In order to extend the deasible size of simulation domains in space and time, adaptively refined computational grids are a very effficient tool. The reduce the number of data points and, therewith, of operations to a minimum for a given accuracy. In scenarions changing over the simulated time span, the lokal grid resolution has to be adapted dynamically, in addition. Tree-structured grids such as octrees have the clear advantage compared to other, in particular unsstructured grid types, to come along with very low memory requirements due to their strict structuredness. At the same time, they can be efficiently partitioned with good load balancing propoerties. In spite of the strict structure, their offer arbitrarily local grid refinement options. The difficulty in using these grids for existing simulation applications, however, are due to the particular structure and the wish to fully exploit the theoretical efficiency. In the ideal case, a solver algorithm exactly follows to the tree-structure of the grid which, in general, requires significant and prohibitively time consuming changes of the whole simulation code. As a consequence, many applications treat tree-structured grids technically the same as unstructured grids. i.e., store all relations between grid nodes, edges, faces, and elements and, thus, loose most of the advantages given by the grid structure. As for todays and to an even larger extend tomorrows computing architectures investments in saving memory and efficiently arranging data access operations as well as a good parallelizability are decisive for the overall efficiency of a simulation code, an urgent need for the development of concepts implementing tree-structured grids based on efficient data structures still enabling application codes to process grid data data using simple iterators, i.e., loops over certain grid elements arises. In order to optimally profit from cache hierarchies, the underlying data structures should in addition ensure a high spatial and temporal locality of data access and maintain these also in case of dynamically grid refinement or coarsening. The task of the project is the development and implementation of such a concept as well as the application to problems in the collaborative research centre, that urgently need to enlarge the size of the simulation domain in space and time in order to achieve physically meaningful results and new scientific insights.
People
- Miriam Mehl
- Michael Lahnert
- Carsten Burstedde, INS, Universität Bonn