A comparison of preconditioners for solving linear systems arising from graph laplacians∗

We consider the solution of linear systems corresponding to the combinatorial and normalized graph Laplacians of large unstructured networks. We only consider undirected graphs, so the corresponding matrices are symmetric. A promising approach to solving these problems is to use a class of support graph preconditioners. We previously implemented such a preconditioner in Trilinos in serial using the Epetra software stack. This work extends that implementation to run in parallel on distributed memory systems and migrates the implementation to the Tpetra software stack to help with future development. This preconditioner is compared against other preconditioners currently available in Trilinos. We show that domain decomposition is an effective preconditioning method for network problems. Our support graph preconditioner can be used as a local (serial) subdomain solver.