On Fri, Jan 23, 2009 at 12:01 PM, Derek Gaston <fried...@gmail.com> wrote: > Alright! Now we have a debate! Let me see if I can persuade you... and if > I can't... I'm probably going to code it up anyway to give you a chance to > see what I mean. > > First, let's look at the two different forms of preconditioning (I'll be > using GMRES the whole time because it's easy to think about)... > > Solving: Ax=b > > Left Preconditioning: Find P^-1 Ax = P^-1b > Right Preconditioning: Find A P^-1 P x = b
You're right, I wasn't taking right-preconditioning into account in my previous email. > Further, from Axelsson: Iterative Solution Methods (2000) pg. 472 when > talking about left preconditioning GMRES: > > "The statement h:=C^-1 r is to be interpreted as solving the system Ch = r." > > Where h = y and C = P. What you've perfectly described is a Preconditioner object that *uses* a LinearSolver during its application, not something which "is a" LinearSolver. Of course, this doesn't preclude you from also having a Preconditioner::solve() member, which just applies the preconditioner. It doesn't, in my opinion, make it a LinearSolver, in the sense in which we use that name in Libmesh. > You say that a Preconditioner doesn't satisfy the "is a" relationship for > inheritance... but I hope I've shown you that in fact it does. A > Preconditioner "is a" LinearSolver that solves a specific Py=q system... the > solution of which is used internally by another LinearSolver. Perhaps, but in LibMesh a LinearSolver isn't a just thing that "solves a specific Py=q system," although it does do that. It's an abstract interface to 3rd-party concrete linear algebra libraries as I mentioned before. So, it's a little unfortunate that we have already taken the name that you would like to use but I still argue strongly against adding your proposed Preconditioner to this hierarchy. We might need to have a discussion about expanding the meaning of LinearSolver in libmesh, but I think the current system is elegant and relatively simple to understand for new users. -- John ------------------------------------------------------------------------------ This SF.net email is sponsored by: SourcForge Community SourceForge wants to tell your story. http://p.sf.net/sfu/sf-spreadtheword _______________________________________________ Libmesh-devel mailing list Libmesh-devel@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/libmesh-devel
