Hello - I have a simple question I was hoping to get advice on related to setting the linear solver tolerance for an iterative solver. In the tutorial examples (and in most of the codes I have seen and written) the solver tolerance is some fraction of the initial right hand side 2-norm (e.g. tol = 1.0e-8 * rhs.l2_norm() ). However, I'm questioning this strategy for a nonlinear problem using Newton's method to solve the nonlinear system. As the iterations progress, the initial norm of the right hand side (i.e. the norm of the residual) is decreasing substantially. For a number of problems that I am trying to solve, this causes my tolerance to drop below machine precision at some point (if this happens I take 1e-15 to be the tolerance).
I would like to have a tolerance setting strategy that allows me to have a reasonable and consistent number of iterations for each linear solve required in a Newton increment. Due to this issue the number of linear solver iterations in a single Newton increment can vary drastically (~10 to ~600) even though the properties of the matrix (like the condition number which I have checked) are not changing very much (I am using the AMG preconditioner in Trilinos and also use the one in PETSc). Does anyone have a better strategy for setting the linear solver tolerance other than trial and error (or simply a different strategy that I could try)? From what I remember, the iterative solvers in deal.II are checking the 2-norm of the residual against the tolerance, but correct me if I am wrong please. Thank you in advance for any comments or advice, Jonathan -- The deal.II project is located at http://www.dealii.org/ For mailing list/forum options, see https://groups.google.com/d/forum/dealii?hl=en --- You received this message because you are subscribed to the Google Groups "deal.II User Group" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/dealii/73d5e1f9-6897-4096-bb34-bf46c3c64b80%40googlegroups.com.
