Data Partitioning Methods and Parallel Block-Oriented PDE Solvers

Abstract: Data partitioning methods for block-structured problems within scientific computing have been studied. The applications are variational data assimilation in meteorology, ocean modeling, and airflow simulation with multiblock grids. Parallel computers offer in a cost efficient way the computational power and memory that is needed for these kinds of applications. An appropriate data partitioning is then necessary to get a high parallel efficiency and utilization of the parallel computer.In the meteorological and oceanographical applications the problem with an irregular workload distribution is treated. In meteorological data assimilation, weather observations are merged together with the dynamical flow model in order to compute an initial state of the atmosphere at a given time. Here, the observations are irregularly distributed in space and time. In ocean modeling the workload varies due to sea depth and ice conditions. New data partitioning methods have been developed for these applications. The new methods are better adapted to the problems and thus give higher efficiency than previous data partitioning methods.In the multiblock applications an additional difficulty is the irregular data dependencies. The blocks in a multiblock grid are usually of different sizes and irregularly coupled. This makes the data partitioning non-trivial. New methods have been developed and different strategies have been investigated - both experimentally and theoretically - using a compressible Navier-Stokes solver as a model problem. The behavior of the different strategies depends very much on the number of subgrids and their sizes as well as the number of processors.Moreover, software tools for block-oriented PDE solvers have been constructed. The tools are written in Fortran 90 with an object-oriented design and support explicit finite difference methods and multiblock grids. Programs using the tools run on parallel computers and the proposed data partitioning methods are utilized.