Ein Programm für die Parallelisierung dynamisch adaptiver Mehrgitterverfahren

In this thesis dynamic adaptive multi-grid methods are parallelized. In dynamic adaptive multi-grid methods a domain is covered by a grid, and this grid is utilized to calculate objective function values. The objective function at a specific grid point at time t is calculated according to the values of this point and its neighbors at time t-1. The accuracy of this method can be improved by applying coarser and finer grids, where the latter concentrate on subdomains which may change over time. The parallelization of such methods usually is conducted by bisection of the grid and distributed calculation of the partial objective function values. In this thesis a scheduling approach for the redistribution of partial domains by transferring sets of grid points is presented. The design of the applied multi-grid structures supports almost any distribution of grid points. The grids’ data structures are generated once and changed only when required. Thus, no dynamic memory allocation is necessary during iterations. In addition to the multi-grid further structures are necessary, e.g. a structure called Farbenfeld (color field) records on which CPU core certain boundary points of the grid are located. During the parallel adaptive refinement phase a decision criterion is applied in order to create 5x5 fine grid points for one coarse grid point fullfilling the criterion. This is performed using complex data structures only necessitating local modifications to the grid, significantly reducing computation time. Lastly, load balancing is performed by calculating Lasttransferwerte (load transfer values), which specify the number of grid points to be send from one core to another. For this purpose the PLB method and a variant of it are utilized, which usually are applied to complex combinatorial optimization problems. Subsequently, the specific grid points to be transferred from one core to its neighboring cores are chosen and the necessary information for restructuring is send to the affected CPU cores. In addition to the multi-grid structures the structures used by parallel adaptive refinement phase need to be modified. If load is transferred in multiple consecutive load balancing phases, grid points need to be passed on to other neighboring cores. If neighboring grid points are migrated simultaneously during load balancing, a data structure Zwischenkorrektur (intermediate correction) is utilized to keep intact the Farbenfeld. xiv INHALTSVERZEICHNIS