Recent Advances in Graph Partitioning

We survey recent trends in practical algorithms for balanced graph partitioning together with applications and future research directions

ESSEX: Equipping Sparse Solvers for Exascale

The ESSEX project investigates computational issues arising at exascale for large-scale sparse eigenvalue problems and develops programming concepts and numerical methods for their solution. The project pursues a coherent co-design of all software layers where a holistic performance engineering process guides code development across the classic boundaries of application, numerical method and basic kernel library. Within ESSEX the numerical methods cover both widely applicable solvers such as classic Krylov, Jacobi-Davidson or recent FEAST methods as well as domain specific iterative schemes relevant for the ESSEX quantum physics application. This report introduces the project structure and presents selected results which demonstrate the potential impact of ESSEX for efficient sparse solvers on highly scalable heterogeneous supercomputers

Reproducibility, accuracy and performance of the Feltor code and library on parallel computer architectures

Feltor is a modular and free scientific software package. It allows developing platform independent code that runs on a variety of parallel computer architectures ranging from laptop CPUs to multi-GPU distributed memory systems. Feltor consists of both a numerical library and a collection of application codes built on top of the library. Its main target are two- and three-dimensional drift- and gyro-fluid simulations with discontinuous Galerkin methods as the main numerical discretization technique. We observe that numerical simulations of a recently developed gyro-fluid model produce non-deterministic results in parallel computations. First, we show how we restore accuracy and bitwise reproducibility algorithmically and programmatically. In particular, we adopt an implementation of the exactly rounded dot product based on long accumulators, which avoids accuracy losses especially in parallel applications. However, reproducibility and accuracy alone fail to indicate correct simulation behaviour. In fact, in the physical model slightly different initial conditions lead to vastly different end states. This behaviour translates to its numerical representation. Pointwise convergence, even in principle, becomes impossible for long simulation times. In a second part, we explore important performance tuning considerations. We identify latency and memory bandwidth as the main performance indicators of our routines. Based on these, we propose a parallel performance model that predicts the execution time of algorithms implemented in Feltor and test our model on a selection of parallel hardware architectures. We are able to predict the execution time with a relative error of less than 25% for problem sizes between 0.1 and 1000 MB. Finally, we find that the product of latency and bandwidth gives a minimum array size per compute node to achieve a scaling efficiency above 50% (both strong and weak)