4.11 Contributions

So far, we presented a single-threaded framework for DG simulations based on the Sierpiński SFC with stack- and stream-based communication via edges and vertices. These communication schemes are based on previous research for vertex- [BSVB08] and edge-based [BBSV10] simulations. Our new contributions are summarized here:

• We gave a formal introduction of the Sierpiński SFC including a formal proof of the correct stack-communication system.
• We developed a framework for such communication schemes and introduced clear interfaces offered to the application developer to hide the stack-based communication complexity.
• The code generator does not only lead to an efficient method to generate tailored and thus optimized code based on the user requirements, but also leads to optimizations such as parameter unrolling to avoid most if-branching mispredictions.
• We separated the stacks into their functional utilization, see Section 4.5. This avoids obsolete access of memory e.g. by separation of structure, cell-data and adaptivity state stacks.
• An automaton table considers the propagation direction of adaptivity information.
• SIMD optimizations allow vectorized computation of fluxes for finite volume simulations.
• A prospective stack reallocation for a good balance between memory requirements and frequent stack reallocation is derived.