SUMMARY This article studies the performance and scalability of a geometric multigrid solver implemented within the hierarchical hybrid grids (HHG) software package on current high performance computing clusters up to nearly 300,000 cores. HHG is based on unstructured tetrahedral finite elements that are regularly refined to obtain a block‐structured computational grid. One challenge is the parallel mesh generation from an unstructured input grid that roughly approximates a human head within a 3D magnetic resonance imaging data set. This grid is then regularly refined to create the HHG grid hierarchy. As test platforms, a BlueGene/P cluster located at Jülich supercomputing center and an Intel Xeon 5650 cluster located at the local computing center in Erlangen are chosen. To estimate the quality of our implementation and to predict runtime for the multigrid solver, a detailed performance and communication model is developed and used to evaluate the measured single node performance, as well as weak and strong scaling experiments on both clusters. Thus, for a given problem size, one can predict the number of compute nodes that minimize the overall runtime of the multigrid solver. Overall, HHG scales up to the full machines, where the biggest linear system solved on Jugene had more than one trillion unknowns. Copyright © 2012 John Wiley & Sons, Ltd.

We developed and optimized a multigrid method on the QPACE cluster. The QPACE cluster is an acclerator-based cluster using the Power Cell 8i CPU that is built by the special research field SFB TR 55 for Lattice Quantum Chromo dynamics computations. The cluster uses a custom 3D to rus network build using FPGAs. Our goal was to evaluate the QPACE architecture for a type of algorithm that uses a communication pattern not limited to nearest neighbor communication. We provide a model of the communication network taking into account the specific characteristics of the network and the network processor. For the implementation we chose to use an accelerator-centric programming model by using the SPUs, only.

This paper describes computational models for particle-laden flows based on a fully resolved fluid-structure interaction. The flow simulation uses the Lattice Boltzmann method, while the particles are handled by a rigid body dynamics algorithm. The particles can have individual non-spherical shapes, creating the need for a non-trivial collision detection and special contact models. An explicit coupling algorithm transfers momenta from the fluid to the particles in each time step, while the particles impose moving boundaries for the flow solver. All algorithms and their interaction are fully parallelized. Scaling experiments and a careful performance analysis are presented for up to 294912 processor cores of the Blue Gene at the Jülich Supercomputing center. The largest simulations involve 264 million particles that are coupled to a fluid which is simultaneously resolved by 150 billion cells for the Lattice Boltzmann method. The paper will conclude with a computational experiment for the segregation of suspensions of particles of different density, as an example of the many industrial applications that are enabled by this new methodology.