar possible for the matrix-free-approach?
>
Sure, you can always write a wrapper around the actual vmult call (which I
assume is happening in compute_residual()).
Best,
Daniel
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