On Mon, Jun 22, 2015 at 1:13 PM, Stephan Kramer <s.kramer at imperial.ac.uk> wrote:Dear petsc devs I've been trying to move our code from using KSPSetNullSpace to use MatSetNullSpace instead. Although I appreciate the convenience of the nullspace being propagated automatically through the solver hierarchy, I'm still a little confused on how to deal with the case that mat/=pmat in a ksp. If I read the code correctly I need to call MatSetNullSpace on the pmat in order for a ksp to project that nullspace out of the residual during the krylov iteration. However the nullspaces of mat and pmat are not necessarily the same. For instance, what should I do if the system that I want to solve has a nullspace (i.e. the `mat` has a null vector), but the preconditioner matrix does not. As an example of existing setups that we have for which this is the case: take a standard Stokes velocity, pressure system - where we want to solve for pressure through a Schur complement. Suppose the boundary conditions are Dirichlet for velocity on all boundaries, then the pressure equation has the standard, constant nullspace. A frequently used preconditioner is the "scaled pressure mass matrix" where G^T K^{-1} G is approximated by a pressure mass matrix that is scaled by the value of the viscosity. So in this case the actual system has a nullspace, but the preconditioner matrix does not. The way we previously used to solve this is by setting the nullspace on the ksp of the Schur system, where the mat comes from MatCreateSchurComplement and the pmat is the scaled mass matrix. We then set the pctype to PCKSP and do not set a nullspace on its associated ksp. I don't really see how I can do this using only MatSetNullSpace - unless I create a copy of the mass matrix and have one copy with and one copy without a nullspace so that I could use the one with the nullspace for the pmat of the Schur ksp (and thus the mat of the pcksp) and the copy without the nullspace as the pmat for the pcksp. We would very much appreciate some guidance on what the correct way to deal with this kind of situation isI can understand that this is inconsistent (we have not really thought of a good way to make this consistent). However, does this produce the wrong results? If A has a null space, won't you get the same answer by attaching it to P, or am I missing the import of the above example?
Attaching the nullspace to P means it will be applied in the PCKSP solve as well - which in this case is just a mass matrix solve which doesn't have a nullspace. I was under the impression that removing a nullspace in a solve where the matrix doesn't having one, would lead to trouble - but I'm happy to be told wrong. Cheers Stephan
