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Andreas Dedner University of Warwick Friday November 22, 2013 Mesa Laboratory – Chapman Room 11:00 AM Implicit time stepping in numerical weather- and climate- prediction can be accelerated by solving a linear elliptic problem in each time step (Schur complement or Helmholtz equation). This part of a dynamical core accounts for a significant proportion of the overall runtime. To run the model operationally, the solver has to scale to hundreds of thousands of processor cores on modern computer architectures. In addition to investigating the scalability of implicit time stepping algorithm using existing solvers in the Distributed and Unified Numerics Environment (DUNE) and the Hypre library, we also implemented a matrix-free parallel geometric multigrid code with a vertical line smoother. We demonstrate the scalability of the solver on up to 65536 cores of the Hector supercomputer. We investigate different options to make use the tensor structure of the underlying mesh, which is unstructured in the horizontal but structured in the vertical. We demonstrate the effectiveness of our method for different test cases.