Are you thinking about this PR again? https://bitbucket.org/petsc/petsc/pull-requests/506 There's an issue here that Krylov methods operate in the discrete inner product while some higher level operations are of interest in (approximations of) continuous inner products (or norms). The object in PETSc that endows continuous attributes (like a hierarchy, subdomains, fields) on discrete quantities is DM, so my first inclination is that any continuous interpretation of vectors, including inner products and norms, belongs in DM. "Munson, Todd" <[email protected]> writes:

There is a bit of code in TAO that allows the user to change the norm to a matrix norm. This was introduced to get some mesh independent behavior in one example (tao/examples/tutorials/ex3.c). That norm, however, does not propagate down into the KSP methods and is only used for testing convergence of the nonlinear problem.

A few questions then: Is similar functionality needed in SNES? Are TAO and SNES even the right place for this functionality? Should it belong to the Vector class so that you can change the inner products and have all the KSP methods (hopefully) work correctly?

Note: that this discussion brings us to the brink of supporting an optimize-then-discretize approach. I am not convinced we should go down that rabbit hole.

Thanks, Todd.