Preconditioners for Soil-Structure Interaction Problems with Significant Material Stiffness Contrast

Ph.DDOCTOR OF PHILOSOPH

Iterative methods for shifted positive definite linear systems and time discretization of the heat equation

In earlier work we have studied a method for discretization in time of a parabolic problem which consists in representing the exact solution as an integral in the complex plane and then applying a quadrature formula to this integral. In application to a spatially semidiscrete finite element version of the parabolic problem, at each quadrature point one then needs to solve a linear algebraic system having a positive definite matrix with a complex shift, and in this paper we study iterative methods for such systems. We first consider the basic and a preconditioned version of the Richardson algorithm, and then a conjugate gradient method as well as a preconditioned version thereof

ブロック赤黒順序付けによるPoissonソルバーの並列化とParticie-in-Cellプラズマシミュレーションへの応用

電気通信大学202

On-line cascading event tracking and avoidance decision support tool

Cascading outages in power systems are costly events that power system operators and planners actively seek to avoid. Such events can quickly result in power outages for millions of customers. Although it is unreasonable to claim that blackouts can be completely prevented, we can nonetheless reduce the frequency and impact of such high consequence events. Power operators can take actions if they have the right information provided by tools for monitoring and managing the risk of cascading outages. Such tools are being developed in this research project by identifying contingencies that could initiate cascading outages and by determining operator actions to avoid the start of a cascade.;A key to cascading outage defense is the level of grid operator situational awareness. Severe disturbances and complex unfolding of post-disturbance phenomena, including interdependent events, demand critical actions to be taken on the part of the operators, thus making operators dependent on decision support tools and automatic controls. In other industries (e.g., airline, nuclear, process control), control operators employ computational capabilities that help them predict system response and identify corrective actions. Power system operators should have a similar capability with online simulation tools.;To create an online simulator to help operators identify the potential for and actions to avoid cascades, we developed a systematic way to identify power system initiating contingencies for operational use. The work extends the conventional contingency list by including a subset of high-order contingencies identified through topology processing. The contingencies are assessed via an online, mid-term simulator, designed to provide generalized, event-based, corrective control and decision support for operators with very high computational efficiency. Speed enhancement is obtained algorithmically by employing a multi-frontal linear solver within an implicit integration scheme. The contingency selection and simulation capabilities were illustrated on two systems: a test system with six generators and the IEEE RTS-96 with 33 generators. Comparisons with commercial grade simulators indicate the developed simulator is accurate and fast

Solution of partial differential equations on vector and parallel computers

The present status of numerical methods for partial differential equations on vector and parallel computers was reviewed. The relevant aspects of these computers are discussed and a brief review of their development is included, with particular attention paid to those characteristics that influence algorithm selection. Both direct and iterative methods are given for elliptic equations as well as explicit and implicit methods for initial boundary value problems. The intent is to point out attractive methods as well as areas where this class of computer architecture cannot be fully utilized because of either hardware restrictions or the lack of adequate algorithms. Application areas utilizing these computers are briefly discussed

CYBER 200 Applications Seminar

Applications suited for the CYBER 200 digital computer are discussed. Various areas of application including meteorology, algorithms, fluid dynamics, monte carlo methods, petroleum, electronic circuit simulation, biochemistry, lattice gauge theory, economics and ray tracing are discussed

Heterogeneous multicore systems for signal processing

This thesis explores the capabilities of heterogeneous multi-core systems, based on multiple Graphics Processing Units (GPUs) in a standard desktop framework. Multi-GPU accelerated desk side computers are an appealing alternative to other high performance computing (HPC) systems: being composed of commodity hardware components fabricated in large quantities, their price-performance ratio is unparalleled in the world of high performance computing. Essentially bringing “supercomputing to the masses”, this opens up new possibilities for application fields where investing in HPC resources had been considered unfeasible before. One of these is the field of bioelectrical imaging, a class of medical imaging technologies that occupy a low-cost niche next to million-dollar systems like functional Magnetic Resonance Imaging (fMRI). In the scope of this work, several computational challenges encountered in bioelectrical imaging are tackled with this new kind of computing resource, striving to help these methods approach their true potential. Specifically, the following main contributions were made: Firstly, a novel dual-GPU implementation of parallel triangular matrix inversion (TMI) is presented, addressing an crucial kernel in computation of multi-mesh head models of encephalographic (EEG) source localization. This includes not only a highly efficient implementation of the routine itself achieving excellent speedups versus an optimized CPU implementation, but also a novel GPU-friendly compressed storage scheme for triangular matrices. Secondly, a scalable multi-GPU solver for non-hermitian linear systems was implemented. It is integrated into a simulation environment for electrical impedance tomography (EIT) that requires frequent solution of complex systems with millions of unknowns, a task that this solution can perform within seconds. In terms of computational throughput, it outperforms not only an highly optimized multi-CPU reference, but related GPU-based work as well. Finally, a GPU-accelerated graphical EEG real-time source localization software was implemented. Thanks to acceleration, it can meet real-time requirements in unpreceeded anatomical detail running more complex localization algorithms. Additionally, a novel implementation to extract anatomical priors from static Magnetic Resonance (MR) scansions has been included

On High Performance Computing in Geodesy : Applications in Global Gravity Field Determination

Autonomously working sensor platforms deliver an increasing amount of precise data sets, which are often usable in geodetic applications. Due to the volume and quality, models determined from the data can be parameterized more complex and in more detail. To derive model parameters from these observations, the solution of a high dimensional inverse data fitting problem is often required. To solve such high dimensional adjustment problems, this thesis proposes a systematical, end-to-end use of a massive parallel implementation of the geodetic data analysis, using standard concepts of massive parallel high performance computing. It is shown how these concepts can be integrated into a typical geodetic problem, which requires the solution of a high dimensional adjustment problem. Due to the proposed parallel use of the computing and memory resources of a compute cluster it is shown, how general Gauss-Markoff models become solvable, which were only solvable by means of computationally motivated simplifications and approximations before. A basic, easy-to-use framework is developed, which is able to perform all relevant operations needed to solve a typical geodetic least squares adjustment problem. It provides the interface to the standard concepts and libraries used. Examples, including different characteristics of the adjustment problem, show how the framework is used and can be adapted for specific applications. In a computational sense rigorous solutions become possible for hundreds of thousands to millions of unknown parameters, which have to be estimated from a huge number of observations. Three special problems with different characteristics, as they arise in global gravity field recovery, are chosen and massive parallel implementations of the solution processes are derived. The first application covers global gravity field determination from real data as collected by the GOCE satellite mission (comprising 440 million highly correlated observations, 80,000 parameters). Within the second application high dimensional global gravity field models are estimated from the combination of complementary data sets via the assembly and solution of full normal equations (scenarios with 520,000 parameters, 2 TB normal equations). The third application solves a comparable problem, but uses an iterative least squares solver, allowing for a parameter space of even higher dimension (now considering scenarios with two million parameters). This thesis forms the basis for a flexible massive parallel software package, which is extendable according to further current and future research topics studied in the department. Within this thesis, the main focus lies on the computational aspects.Autonom arbeitende Sensorplattformen liefern präzise geodätisch nutzbare Datensätze in größer werdendem Umfang. Deren Menge und Qualität führt dazu, dass Modelle die aus den Beobachtungen abgeleitet werden, immer komplexer und detailreicher angesetzt werden können. Zur Bestimmung von Modellparametern aus den Beobachtungen gilt es oftmals, ein hochdimensionales inverses Problem im Sinne der Ausgleichungsrechnung zu lösen. Innerhalb dieser Arbeit soll ein Beitrag dazu geleistet werden, Methoden und Konzepte aus dem Hochleistungsrechnen in der geodätischen Datenanalyse strukturiert, durchgängig und konsequent zu verwenden. Diese Arbeit zeigt, wie sich diese nutzen lassen, um geodätische Fragestellungen, die ein hochdimensionales Ausgleichungsproblem beinhalten, zu lösen. Durch die gemeinsame Nutzung der Rechen- und Speicherressourcen eines massiv parallelen Rechenclusters werden Gauss-Markoff Modelle lösbar, die ohne den Einsatz solcher Techniken vorher höchstens mit massiven Approximationen und Vereinfachungen lösbar waren. Ein entwickeltes Grundgerüst stellt die Schnittstelle zu den massiv parallelen Standards dar, die im Rahmen einer numerischen Lösung von typischen Ausgleichungsaufgaben benötigt werden. Konkrete Anwendungen mit unterschiedlichen Charakteristiken zeigen das detaillierte Vorgehen um das Grundgerüst zu verwenden und zu spezifizieren. Rechentechnisch strenge Lösungen sind so für Hunderttausende bis Millionen von unbekannten Parametern möglich, die aus einer Vielzahl von Beobachtungen geschätzt werden. Drei spezielle Anwendungen aus dem Bereich der globalen Bestimmung des Erdschwerefeldes werden vorgestellt und die Implementierungen für einen massiv parallelen Hochleistungsrechner abgeleitet. Die erste Anwendung beinhaltet die Bestimmung von Schwerefeldmodellen aus realen Beobachtungen der Satellitenmission GOCE (welche 440 Millionen korrelierte Beobachtungen umfasst, 80,000 Parameter). In der zweite Anwendung werden globale hochdimensionale Schwerefelder aus komplementären Daten über das Aufstellen und Lösen von vollen Normalgleichungen geschätzt (basierend auf Szenarien mit 520,000 Parametern, 2 TB Normalgleichungen). Die dritte Anwendung löst dasselbe Problem, jedoch über einen iterativen Löser, wodurch der Parameterraum noch einmal deutlich höher dimensional sein kann (betrachtet werden nun Szenarien mit 2 Millionen Parametern). Die Arbeit bildet die Grundlage für ein massiv paralleles Softwarepaket, welches schrittweise um Spezialisierungen, abhängig von aktuellen Forschungsprojekten in der Arbeitsgruppe, erweitert werden wird. Innerhalb dieser Arbeit liegt der Fokus rein auf den rechentechnischen Aspekten

On high performance computing in geodesy : applications in global gravity field determination

Autonomously working sensor platforms deliver an increasing amount of precise data sets, which are often usable in geodetic applications. Due to the volume and quality, models determined from the data can be parameterized more complex and in more detail. To derive model parameters from these observations, the solution of a high dimensional inverse data fitting problem is often required. To solve such high dimensional adjustment problems, this thesis proposes a systematical, end-to-end use of a massive parallel implementation of the geodetic data analysis, using standard concepts of massive parallel high performance computing. It is shown how these concepts can be integrated into a typical geodetic problem, which requires the solution of a high dimensional adjustment problem. Due to the proposed parallel use of the computing and memory resources of a compute cluster it is shown, how general Gauss-Markoff models become solvable, which were only solvable by means of computationally motivated simplifications and approximations before. A basic, easy-to-use framework is developed, which is able to perform all relevant operations needed to solve a typical geodetic least squares adjustment problem. It provides the interface to the standard concepts and libraries used. Examples, including different characteristics of the adjustment problem, show how the framework is used and can be adapted for specific applications. In a computational sense rigorous solutions become possible for hundreds of thousands to millions of unknown parameters, which have to be estimated from a huge number of observations. Three special problems with different characteristics, as they arise in global gravity field recovery, are chosen and massive parallel implementations of the solution processes are derived. The first application covers global gravity field determination from real data as collected by the GOCE satellite mission (comprising 440 million highly correlated observations, 80,000 parameters). Within the second application high dimensional global gravity field models are estimated from the combination of complementary data sets via the assembly and solution of full normal equations (scenarios with 520,000 parameters, 2 TB normal equations). The third application solves a comparable problem, but uses an iterative least squares solver, allowing for a parameter space of even higher dimension (now considering scenarios with two million parameters). This thesis forms the basis for a flexible massive parallel software package, which is extendable according to further current and future research topics studied in the department. Within this thesis, the main focus lies on the computational aspects.Autonom arbeitende Sensorplattformen liefern präzise geodätisch nutzbare Datensätze in größer werdendem Umfang. Deren Menge und Qualität führt dazu, dass Modelle die aus den Beobachtungen abgeleitet werden, immer komplexer und detailreicher angesetzt werden können. Zur Bestimmung von Modellparametern aus den Beobachtungen gilt es oftmals, ein hochdimensionales inverses Problem im Sinne der Ausgleichungsrechnung zu lösen. Innerhalb dieser Arbeit soll ein Beitrag dazu geleistet werden, Methoden und Konzepte aus dem Hochleistungsrechnen in der geodätischen Datenanalyse strukturiert, durchgängig und konsequent zu verwenden. Diese Arbeit zeigt, wie sich diese nutzen lassen, um geodätische Fragestellungen, die ein hochdimensionales Ausgleichungsproblem beinhalten, zu lösen. Durch die gemeinsame Nutzung der Rechen- und Speicherressourcen eines massiv parallelen Rechenclusters werden Gauss-Markoff Modelle lösbar, die ohne den Einsatz solcher Techniken vorher höchstens mit massiven Approximationen und Vereinfachungen lösbar waren. Ein entwickeltes Grundgerüst stellt die Schnittstelle zu den massiv parallelen Standards dar, die im Rahmen einer numerischen Lösung von typischen Ausgleichungsaufgaben benötigt werden. Konkrete Anwendungen mit unterschiedlichen Charakteristiken zeigen das detaillierte Vorgehen um das Grundgerüst zu verwenden und zu spezifizieren. Rechentechnisch strenge Lösungen sind so für Hunderttausende bis Millionen von unbekannten Parametern möglich, die aus einer Vielzahl von Beobachtungen geschätzt werden. Drei spezielle Anwendungen aus dem Bereich der globalen Bestimmung des Erdschwerefeldes werden vorgestellt und die Implementierungen für einen massiv parallelen Hochleistungsrechner abgeleitet. Die erste Anwendung beinhaltet die Bestimmung von Schwerefeldmodellen aus realen Beobachtungen der Satellitenmission GOCE (welche 440 Millionen korrelierte Beobachtungen umfasst, 80,000 Parameter). In der zweite Anwendung werden globale hochdimensionale Schwerefelder aus komplementären Daten über das Aufstellen und Lösen von vollen Normalgleichungen geschätzt (basierend auf Szenarien mit 520,000 Parametern, 2 TB Normalgleichungen). Die dritte Anwendung löst dasselbe Problem, jedoch über einen iterativen Löser, wodurch der Parameterraum noch einmal deutlich höher dimensional sein kann (betrachtet werden nun Szenarien mit 2 Millionen Parametern). Die Arbeit bildet die Grundlage für ein massiv paralleles Softwarepaket, welches schrittweise um Spezialisierungen, abhängig von aktuellen Forschungsprojekten in der Arbeitsgruppe, erweitert werden wird. Innerhalb dieser Arbeit liegt der Fokus rein auf den rechentechnischen Aspekten