Refactoring the UrQMD model for many-core architectures

Ultrarelativistic Quantum Molecular Dynamics is a physics model to describe the transport, collision, scattering, and decay of nuclear particles. The UrQMD framework has been in use for nearly 20 years since its first development. In this period computing aspects, the design of code, and the efficiency of computation have been minor points of interest. Nowadays an additional issue arises due to the fact that the run time of the framework does not diminish any more with new hardware generations. The current development in computing hardware is mainly focused on parallelism. Especially in scientific applications a high order of parallelisation can be achieved due to the superposition principle. In this thesis it is shown how modern design criteria and algorithm redesign are applied to physics frameworks. The redesign with a special emphasise on many-core architectures allows for significant improvements of the execution speed. The most time consuming part of UrQMD is a newly introduced relativistic hydrodynamic phase. The algorithm used to simulate the hydrodynamic evolution is the SHASTA. As the sequential form of SHASTA is successfully applied in various simulation frameworks for heavy ion collisions its possible parallelisation is analysed. Two different implementations of SHASTA are presented. The first one is an improved sequential implementation. By applying a more concise design and evading unnecessary memory copies, the execution time could be reduced to the half of the FORTRAN version’s execution time. The usage of memory could be reduced by 80% compared to the memory needed in the original version. The second implementation concentrates fully on the usage of many-core architectures and deviates significantly from the classical implementation. Contrary to the sequential implementation, it follows the recalculate instead of memory look-up paradigm. By this means the execution speed could be accelerated up to a factor of 460 on GPUs. Additionally a stability analysis of the UrQMD model is presented. Applying metapro- gramming UrQMD is compiled and executed in a massively parallel setup. The resulting simulation data of all parallel UrQMD instances were hereafter gathered and analysed. Hence UrQMD could be proven of high stability to the uncertainty of experimental data. As a further application of modern programming paradigms a prototypical implementa- tion of the worldline formalism is presented. This formalism allows for a direct calculation of Feynman integrals and constitutes therefore an interesting enhancement for the UrQMD model. Its massively parallel implementation on GPUs is examined

First-Order Model Checking on Generalisations of Pushdown Graphs

We study the first-order model checking problem on two generalisations of pushdown graphs. The first class is the class of nested pushdown trees. The other is the class of collapsible pushdown graphs. Our main results are the following. First-order logic with reachability is uniformly decidable on nested pushdown trees. Considering first-order logic without reachability, we prove decidability in doubly exponential alternating time with linearly many alternations. First-order logic with regular reachability predicates is uniformly decidable on level 2 collapsible pushdown graphs. Moreover, nested pushdown trees are first-order interpretable in collapsible pushdown graphs of level 2. This interpretation can be extended to an interpretation of the class of higher-order nested pushdown trees in the collapsible pushdown graph hierarchy. We prove that the second level of this new hierarchy of nested trees has decidable first-order model checking. Our decidability result for collapsible pushdown graph relies on the fact that level 2 collapsible pushdown graphs are uniform tree-automatic. Our last result concerns tree-automatic structures in general. We prove that first-order logic extended by Ramsey quantifiers is decidable on all tree-automatic structures.Comment: phd thesis, 255 page

Mathematical aspects of stress field simulations in deep geothermal reservoirs

This report gives an insight into basics of stress field simulations for geothermal reservoirs. The quasistatic equations of poroelasticity are deduced from constitutive equations, balance of mass and balance of momentum. Existence and uniqueness of a weak solution is shown. In order of to find an approximate solution numerically, usage of the so–called method of fundamental solutions is a promising way. The idea of this method as well as a sketch of how convergence may be proven are given

Variants of the Shortest Path Problem

The shortest path problem in which the $(s,t)$-paths $P$ of a given digraph $G =(V,E)$ are compared with respect to the sum of their edge costs is one of the best known problems in combinatorial optimization. The paper is concerned with a number of variations of this problem having different objective functions like bottleneck, balanced, minimum deviation, algebraic sum, $k$-sum and $k$-max objectives, $(k_1, k_2)-max, (k_1, k_2)$-balanced and several types of trimmed-mean objectives. We give a survey on existing algorithms and propose a general model for those problems not yet treated in literature. The latter is based on the solution of resource constrained shortest path problems with equality constraints which can be solved in pseudo-polynomial time if the given graph is acyclic and the number of resources is fixed. In our setting, however, these problems can be solved in strongly polynomial time. Combining this with known results on $k$-sum and $k$-max optimization for general combinatorial problems, we obtain strongly polynomial algorithms for a variety of path problems on acyclic and general digraphs

A new solution approach for solving the 2-facility location problem in the plane with block norms

Motivated by the time-dependent location problem over T time-periods introduced in Maier and Hamacher (2015) we consider the special case of two time-steps, which was shown to be equivalent to the static 2-facility location problem in the plane. Geometric optimality conditions are stated for the median objective. When using block norms, these conditions are used to derive a polygon grid inducing a subdivision of the plane based on normal cones, yielding a new approach to solve the 2-facility location problem in polynomial time. Combinatorial algorithms for the 2-facility location problem based on geometric properties are deduced and their complexities are analyzed. These methods differ from others as they are completely working on geometric objects to derive the optimal solution set

Mathematical aspects of stress field simulations in deep geothermal reservoirs

This report gives an insight into basics of stress field simulations for geothermal reservoirs. The quasistatic equations of poroelasticity are deduced from constitutive equations, balance of mass and balance of momentum. Existence and uniqueness of a weak solution is shown. In order of to find an approximate solution numerically, usage of the so–called method of fundamental solutions is a promising way. The idea of this method as well as a sketch of how convergence may be proven are given

On ageing effects in analogue integrated circuits

The behaviour of electronic circuits is influenced by ageing effects. Modelling the behaviour of circuits is a standard approach for the design of faster, smaller, more reliable and more robust systems. In this thesis, we propose a formalization of robustness that is derived from a failure model, which is based purely on the behavioural specification of a system. For a given specification, simulation can reveal if a system does not comply with a specification, and thus provide a failure model. Ageing usually works against the specified properties, and ageing models can be incorporated to quantify the impact on specification violations, failures and robustness. We study ageing effects in the context of analogue circuits. Here, models must factor in infinitely many circuit states. Ageing effects have a cause and an impact that require models. On both these ends, the circuit state is highly relevant, an must be factored in. For example, static empirical models for ageing effects are not valid in many cases, because the assumed operating states do not agree with the circuit simulation results. This thesis identifies essential properties of ageing effects and we argue that they need to be taken into account for modelling the interrelation of cause and impact. These properties include frequency dependence, monotonicity, memory and relaxation mechanisms as well as control by arbitrary shaped stress levels. Starting from decay processes, we define a class of ageing models that fits these requirements well while remaining arithmetically accessible by means of a simple structure. Modeling ageing effects in semiconductor circuits becomes more relevant with higher integration and smaller structure sizes. With respect to miniaturization, digital systems are ahead of analogue systems, and similarly ageing models predominantly focus on digital applications. In the digital domain, the signal levels are either on or off or switching in between. Given an ageing model as a physical effect bound to signal levels, ageing models for components and whole systems can be inferred by means of average operation modes and cycle counts. Functional and faithful ageing effect models for analogue components often require a more fine-grained characterization for physical processes. Here, signal levels can take arbitrary values, to begin with. Such fine-grained, physically inspired ageing models do not scale for larger applications and are hard to simulate in reasonable time. To close the gap between physical processes and system level ageing simulation, we propose a data based modelling strategy, according to which measurement data is turned into ageing models for analogue applications. Ageing data is a set of pairs of stress patterns and the corresponding parameter deviations. Assuming additional properties, such as monotonicity or frequency independence, learning algorithm can find a complete model that is consistent with the data set. These ageing effect models decompose into a controlling stress level, an ageing process, and a parameter that depends on the state of this process. Using this representation, we are able to embed a wide range of ageing effects into behavioural models for circuit components. Based on the developed modelling techniques, we introduce a novel model for the BTI effect, an ageing effect that permits relaxation. In the following, a transistor level ageing model for BTI that targets analogue circuits is proposed. Similarly, we demonstrate how ageing data from analogue transistor level circuit models lift to purely behavioural block models. With this, we are the first to present a data based hierarchical ageing modeling scheme. An ageing simulator for circuits or system level models computes long term transients, solutions of a differential equation. Long term transients are often close to quasi-periodic, in some sense repetitive. If the evaluation of ageing models under quasi-periodic conditions can be done efficiently, long term simulation becomes practical. We describe an adaptive two-time simulation algorithm that basically skips periods during simulation, advancing faster on a second time axis. The bottleneck of two-time simulation is the extrapolation through skipped frames. This involves both the evaluation of the ageing models and the consistency of the boundary conditions. We propose a simulator that computes long term transients exploiting the structure of the proposed ageing models. These models permit extrapolation of the ageing state by means of a locally equivalent stress, a sort of average stress level. This level can be computed efficiently and also gives rise to a dynamic step control mechanism. Ageing simulation has a wide range of applications. This thesis vastly improves the applicability of ageing simulation for analogue circuits in terms of modelling and efficiency. An ageing effect model that is a part of a circuit component model accounts for parametric drift that is directly related to the operation mode. For example asymmetric load on a comparator or power-stage may lead to offset drift, which is not an empiric effect. Monitor circuits can report such effects during operation, when they become significant. Simulating the behaviour of these monitors is important during their development. Ageing effects can be compensated using redundant parts, and annealing can revert broken components to functional. We show that such mechanisms can be simulated in place using our models and algorithms. The aim of automatized circuit synthesis is to create a circuit that implements a specification for a certain use case. Ageing simulation can identify candidates that are more reliable. Efficient ageing simulation allows to factor in various operation modes and helps refining the selection. Using long term ageing simulation, we have analysed the fitness of a set of synthesized operational amplifiers with similar properties concerning various use cases. This procedure enables the selection of the most ageing resilient implementation automatically.Viele alltägliche Geräte in Haushalt, Verkehr, zur Kommunikation oder Medizintechnik werden seit Mitte des zwanzigsten Jahrhunderts von elektronischen Schaltungen beherrscht. Solche Schaltungen messen, steuern und regeln wichtige Eigenschaften, Funktionen und Prozesse und ermöglichen immer weiter ausgefeilte Anwendungen, höhere Effizienz und neue Einsatzmöglichkeiten. Grundsätzlich besteht ein Interesse an der einwandfreien Funktionalität solcher Geräte. Mit elektronischen Halbleiterschaltungen werden zunehmend kleinere Bauteile in diese Geräte verbaut. Einerseits führt dies zu einer wachsenden Systemkomplexität bei mitunter gleichbleibenden Abmessungen, andererseits werden im Zuge der Miniaturisierung physikalische Grenzen erreicht und bisweilen überwunden. Die Einzelteile eines Systems sind nach Fertigung nicht zugänglich und können nicht ausgetauscht werden. Als Konsequenz erwartet man einen Ausfall, sobald ein Einzelteil nicht mehr funktioniert. Um solchen Ausfällen vorzubeugen, möchte man gerne vor der Serienproduktion in Erfahrung bringen, wie sie zustande kommen. Hierzu bedarf es geeigneten Modellen und Analysemethoden. Die Entwicklung solcher im Falle von Analogschaltungen ist der Schwerpunkt dieser Arbeit..

Automatische bildanalytische Zellrekonstruktion für PMI-Hartschäume

Im Projekt MAFoaM - Modular Algorithms for closed Foam Mechanics - des Fraunhofer ITWM in Zusammenarbeit mit dem Fraunhofer IMWS wurde eine Methode zur Analyse und Simulation geschlossenzelliger PMI-Hartschäume entwickelt. Die Zellstruktur der Hartschäume wurde auf Basis von CT-Aufnahmen modelliert, um ihr Verformungs- und Versagensverhalten zu simulieren, d.h. wie sich die Schäume unter Belastungen bis hin zum totalen Defekt verhalten. In der Diplomarbeit wird die bildanalytische Zellrekonstruktion für PMI-Hartschäume automatisiert. Die Zellrekonstruktion dient der Bestimmung von Mikrostrukturgrößen, also geometrischer Eigenschaften der Schaumzellen, wie z.B. Mittelwert und Varianz des Zellvolumens oder der Zelloberfläche

A posteriori Fehlerschätzer für gemischte Finite Elemente in der linearen Elastizität

Es werden ausgehend vom PEERS-Element bzw. von Stenbergs Familie gemischter Finiter Elemente für die lineare Elastizität a posteriori Fehlerschätzer entwickelt. Dabei werden sowohl ein residueller Fehlerschätzer für die natürliche Norm auf den verwendeten Räumen als auch Fehlerschätzer basierend auf lokalen Hilfsproblemen betrachtet. Für letztere wird zunächst die Stabilität von Stenbergs Elementen bezüglich dieser Norm bewiesen. Die Fehlerschätzer sind zuverlässig und effizient, desweiteren wird darauf geachtet, dass die Abschätzungen robust bezüglich der Lamè-Parameter sind

On planar exponential and logarithm series

In der vorliegenden Arbeit wird die Liftung einiger Potenzreihen in die planare (= nicht-kommutative, nicht-assoziative) Potenzreihenalgebra vorgestellt. Die Monome dieser Potenzreihen sind planare, reduzierte Wurzelbäume, versehen mit dem Graftingprodukt. Unter Anderem werden die planare Exponential-, Logarithmus- und Wurzel-Reihe eingeführt. Es werden Eigenschaften dieser Reihen untersucht und mit den Eigenschaften aus der klassischen Algebra verglichen. Weiterhin werden Rekursionsformeln für die Berechnung der Koeffizienten angegeben. Es stellt sich heraus, dass es zu jedem Wurzelbaum $\it V$ eine eindeutige Exponentialreihe \textit {exp_V(x)} mit Eigenschaften, die analog zu den klassischen sind, gibt. Analoge Ergebnisse erhalten wir für die anderen Potenzreihen. Es werden ebenfalls $\lambda$-Deformationen von diesen Potenzreihen vorgestellt, wie auch inverse Reihen bzgl. des Graftingprodukts und weitere Aspekte und Anwendungen von planaren Potenzreihen