Dynamically adaptive multigrid on parallel computers for a semi-implicit discretization of the shallow water equations

Numerical weather forecasting and climate predictions require enormous computing power since high resolution and accuracy are necessary to achieve reliable results. The overall idea of this dissertation on scientific computing is to develop and implement a numerically highly efficient basic meteorological model for parallel environments. Numerical acceleration is achieved by adaptive multigrid in two ways: Firstly, the resolution of the finite difference discretization is locally adapted to the actual requirements of the weather situation. High resolution is provided only where it is necessary (e. g. strong low pressure areas). Since the weather situation changes in a time dependent simulation the refinement areas have to be adapted. This dynamic adaptation is controlled by a refinement criterion based on the estimation of the local spatial discretization error and performed fully automatically. Secondly, multigrid is used to increase the sizes of stable time steps. The applied semi{implicit time scheme results in a Helmholtz equation, which is solved by MLAT. The cycling is adapted to the stability requirements of the actual model problem. In general, one very cheap multigrid cycle suffices. The numerical algorithm is portably implemented on parallel environments by the grid partitioning approach with explicit message passing. A dynamic load balance algorithm considers neighborhood relationships in order to reduce data transfer