Evaluation of an efficient stack-rle clustering concept for dynamically adaptive grids

One approach for tackling the challenge of efficient implementations for parallel PDE simulations on dynamically changing grids is the usage of space-filling curves (SFCs). While SFC algorithms possess advantageous properties such as low memory requirements and close-to-optimal partitioning approaches with linear complexity, they require efficient communication strategies for keeping and utilizing the connectivity information, in particular for dynamically changing grids. Our approach is to use a sparse communication graph to store the connectivity information and to transfer data blockwise. This permits efficient generation of multiple partitions per memory context (denoted by clustering), which|in combination with a run-length encoding (RLE)|directly leads to elegant solutions for shared, distributed, and hybrid parallelization and allows cluster-based optimizations. While previous work focused on specific aspects, we present in this paper an overall compact summary of the stack-RLE clustering approach complete with aspects of the vertex-based communication that facilitate understanding the approach. The central contribution of this work is the proof of suitability of the stack-RLE clustering approach for an efficient realization of different, relevant building blocks of scientific computing methodology and real-life computer science and engineering (CSE) applications: We show 95% strong scalability for small-scale scalability benchmarks on 512 cores and weak scalability of over 90% on 8192 cores for finite-volume solvers and changing grid structure in every time step; optimizations of simulation data backends by writer tasks; comparisons of analytical benchmarks to analyze the adaptivity criteria; and a tsunami simulation as a representative real-world showcase of a wave propagation for our approach which reduces the overall workload by 95% for parallel fully adaptive mesh refinement and, based on a comparison with SFC-ordered regular grid cells, reduces the computation time by a factor of 7:6 with improved results and a factor of 62:2 with results of similar accuracy of buoy station data.