This thesis covers the implementation of a hardware-aware arbitrary high order derivative discontinuous galerkin (ADER-DG) method for hyperbolic partial differential equations. This method has been of a particular interest recently, as it is able to obtain a high order solution in space and time. A specific focus of this thesis is on the optimization of such a method on a current architecture. While the implemention is only used to solve a three-dimensional advection problem, it is also applicable to other hyperbolic problems like, e.g., the elastic wave equation. A brief introduction to the mathematics of the approach is given, followed by a thorough analysis of the characteristics of the method. The implementation is optimized for running on Intel Xeon E5-2697 v3 CPUs. The matrix-matrix multiplications in the method are performed using efficient library implementations and a hybrid OpenMP/MPI implementation is presented. Overall it is shown that the ADER-DG method is suitable for performance optimization on supercomputers and can be used to attain a high order of accuracy. Results for single and multi node performance on such an architecture are presented. In particular, convergence order, FLOPS and scaling are investigated. On a single node 50% of the theoretical peak performance and on 64 nodes up to 38% theoretical peak performance are reached.     «

This thesis covers the implementation of a hardware-aware arbitrary high order derivative discontinuous galerkin (ADER-DG) method for hyperbolic partial differential equations. This method has been of a particular interest recently, as it is able to obtain a high order solution in space and time. A specific focus of this thesis is on the optimization of such a method on a current architecture. While the implemention is only used to solve a three-dimensional advection problem, it is also applicab...     »