Recent Advances in Graph Partitioning

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

Hierarchical path-finding for Navigation Meshes (HNA*)

Path-finding can become an important bottleneck as both the size of the virtual environments and the number of agents navigating them increase. It is important to develop techniques that can be efficiently applied to any environment independently of its abstract representation. In this paper we present a hierarchical NavMesh representation to speed up path-finding. Hierarchical path-finding (HPA*) has been successfully applied to regular grids, but there is a need to extend the benefits of this method to polygonal navigation meshes. As opposed to regular grids, navigation meshes offer representations with higher accuracy regarding the underlying geometry, while containing a smaller number of cells. Therefore, we present a bottom-up method to create a hierarchical representation based on a multilevel k-way partitioning algorithm (MLkP), annotated with sub-paths that can be accessed online by our Hierarchical NavMesh Path-finding algorithm (HNA*). The algorithm benefits from searching in graphs with a much smaller number of cells, thus performing up to 7.7 times faster than traditional A¿ over the initial NavMesh. We present results of HNA* over a variety of scenarios and discuss the benefits of the algorithm together with areas for improvement.Peer ReviewedPostprint (author's final draft

Parallel Anisotropic Unstructured Grid Adaptation

Computational Fluid Dynamics (CFD) has become critical to the design and analysis of aerospace vehicles. Parallel grid adaptation that resolves multiple scales with anisotropy is identified as one of the challenges in the CFD Vision 2030 Study to increase the capacity and capability of CFD simulation. The Study also cautions that computer architectures are undergoing a radical change and dramatic increases in algorithm concurrency will be required to exploit full performance. This paper reviews four different methods to parallel anisotropic grid generation. They cover both ends of the spectrum: (i) using existing state-of-the-art software optimized for a single core and modifying it for parallel platforms and (ii) designing and implementing scalable software with incomplete, but rapidly maturating functionality. A brief overview for each grid adaptation system is presented in the context of a telescopic approach for multilevel concurrency. These methods employ different approaches to enable parallel execution, which provides a unique opportunity to illustrate the relative behavior of each approach. Qualitative and quantitative metric evaluations are used to draw lessons for future developments in this critical area for parallel CFD simulation

GRChombo : Numerical Relativity with Adaptive Mesh Refinement

In this work, we introduce GRChombo: a new numerical relativity code which incorporates full adaptive mesh refinement (AMR) using block structured Berger-Rigoutsos grid generation. The code supports non-trivial "many-boxes-in-many-boxes" mesh hierarchies and massive parallelism through the Message Passing Interface (MPI). GRChombo evolves the Einstein equation using the standard BSSN formalism, with an option to turn on CCZ4 constraint damping if required. The AMR capability permits the study of a range of new physics which has previously been computationally infeasible in a full 3+1 setting, whilst also significantly simplifying the process of setting up the mesh for these problems. We show that GRChombo can stably and accurately evolve standard spacetimes such as binary black hole mergers and scalar collapses into black holes, demonstrate the performance characteristics of our code, and discuss various physics problems which stand to benefit from the AMR technique.Comment: 48 pages, 24 figure