A tetrahedral space-filling curve for non-conforming adaptive meshes

We introduce a space-filling curve for triangular and tetrahedral red-refinement that can be computed using bitwise interleaving operations similar to the well-known Z-order or Morton curve for cubical meshes. To store sufficient information for random access, we define a low-memory encoding using 10 bytes per triangle and 14 bytes per tetrahedron. We present algorithms that compute the parent, children, and face-neighbors of a mesh element in constant time, as well as the next and previous element in the space-filling curve and whether a given element is on the boundary of the root simplex or not. Our presentation concludes with a scalability demonstration that creates and adapts selected meshes on a large distributed-memory system.Comment: 33 pages, 12 figures, 8 table

Enhancing speed and scalability of the ParFlow simulation code

Regional hydrology studies are often supported by high resolution simulations of subsurface flow that require expensive and extensive computations. Efficient usage of the latest high performance parallel computing systems becomes a necessity. The simulation software ParFlow has been demonstrated to meet this requirement and shown to have excellent solver scalability for up to 16,384 processes. In the present work we show that the code requires further enhancements in order to fully take advantage of current petascale machines. We identify ParFlow's way of parallelization of the computational mesh as a central bottleneck. We propose to reorganize this subsystem using fast mesh partition algorithms provided by the parallel adaptive mesh refinement library p4est. We realize this in a minimally invasive manner by modifying selected parts of the code to reinterpret the existing mesh data structures. We evaluate the scaling performance of the modified version of ParFlow, demonstrating good weak and strong scaling up to 458k cores of the Juqueen supercomputer, and test an example application at large scale.Comment: The final publication is available at link.springer.co

Essays on the Economics of Congestion Management - Theory and Model-based Analysis for Central Western Europe

Concerning the design of (regional) electricity markets, the weighting of uniform pricing with re-dispatch on the one hand and zonal or even nodal pricing on the other hand largely depends on the trade-off between price signals, short and long-term incentives, liquidity and competition. The combination of the said aspects determines the overall efficiency of a market design and its congestion management. The thesis at hand addresses itself to various aspects of the described trade-off. With regard to the European context, the thesis presents a methodology to identify suitable bidding zones under consideration of the fundamental market structure. Furthermore, the static and dynamic efficiency of different re-dispatch designs is analysed theoretically. Subsequently, the influence of congestion management designs on the distribution of producer and consumer surplus is quantified for the case of Germany. Additionally, the magnitude of the losses in efficiency induced by re-dispatch models is assessed

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

Simulation of evacuation processes using a bionics-inspired cellular automaton model for pedestrian dynamics

We present simulations of evacuation processes using a recently introduced cellular automaton model for pedestrian dynamics. This model applies a bionics approach to describe the interaction between the pedestrians using ideas from chemotaxis. Here we study a rather simple situation, namely the evacuation from a large room with one or two doors. It is shown that the variation of the model parameters allows to describe different types of behaviour, from regular to panic. We find a non-monotonic dependence of the evacuation times on the coupling constants. These times depend on the strength of the herding behaviour, with minimal evacuation times for some intermediate values of the couplings, i.e. a proper combination of herding and use of knowledge about the shortest way to the exit.Comment: 19 pages, 13 pictures, accepted for publication in Physica