Part II: Essential numerics of hyperbolic PDEs
For the development of our framework, we first determine the interface requirements with
representative standard models for wave propagations. Here, we consider the shallow water equations
(which are depth-averaged Navier-Stokes equations) and the Euler equations as two representatives of
the fundamental equations in fluid mechanics. For the discretization, we use the discontinuous
Galerkin method which is well-researched for the considered models. Afterwards, we determine data
access and data exchange patterns of this model.
Part III: Efficient framework for simulations on dynamically adaptive grids
We start with an introduction to existing work on stack- and stream-based simulations based on
SFC-induced grids. These stacks and streams account for issue (a). This is followed by a verification of
the correct stack communication and extensions to higher-order time-stepping methods. For usability
reasons (d), we separate the grid traversals and the kernels operating on the grid data. Based on the
underlying grid traversal, we present further optimizations.
Then, we introduce our new parallelization approach which is based on a partitioning of the domain into intervals of the SFC. We derive properties of the SFC-based stack communication system which shows the validity of a run-length encoded (RLE) communication scheme, yielding a cluster-based parallelization approach. This RLE communication scheme yields several advantages, e.g. the possibility of implicitly updating the meta information based on transferred adaptivity markers and block-wise communication resulting in shared- and distributed-memory support (c). In combination with the stack-based communication system, clustering directly leads to an efficient data migration for distributed-memory systems (d). We close the parallelization section with cluster-based optimizations and scalability results for simulations on dynamically adaptive grids which are parallelized with OpenMP and TBB for shared- and MPI for distributed-memory parallelization models.
The scalability benchmarks show the efficiency of the parallelization, whereas we tested the real applicability of our dynamically adaptive simulations with analytical benchmarks and a realistic Tsunami simulation. Furthermore, we present other implemented application scenarios such as interactive steering with an OpenGL back end, efficient writing of grid data to persistent memory, simulations on the sphere and multi-layer simulations.
Part IV: Invasive Computing
Once running simulations on dynamically adaptive grids, the workload can change over the
simulation’s run time, hence also the resource requirements vary. For state-of-the-art parallelization
models in high-performance computing, such a change in resource requirements is not considered so
far for concurrently running applications. Here, a dynamical redistribution of resources would have the
potential of improving the overall system’s efficiency.
In Part IV, we evaluated such a dynamic resource management on shared-memory HPC systems with the Invasive Computing paradigm. We realized this with an Invasive resource manager which receives application-specific information to optimize the distribution of the computational resources among concurrently running applications. Several experiments have been conducted with this resource manager based on our simulations on dynamically adaptive grids developed in the previous part of this thesis.