Das unstetige Galerkinverfahren für Strömungen mit freier Oberfläche und im Grundwasserbereich in geophysikalischen Anwendungen

Free surface flows and subsurface flows appear in a broad range of geophysical applications and in many environmental settings situations arise which even require the coupling of free surface and subsurface flows. Many of these application scenarios are characterized by large domain sizes and long simulation times. Hence, they need considerable amounts of computational work to achieve accurate solutions and the use of efficient algorithms and high performance computing resources to obtain results within a reasonable time frame is mandatory. Discontinuous Galerkin methods are a class of numerical methods for solving differential equations that share characteristics with methods from the finite volume and finite element frameworks. They feature high approximation orders, offer a large degree of flexibility, and are well-suited for parallel computing. This thesis consists of eight articles and an extended summary that describe the application of discontinuous Galerkin methods to mathematical models including free surface and subsurface flow scenarios with a strong focus on computational aspects. It covers discretization and implementation aspects, the parallelization of the method, and discrete stability analysis of the coupled model.Für viele geophysikalische Anwendungen spielen Strömungen mit freier Oberfläche und im Grundwasserbereich oder sogar die Kopplung dieser beiden eine zentrale Rolle. Oftmals charakteristisch für diese Anwendungsszenarien sind große Rechengebiete und lange Simulationszeiten. Folglich ist das Berechnen akkurater Lösungen mit beträchtlichem Rechenaufwand verbunden und der Einsatz effizienter Lösungsverfahren sowie von Techniken des Hochleistungsrechnens obligatorisch, um Ergebnisse innerhalb eines annehmbaren Zeitrahmens zu erhalten. Unstetige Galerkinverfahren stellen eine Gruppe numerischer Verfahren zum Lösen von Differentialgleichungen dar, und kombinieren Eigenschaften von Methoden der Finiten Volumen- und Finiten Elementeverfahren. Sie ermöglichen hohe Approximationsordnungen, bieten einen hohen Grad an Flexibilität und sind für paralleles Rechnen gut geeignet. Diese Dissertation besteht aus acht Artikeln und einer erweiterten Zusammenfassung, in diesen die Anwendung unstetiger Galerkinverfahren auf mathematische Modelle inklusive solcher für Strömungen mit freier Oberfläche und im Grundwasserbereich beschrieben wird. Die behandelten Themen umfassen Diskretisierungs- und Implementierungsaspekte, die Parallelisierung der Methode sowie eine diskrete Stabilitätsanalyse des gekoppelten Modells

Accelerating The Discontinuous Galerkin Cell-Vertex Scheme (Dg-Cvs) Solver On Cpu-Gpu Heterogeneous Systems

Dg-Cvs (Discontinuous Galerkin Cell-Vertex Scheme) is an efficient, accurate and robust numerical solver for general hyperbolic conservation laws. It can solve a broad range of conservation laws such as the shallow water equation and Magnetohydrodynamics equations. Dg-Cvs is a Riemann-Solver-free high order space-time method for arbitrary space conservation laws. It fuses the discontinuous Galerkin (dg) method and the conservation element/solution element (ce/se) method to take advantage of the best features of both methods. Thanks to the ce/se method, the time derivative of the solution is treated as an independent unknown, which is amendable to gpu\u27s parallel execution. In this thesis, we use a cpu-gpu heterogeneous processor to accelerate Dg-Cvs to demonstrate that complex scientific applications can benefit from a heterogeneous computing system. There are challenges that such scientific program poses on the gpu architecture such as thread divergence and low kernel occupancy. We developed optimizations to address these concerns. Our proposed optimizations include thread remapping to minimize thread divergence and register pressure reduction to increase kernel occupancy. Our experiment results show that Dg-Cvs on gpu outperforms cpu by up to 57\% before optimization and 145\% afterwards. We also use Dg-Cvs as a real world application to explore the possibility of using shared virtual memory (svm) for tighter collaboration between cpu and gpu. However, svm did not help improve the performance due to the overhead of address translation and atomic operations. We developed a microbenchmark to better understand the performance impact of svm

Failure-awareness and dynamic adaptation in data scheduling

Over the years, scientific applications have become more complex and more data intensive. Especially large scale simulations and scientific experiments in areas such as physics, biology, astronomy and earth sciences demand highly distributed resources to satisfy excessive computational requirements. Increasing data requirements and the distributed nature of the resources made I/O the major bottleneck for end-to-end application performance. Existing systems fail to address issues such as reliability, scalability, and efficiency in dealing with wide area data access, retrieval and processing. In this study, we explore data-intensive distributed computing and study challenges in data placement in distributed environments. After analyzing different application scenarios, we develop new data scheduling methodologies and the key attributes for reliability, adaptability and performance optimization of distributed data placement tasks. Inspired by techniques used in microprocessor and operating system architectures, we extend and adapt some of the known low-level data handling and optimization techniques to distributed computing. Two major contributions of this work include (i) a failure-aware data placement paradigm for increased fault-tolerance, and (ii) adaptive scheduling of data placement tasks for improved end-to-end performance. The failure-aware data placement includes early error detection, error classification, and use of this information in scheduling decisions for the prevention of and recovery from possible future errors. The adaptive scheduling approach includes dynamically tuning data transfer parameters over wide area networks for efficient utilization of available network capacity and optimized end-to-end data transfer performance

A Simulation Suite for Lattice-Boltzmann based Real-Time CFD Applications Exploiting Multi-Level Parallelism on Modern Multi- and Many-Core Architectures

We present a software approach to hardware-oriented numerics which builds upon an augmented, previously published open-source set of libraries facilitating portable code development and optimisation on a wide range of modern computer architectures. In order to maximise eficiency, we exploit all levels of arallelism, including vectorisation within CPU cores, the Cell BE and GPUs, shared memory thread-level parallelism between cores, and parallelism between heterogeneous distributed memory resources in clusters. To evaluate and validate our approach, we implement a collection of modular building blocks for the easy and fast assembly and development of CFD applications based on the shallow water equations: We combine the Lattice-Boltzmann method with i-uid-structure interaction techniques in order to achieve real-time simulations targeting interactive virtual environments. Our results demonstrate that recent multi-core CPUs outperform the Cell BE, while GPUs are significantly faster than conventional multi-threaded SSE code. In addition, we verify good scalability properties of our application on small clusters

Efficient Algorithms for Coastal Geographic Problems

The increasing performance of computers has made it possible to solve algorithmically problems for which manual and possibly inaccurate methods have been previously used. Nevertheless, one must still pay attention to the performance of an algorithm if huge datasets are used or if the problem iscomputationally difficult. Two geographic problems are studied in the articles included in this thesis. In the first problem the goal is to determine distances from points, called study points, to shorelines in predefined directions. Together with other in-formation, mainly related to wind, these distances can be used to estimate wave exposure at different areas. In the second problem the input consists of a set of sites where water quality observations have been made and of the results of the measurements at the different sites. The goal is to select a subset of the observational sites in such a manner that water quality is still measured in a sufficient accuracy when monitoring at the other sites is stopped to reduce economic cost. Most of the thesis concentrates on the first problem, known as the fetch length problem. The main challenge is that the two-dimensional map is represented as a set of polygons with millions of vertices in total and the distances may also be computed for millions of study points in several directions. Efficient algorithms are developed for the problem, one of them approximate and the others exact except for rounding errors. The solutions also differ in that three of them are targeted for serial operation or for a small number of CPU cores whereas one, together with its further developments, is suitable also for parallel machines such as GPUs.Tietokoneiden suorituskyvyn kasvaminen on tehnyt mahdolliseksi ratkaista algoritmisesti ongelmia, joita on aiemmin tarkasteltu paljon ihmistyötä vaativilla, mahdollisesti epätarkoilla, menetelmillä. Algoritmien suorituskykyyn on kuitenkin toisinaan edelleen kiinnitettävä huomiota lähtömateriaalin suuren määrän tai ongelman laskennallisen vaikeuden takia. Väitöskirjaansisältyvissäartikkeleissatarkastellaankahtamaantieteellistä ongelmaa. Ensimmäisessä näistä on määritettävä etäisyyksiä merellä olevista pisteistä lähimpään rantaviivaan ennalta määrätyissä suunnissa. Etäisyyksiä ja tuulen voimakkuutta koskevien tietojen avulla on mahdollista arvioida esimerkiksi aallokon voimakkuutta. Toisessa ongelmista annettuna on joukko tarkkailuasemia ja niiltä aiemmin kerättyä tietoa erilaisista vedenlaatua kuvaavista parametreista kuten sameudesta ja ravinteiden määristä. Tehtävänä on valita asemajoukosta sellainen osa joukko, että vedenlaatua voidaan edelleen tarkkailla riittävällä tarkkuudella, kun mittausten tekeminen muilla havaintopaikoilla lopetetaan kustannusten säästämiseksi. Väitöskirja keskittyy pääosin ensimmäisen ongelman, suunnattujen etäisyyksien, ratkaisemiseen. Haasteena on se, että tarkasteltava kaksiulotteinen kartta kuvaa rantaviivan tyypillisesti miljoonista kärkipisteistä koostuvana joukkonapolygonejajaetäisyyksiäonlaskettavamiljoonilletarkastelupisteille kymmenissä eri suunnissa. Ongelmalle kehitetään tehokkaita ratkaisutapoja, joista yksi on likimääräinen, muut pyöristysvirheitä lukuun ottamatta tarkkoja. Ratkaisut eroavat toisistaan myös siinä, että kolme menetelmistä on suunniteltu ajettavaksi sarjamuotoisesti tai pienellä määrällä suoritinytimiä, kun taas yksi menetelmistä ja siihen tehdyt parannukset soveltuvat myös voimakkaasti rinnakkaisille laitteille kuten GPU:lle. Vedenlaatuongelmassa annetulla asemajoukolla on suuri määrä mahdollisia osajoukkoja. Lisäksi tehtävässä käytetään aikaa vaativia operaatioita kuten lineaarista regressiota, mikä entisestään rajoittaa sitä, kuinka monta osajoukkoa voidaan tutkia. Ratkaisussa käytetäänkin heuristiikkoja, jotkaeivät välttämättä tuota optimaalista lopputulosta.Siirretty Doriast

A Simulation Suite for Lattice-Boltzmann based Real-Time CFD Applications Exploiting Multi-Level Parallelism on Modern Multi- and Many-Core Architectures

We present a software approach to hardware-oriented numerics which builds upon an augmented, previously published open-source set of libraries facilitating portable code development and optimisation on a wide range of modern computer architectures. In order to maximise eficiency, we exploit all levels of arallelism, including vectorisation within CPU cores, the Cell BE and GPUs, shared memory thread-level parallelism between cores, and parallelism between heterogeneous distributed memory resources in clusters. To evaluate and validate our approach, we implement a collection of modular building blocks for the easy and fast assembly and development of CFD applications based on the shallow water equations: We combine the Lattice-Boltzmann method with i-uid-structure interaction techniques in order to achieve real-time simulations targeting interactive virtual environments. Our results demonstrate that recent multi-core CPUs outperform the Cell BE, while GPUs are significantly faster than conventional multi-threaded SSE code. In addition, we verify good scalability properties of our application on small clusters

RUNTIME METHODS TO IMPROVE ENERGY EFFICIENCY IN SUPERCOMPUTING APPLICATIONS

Energy efficiency in supercomputing is critical to limit operating costs and carbon footprints. While the energy efficiency of future supercomputing centers needs to improve at all levels, the energy consumed by the processing units is a large fraction of the total energy consumed by High Performance Computing (HPC) systems. HPC applications use a parallel programming paradigm like the Message Passing Interface (MPI) to coordinate computation and communication among thousands of processors. With dynamically-changing factors both in hardware and software affecting energy usage of processors, there exists a need for power monitoring and regulation at runtime to achieve savings in energy. This dissertation highlights an adaptive runtime framework that enables processors with core-specific power control by dynamically adapting to workload characteristics to reduce power with little or no performance impact. Two opportunities to improve the energy efficiency of processors running MPI applications are identified - computational workload imbalance and waiting on memory. Monitoring of performance and power regulation is performed by the framework transparently within the MPI runtime system, eliminating the need for code changes to MPI applications. The effect of enforcing power limits (capping) on processors is also investigated. Experiments on 32 nodes (1024 cores) show that in presence of workload imbalance, the runtime reduces Central Processing Unit (CPU) frequency on cores not on the critical path, thereby reducing power and hence energy usage without deteriorating performance. Using this runtime, six MPI mini-applications and a full MPI application show an overall 20% decrease in energy use with less than 1% increase in execution time. In addition, the lowering of frequency on non-critical cores reduces run-to-run performance variation and improves performance. For the full application, an average speedup of 11% is seen, while the power is lowered by about 31% for an energy savings of up to 42%. Another experiment on 16 nodes (256 cores) that are power capped also shows performance improvement along with power reduction. Thus, energy optimization can also be a performance optimization. For applications that are limited by memory access times, memory metrics identified facilitate lowering of power by up to 32% without adversely impacting performance.Doctor of Philosoph

Summary of Research 1994

The views expressed in this report are those of the authors and do not reflect the official policy or position of the Department of Defense or the U.S. Government.This report contains 359 summaries of research projects which were carried out under funding of the Naval Postgraduate School Research Program. A list of recent publications is also included which consists of conference presentations and publications, books, contributions to books, published journal papers, and technical reports. The research was conducted in the areas of Aeronautics and Astronautics, Computer Science, Electrical and Computer Engineering, Mathematics, Mechanical Engineering, Meteorology, National Security Affairs, Oceanography, Operations Research, Physics, and Systems Management. This also includes research by the Command, Control and Communications (C3) Academic Group, Electronic Warfare Academic Group, Space Systems Academic Group, and the Undersea Warfare Academic Group

Journal of Telecommunications and Information Technology, nr 4

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