Recursive Algorithms for Distributed Forests of Octrees

The forest-of-octrees approach to parallel adaptive mesh refinement and coarsening (AMR) has recently been demonstrated in the context of a number of large-scale PDE-based applications. Although linear octrees, which store only leaf octants, have an underlying tree structure by definition, it is not often exploited in previously published mesh-related algorithms. This is because the branches are not explicitly stored, and because the topological relationships in meshes, such as the adjacency between cells, introduce dependencies that do not respect the octree hierarchy. In this work we combine hierarchical and topological relationships between octree branches to design efficient recursive algorithms. We present three important algorithms with recursive implementations. The first is a parallel search for leaves matching any of a set of multiple search criteria. The second is a ghost layer construction algorithm that handles arbitrarily refined octrees that are not covered by previous algorithms, which require a 2:1 condition between neighboring leaves. The third is a universal mesh topology iterator. This iterator visits every cell in a domain partition, as well as every interface (face, edge and corner) between these cells. The iterator calculates the local topological information for every interface that it visits, taking into account the nonconforming interfaces that increase the complexity of describing the local topology. To demonstrate the utility of the topology iterator, we use it to compute the numbering and encoding of higher-order $C^0$ nodal basis functions. We analyze the complexity of the new recursive algorithms theoretically, and assess their performance, both in terms of single-processor efficiency and in terms of parallel scalability, demonstrating good weak and strong scaling up to 458k cores of the JUQUEEN supercomputer.Comment: 35 pages, 15 figures, 3 table

Stochastic Transition Model for Discrete Agent Movements

We propose a calibrated two-dimensional cellular automaton model to simulate pedestrian motion behavior. It is a v=4 (3) model with exclusion statistics and random shuffled dynamics. The underlying regular grid structure results in a direction-dependent behavior, which has in particular not been considered within previous approaches. We efficiently compensate these grid-caused deficiencies on model level.Comment: 8 pages, 4 figure

Modeling the desired direction in a force-based model for pedestrian dynamics

We introduce an enhanced model based on the generalized centrifugal force model. Furthermore, the desired direction of pedestrians is investigated. A new approach leaning on the well-known concept of static and dynamic floor-fields in cellular automata is presented. Numerical results of the model are presented and compared with empirical data.Comment: 14 pages 11 figures, submitted to TGF'1

A scalable parallel finite element framework for growing geometries. Application to metal additive manufacturing

This work introduces an innovative parallel, fully-distributed finite element framework for growing geometries and its application to metal additive manufacturing. It is well-known that virtual part design and qualification in additive manufacturing requires highly-accurate multiscale and multiphysics analyses. Only high performance computing tools are able to handle such complexity in time frames compatible with time-to-market. However, efficiency, without loss of accuracy, has rarely held the centre stage in the numerical community. Here, in contrast, the framework is designed to adequately exploit the resources of high-end distributed-memory machines. It is grounded on three building blocks: (1) Hierarchical adaptive mesh refinement with octree-based meshes; (2) a parallel strategy to model the growth of the geometry; (3) state-of-the-art parallel iterative linear solvers. Computational experiments consider the heat transfer analysis at the part scale of the printing process by powder-bed technologies. After verification against a 3D benchmark, a strong-scaling analysis assesses performance and identifies major sources of parallel overhead. A third numerical example examines the efficiency and robustness of (2) in a curved 3D shape. Unprecedented parallelism and scalability were achieved in this work. Hence, this framework contributes to take on higher complexity and/or accuracy, not only of part-scale simulations of metal or polymer additive manufacturing, but also in welding, sedimentation, atherosclerosis, or any other physical problem where the physical domain of interest grows in time

Statistical Models for Pedestrian Behaviour in Front of Bottlenecks

Understanding the movement of human crowds is important for our general understanding of collective behaviour and for applications in building design and event planning. Here, we focus on the flow of a crowd through a narrow bottleneck. We develop statistical models that describe how pedestrian behaviour immediately in front of a bottleneck affects the time lapse between consecutive pedestrians passing through the bottleneck. With this approach, we isolate the most important aspects of pedestrian behaviour from a number of candidate models. We fit our models to experimental data and find that pedestrian interactions immediately in front of the bottleneck appear to be less important for the observed time lapses than interactions further away from the bottleneck. Furthermore, we demonstrate how our approach can be used to rigorously compare microscopic pedestrian behaviours across different contexts by fitting the same statistical models to three separate datasets. We suggest that our approach is a promising tool to establish similarities and differences between simulated and real pedestrian behaviour

Counterflow Extension for the F.A.S.T.-Model

The F.A.S.T. (Floor field and Agent based Simulation Tool) model is a microscopic model of pedestrian dynamics, which is discrete in space and time. It was developed in a number of more or less consecutive steps from a simple CA model. This contribution is a summary of a study on an extension of the F.A.S.T-model for counterflow situations. The extensions will be explained and it will be shown that the extended F.A.S.T.-model is capable of handling various counterflow situations and to reproduce the well known lane formation effect.Comment: Contribution to Crowds and Cellular Automata Workshop 2008. Accepted for publication in "Cellular Automata -- 8th International Conference on Cellular Automata for Research and Industry, ACRI 2008, Yokohama, Japan, September 23-26, Springer 2008, Proceedings

Slab stress and strain rate as constraints on global mantle flow

Dynamically consistent global models of mantle convection with plates are developed that are consistent with detailed constraints on the state of stress and strain rate from deep focus earthquakes. Models that best fit plateness criteria and plate motion data have strong slabs that have high stresses. The regions containing the M_W 8.3 Bolivia and M_W 7.6 Tonga 1994 events are considered in detail. Modeled stress orientations match stress patterns from earthquake focal mechanisms. A yield stress of at least 100 MPa is required to fit plate motions and matches the minimum stress requirement obtained from the stress drop for the Bolivia 1994 deep focus event. The minimum strain rate determined from seismic moment release in the Tonga slab provides an upper limit of ~200 MPa on the strength in the slab

GPU Accelerated Adaptive Wave Propagation Algorithm

The GPU performance of the adaptive wave propagation algorithm is critical to its effectiveness in simulating wave propagation in complex media. This algorithm employs adaptive mesh refinement to improve resolution in areas where the wavefield is changing rapidly. The algorithm\u27s performance is significantly improved by the use of graphics processing units (GPUs), which offer faster computation times than traditional central processing units (CPUs). According to the studies in this poster, GPU acceleration of the adaptive wave propagation algorithm provides significant improvements in simulation speed and scalability, as seen in the simulated examples: scalar advection, shallow water equations, euler, and acoustics. When compared to traditional CPU-based algorithms, the algorithm can handle larger models and produce higher resolution results at a faster rate. The algorithm\u27s efficiency and effectiveness are determined by the specific hardware and software configuration of the GPU used; for this study, we used INL Borah

Counter Chemotactic Flow in Quasi-One-Dimensional Path

Quasi-one-dimensional bidirectional particle flow including the effect of chemotaxis is investigated through a modification of the John-Schadschneider-Chowdhury-Nishinari model. Specifically, we permit multiple lanes to be shared by both directionally traveling particles. The relation between particle density and flux is studied for several evaporation rates of pheromone, and the following results are obtained: i) in the low-particle-density range, the flux is enlarged by pheromone if the pheromone evaporation rate is sufficiently low, ii) in the high particle-density range, the flux is largest at a reasonably high evaporation rate and, iii) if the evaporation rate is at the level intermediate between the above two cases, the flux is kept small in the entire range of particle densities. The mechanism of these behaviors is investigated by observing the spatial-temporal evolution of particles and the average cluster size in the system.Comment: 4 pages, 9 figure