From: Vijay S. Mahadevan <vijay.m@gm...>  20081107 15:51:10

Hi there, Before I even start, I know this is probably going to be a loaded question, but nevertheless, any help would be appreciated. Background: I'm working on solution to large scale PDE systems based on libmesh for discretization and petsc for solution procedures. My physics objects are derived from EquationSystems in libmesh datastructure and can contain one or more implicitsystems in it. I use the JacobianFree Krylov scheme for my nonlinear solve and hence the efficiency of the method is achieved from good preconditioning. I've tried using ILU to precondition my preconditioner (linearized version) of the original nonlinear system and this works well for serial runs. But this does not scale when I run in parallel. So my questions are 1) Is it is possible to use libmesh objects to perform geometric multigrid preconditioning and completely avoid the matrix creation except in the coarsest case ?! I've seen some of Ben's presentation that mentions using multigrid for stokes problems etc. and so am curious as to what this would entail ... For example, would I have to create multiple equationsystems object since the mesh is not associated with just the system. Hence for every multigrid level, I would have a new instance of the physics system but on a coarser mesh level. Is this how you would possibly implement this ?! 2) If I can afford to create the matrix in the finest level, can we use algebraic multigrid procedures to precondition this system in parallel ? Anyone know how this scales ? 3) Also, I was reading about Prometheus (http://www.columbia.edu/~ma2325/prom_intro.html) and it looks promising as both a blackbox solver and preconditioner when the matrix is available and geometric multigrid in 2D (not sure about 3D). Has anyone in this list used this package with Petsc and/or libMesh ?! Again, like I said before, there is a lot of things here you can comment on. Feel free to write your thoughts because I want to get as much input as possible before choosing anything specific. Thanks, Vijay 