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

Optimización del rendimiento y la eficiencia energética en sistemas masivamente paralelos

RESUMEN Los sistemas heterogéneos son cada vez más relevantes, debido a sus capacidades de rendimiento y eficiencia energética, estando presentes en todo tipo de plataformas de cómputo, desde dispositivos embebidos y servidores, hasta nodos HPC de grandes centros de datos. Su complejidad hace que sean habitualmente usados bajo el paradigma de tareas y el modelo de programación host-device. Esto penaliza fuertemente el aprovechamiento de los aceleradores y el consumo energético del sistema, además de dificultar la adaptación de las aplicaciones. La co-ejecución permite que todos los dispositivos cooperen para computar el mismo problema, consumiendo menos tiempo y energía. No obstante, los programadores deben encargarse de toda la gestión de los dispositivos, la distribución de la carga y la portabilidad del código entre sistemas, complicando notablemente su programación. Esta tesis ofrece contribuciones para mejorar el rendimiento y la eficiencia energética en estos sistemas masivamente paralelos. Se realizan propuestas que abordan objetivos generalmente contrapuestos: se mejora la usabilidad y la programabilidad, a la vez que se garantiza una mayor abstracción y extensibilidad del sistema, y al mismo tiempo se aumenta el rendimiento, la escalabilidad y la eficiencia energética. Para ello, se proponen dos motores de ejecución con enfoques completamente distintos. EngineCL, centrado en OpenCL y con una API de alto nivel, favorece la máxima compatibilidad entre todo tipo de dispositivos y proporciona un sistema modular extensible. Su versatilidad permite adaptarlo a entornos para los que no fue concebido, como aplicaciones con ejecuciones restringidas por tiempo o simuladores HPC de dinámica molecular, como el utilizado en un centro de investigación internacional. Considerando las tendencias industriales y enfatizando la aplicabilidad profesional, CoexecutorRuntime proporciona un sistema flexible centrado en C++/SYCL que dota de soporte a la co-ejecución a la tecnología oneAPI. Este runtime acerca a los programadores al dominio del problema, posibilitando la explotación de estrategias dinámicas adaptativas que mejoran la eficiencia en todo tipo de aplicaciones.ABSTRACT Heterogeneous systems are becoming increasingly relevant, due to their performance and energy efficiency capabilities, being present in all types of computing platforms, from embedded devices and servers to HPC nodes in large data centers. Their complexity implies that they are usually used under the task paradigm and the host-device programming model. This strongly penalizes accelerator utilization and system energy consumption, as well as making it difficult to adapt applications. Co-execution allows all devices to simultaneously compute the same problem, cooperating to consume less time and energy. However, programmers must handle all device management, workload distribution and code portability between systems, significantly complicating their programming. This thesis offers contributions to improve performance and energy efficiency in these massively parallel systems. The proposals address the following generally conflicting objectives: usability and programmability are improved, while ensuring enhanced system abstraction and extensibility, and at the same time performance, scalability and energy efficiency are increased. To achieve this, two runtime systems with completely different approaches are proposed. EngineCL, focused on OpenCL and with a high-level API, provides an extensible modular system and favors maximum compatibility between all types of devices. Its versatility allows it to be adapted to environments for which it was not originally designed, including applications with time-constrained executions or molecular dynamics HPC simulators, such as the one used in an international research center. Considering industrial trends and emphasizing professional applicability, CoexecutorRuntime provides a flexible C++/SYCL-based system that provides co-execution support for oneAPI technology. This runtime brings programmers closer to the problem domain, enabling the exploitation of dynamic adaptive strategies that improve efficiency in all types of applications.Funding: This PhD has been supported by the Spanish Ministry of Education (FPU16/03299 grant), the Spanish Science and Technology Commission under contracts TIN2016-76635-C2-2-R and PID2019-105660RB-C22. This work has also been partially supported by the Mont-Blanc 3: European Scalable and Power Efficient HPC Platform based on Low-Power Embedded Technology project (G.A. No. 671697) from the European Union’s Horizon 2020 Research and Innovation Programme (H2020 Programme). Some activities have also been funded by the Spanish Science and Technology Commission under contract TIN2016-81840-REDT (CAPAP-H6 network). The Integration II: Hybrid programming models of Chapter 4 has been partially performed under the Project HPC-EUROPA3 (INFRAIA-2016-1-730897), with the support of the EC Research Innovation Action under the H2020 Programme. In particular, the author gratefully acknowledges the support of the SPMT Department of the High Performance Computing Center Stuttgart (HLRS)

Interactive High Performance Volume Rendering

This thesis is about Direct Volume Rendering on high performance computing systems. As direct rendering methods do not create a lower-dimensional geometric representation, the whole scientific dataset must be kept in memory. Thus, this family of algorithms has a tremendous resource demand. Direct Volume Rendering algorithms in general are well suited to be implemented for dedicated graphics hardware. Nevertheless, high performance computing systems often do not provide resources for hardware accelerated rendering, so that the visualization algorithm must be implemented for the available general-purpose hardware. Ever growing datasets that imply copying large amounts of data from the compute system to the workstation of the scientist, and the need to review intermediate simulation results, make porting Direct Volume Rendering to high performance computing systems highly relevant. The contribution of this thesis is twofold. As part of the first contribution, after devising a software architecture for general implementations of Direct Volume Rendering on highly parallel platforms, parallelization issues and implementation details for various modern architectures are discussed. The contribution results in a highly parallel implementation that tackles several platforms. The second contribution is concerned with the display phase of the “Distributed Volume Rendering Pipeline”. Rendering on a high performance computing system typically implies displaying the rendered result at a remote location. This thesis presents a remote rendering technique that is capable of hiding latency and can thus be used in an interactive environment

格子ボルツマン法による高効率な津波数値解析手法の開発

Tohoku University越村俊一課