Parallel harmonic balance method for analysis of nonlinear mechanical systems

Mechanical vibration analysis and modelling are essential tools used in the design of various mechanical components and structures. In the case of turbine engine design specifically, the ability to accurately predict vibration of various parts is crucial to ensure their safe operation while maintaining efficiency. As the designs become increasingly complex and margins for errors get smaller, high fidelity numerical vibration models are necessary for their analysis. Research of parallel algorithms has progressed significantly in the last decades, thanks to the exponential growth of the world's available computational resources. This work explores the possibilities for parallel implementations for solving large scale nonlinear vibration problems. A C++ code using MPI was developed to validate these implementations in practice. The harmonic balance method is used in combination with finite elements discretisation and applied to an elastic body with the Green-Lagrange nonlinear model for large deformations. A parameter continuation scheme using a predictor-corrector approach is included to compute frequency response functions. A Newton-Raphson solver is used to solve the bordered nonlinear system of equations in the frequency domain. Three different parallel algorithms for solving the linearised problem in each Newton iteration are analysed - a sparse direct solver (using MUMPS library), GMRES (using PETSc library) and an inhouse implementation of FETI. The performance of the solvers is analysed using beam testcases and a fan blade geometry. Scalability of MUMPS and the FETI solver is assessed. Full nonlinear frequency response functions with turning points are also computed. Use of artificial coarse space and preconditioning in FETI is discussed as it greatly impacts convergence properties of the solver. The presented parallel linear solvers show promising scalability results and an ability to solve nonlinear systems of several million degrees of freedom.Open Acces

Evaluation of GPU Acceleration for WRF–SFIRE

WRF–SFIRE is an open source, atmospheric–wildfire model that couples the WRF model with the level set fire spread model to simulate wildfires in real time. This model has many applications and more scientific questions can be asked and answered if the model can be run faster. Nvidia has put a lot of effort into easing the barrier of entry for accelerating applications with their tools to be run on GPUs. Various physical simulations have been successfully ported to utilize GPUs and have benefited from the speed increase. In this research, we take a look at WRF-SFIRE and try to use the Nvida tools to accelerate portions of code. We were successful in offloading work to the GPU. However, the WRF-SFIRE codebase contains too many data dependencies, deeply nested function calls and I/O to effectively utilize the GPU’s resources. We look at specific examples and try to run them on a Titan V GPU. In the end, the compute intensive portions of WRF-SFIRE need to be rewritten to avoid data dependencies in order to leverage GPUs to improve the execution time

Automatic synthesis and optimization of chip multiprocessors

The microprocessor technology has experienced an enormous growth during the last decades. Rapid downscale of the CMOS technology has led to higher operating frequencies and performance densities, facing the fundamental issue of power dissipation. Chip Multiprocessors (CMPs) have become the latest paradigm to improve the power-performance efficiency of computing systems by exploiting the parallelism inherent in applications. Industrial and prototype implementations have already demonstrated the benefits achieved by CMPs with hundreds of cores.CMP architects are challenged to take many complex design decisions. Only a few of them are:- What should be the ratio between the core and cache areas on a chip?- Which core architectures to select?- How many cache levels should the memory subsystem have?- Which interconnect topologies provide efficient on-chip communication?These and many other aspects create a complex multidimensional space for architectural exploration. Design Automation tools become essential to make the architectural exploration feasible under the hard time-to-market constraints. The exploration methods have to be efficient and scalable to handle future generation on-chip architectures with hundreds or thousands of cores.Furthermore, once a CMP has been fabricated, the need for efficient deployment of the many-core processor arises. Intelligent techniques for task mapping and scheduling onto CMPs are necessary to guarantee the full usage of the benefits brought by the many-core technology. These techniques have to consider the peculiarities of the modern architectures, such as availability of enhanced power saving techniques and presence of complex memory hierarchies.This thesis has several objectives. The first objective is to elaborate the methods for efficient analytical modeling and architectural design space exploration of CMPs. The efficiency is achieved by using analytical models instead of simulation, and replacing the exhaustive exploration with an intelligent search strategy. Additionally, these methods incorporate high-level models for physical planning. The related contributions are described in Chapters 3, 4 and 5 of the document.The second objective of this work is to propose a scalable task mapping algorithm onto general-purpose CMPs with power management techniques, for efficient deployment of many-core systems. This contribution is explained in Chapter 6 of this document.Finally, the third objective of this thesis is to address the issues of the on-chip interconnect design and exploration, by developing a model for simultaneous topology customization and deadlock-free routing in Networks-on-Chip. The developed methodology can be applied to various classes of the on-chip systems, ranging from general-purpose chip multiprocessors to application-specific solutions. Chapter 7 describes the proposed model.The presented methods have been thoroughly tested experimentally and the results are described in this dissertation. At the end of the document several possible directions for the future research are proposed

CPU accounting in multi-threaded processors

In recent years, multi-threaded processors have become more and more popular in industry in order to increase the system aggregated performance and per-application performance, overcoming the limitations imposed by the limited instruction-level parallelism, and by power and thermal constraints. Multi-threaded processors are widely used in servers, desktop computers, lap-tops, and mobile devices. However, multi-threaded processors introduce complexities when accounting CPU (computation) capacity (CPU accounting), since the CPU capacity accounted to an application not only depends upon the time that the application is scheduled onto a CPU, but also on the amount of hardware resources it receives during that period. And given that in a multi-threaded processor hardware resources are dynamically shared between applications, the CPU capacity accounted to an application in a multi-threaded processor depends upon the workload in which it executes. This is inconvenient because the CPU accounting of the same application with the same input data set may be accounted significantly different depending upon the workload in which it executes. Deploying systems with accurate CPU accounting mechanisms is necessary to increase fairness among running applications. Moreover, it will allow users to be fairly charged on a shared data center, facilitating server consolidation in future systems. This Thesis analyses the concepts of CPU capacity and CPU accounting for multi-threaded processors. In this study, we demonstrate that current CPU accounting mechanisms are not as accurate as they should be in multi-threaded processors. For this reason, we present two novel CPU accounting mechanisms that improve the accuracy in measuring the CPU capacity for multi-threaded processors with low hardware overhead. We focus our attention on several current multi-threaded processors, including chip multiprocessors and simultaneous multithreading processors. Finally, we analyse the impact of shared resources in multi-threaded processors in operating system CPU scheduler and we propose several schedulers that improve the knowledge of shared hardware resources at the software level

Fast simulation techniques for microprocessor design space exploration

Designing a microprocessor is extremely time-consuming. Computer architects heavily rely on architectural simulators, e.g., to drive high-level design decisions during early stage design space exploration. The benefit of architectural simulators is that they yield relatively accurate performance results, are highly parameterizable and are very flexible to use. The downside, however, is that they are at least three or four orders of magnitude slower than real hardware execution. The current trend towards multicore processors exacerbates the problem; as the number of cores on a multicore processor increases, simulation speed has become a major concern in computer architecture research and development. In this dissertation, we propose and evaluate two simulation techniques that reduce the simulation time significantly: statistical simulation and interval simulation. Statistical simulation speeds up the simulation by reducing the number of dynamically executed instructions. First, we collect a number of program execution characteristics into a statistical profile. From this profile we can generate a synthetic trace that exhibits the same execution behavior but which has a much shorter trace length as compared to the original trace. Simulating this synthetic trace then yields a performance estimate. Interval simulation raises the level of abstraction in architectural simulation; it replaces the core-level cycle-accurate simulation model by a mechanistic analytical model. The analytical model builds on insights from interval analysis: miss events divide the smooth streaming of instructions into so called intervals. The model drives the timing by analyzing the type of the miss events and their latencies, instead of tracking the individual instructions as they propagate through the pipeline stages

GPRM: a high performance programming framework for manycore processors

Processors with large numbers of cores are becoming commonplace. In order to utilise the available resources in such systems, the programming paradigm has to move towards increased parallelism. However, increased parallelism does not necessarily lead to better performance. Parallel programming models have to provide not only flexible ways of defining parallel tasks, but also efficient methods to manage the created tasks. Moreover, in a general-purpose system, applications residing in the system compete for the shared resources. Thread and task scheduling in such a multiprogrammed multithreaded environment is a significant challenge. In this thesis, we introduce a new task-based parallel reduction model, called the Glasgow Parallel Reduction Machine (GPRM). Our main objective is to provide high performance while maintaining ease of programming. GPRM supports native parallelism; it provides a modular way of expressing parallel tasks and the communication patterns between them. Compiling a GPRM program results in an Intermediate Representation (IR) containing useful information about tasks, their dependencies, as well as the initial mapping information. This compile-time information helps reduce the overhead of runtime task scheduling and is key to high performance. Generally speaking, the granularity and the number of tasks are major factors in achieving high performance. These factors are even more important in the case of GPRM, as it is highly dependent on tasks, rather than threads. We use three basic benchmarks to provide a detailed comparison of GPRM with Intel OpenMP, Cilk Plus, and Threading Building Blocks (TBB) on the Intel Xeon Phi, and with GNU OpenMP on the Tilera TILEPro64. GPRM shows superior performance in almost all cases, only by controlling the number of tasks. GPRM also provides a low-overhead mechanism, called “Global Sharing”, which improves performance in multiprogramming situations. We use OpenMP, as the most popular model for shared-memory parallel programming as the main GPRM competitor for solving three well-known problems on both platforms: LU factorisation of Sparse Matrices, Image Convolution, and Linked List Processing. We focus on proposing solutions that best fit into the GPRM’s model of execution. GPRM outperforms OpenMP in all cases on the TILEPro64. On the Xeon Phi, our solution for the LU Factorisation results in notable performance improvement for sparse matrices with large numbers of small blocks. We investigate the overhead of GPRM’s task creation and distribution for very short computations using the Image Convolution benchmark. We show that this overhead can be mitigated by combining smaller tasks into larger ones. As a result, GPRM can outperform OpenMP for convolving large 2D matrices on the Xeon Phi. Finally, we demonstrate that our parallel worksharing construct provides an efficient solution for Linked List processing and performs better than OpenMP implementations on the Xeon Phi. The results are very promising, as they verify that our parallel programming framework for manycore processors is flexible and scalable, and can provide high performance without sacrificing productivity

Per-task energy metering and accounting in the multicore era

Chip multi-core processors (CMPs) are the preferred processing platform across different domains such as data centers, real-time systems and mobile devices. In all those domains, energy is arguably the most expensive resource in a computing system, in particular, with fastest growth. Therefore, measuring the energy usage draws vast attention. Current studies mostly focus on obtaining finer-granularity energy measurement, such as measuring power in smaller time intervals, distributing energy to hardware components or software components. Such studies focus on scenarios where system energy is measured under the assumption that only one program is running in the system. So far, there is no hardware-level mechanism proposed to distribute the system energy to multiple running programs in a resource sharing multi-core system in an exact way. For the first time, we have formalized the need for per-task energy measurement in multicore by establishing a two-fold concept: Per-Task Energy Metering (PTEM) and Sensible Energy Accounting (SEA). In the scenario where many tasks running in parallel in a multicore system: For each task, the target of PTEM is to provide estimate of the actual energy consumption at runtime based on its resource usage during execution; and SEA aims at providing estimates on the energy it would have consumed when running in isolation with a particular fraction of system's resources. Accurately determining the energy consumed by each task in a system will become of prominent importance in future multi-core based systems as it offers several benefits including (i) Selection of appropriate co-runners, (ii) improved energy-aware task scheduling and (iii) energy-aware billing in data centers. We have shown how these two concepts can be applied to the main components of a computing system: the processor and the memory system. At first, we have applied PTEM to the processor by means of tracking the activities and occupancy of all the resources in a per-task basis. Secondly, we have applied PTEM to the memory system by means of tracking the activities and the state switches of memory banks. Then, we have applied SEA to the processor by predicting the activities and execution time for each task when they run with an fraction of chip resources alone. And last, we apply SEA to the memory system, by means of predicting activities, execution time and the time invoking memory system for each task. As for all these works, by trading-off the hardware cost with the estimation accuracy, we have obtained the implementable and affordable cost mechanisms with high accuracy. We have also shown how these techniques can be applied in different scenarios, such as, to detect significant energy usage variations for any particular task and to develop more energy efficient scheduling policy for the multi-core system. These works in this thesis have been published into IEEE/ACM journals and conferences proceedings that can be found in the publication chapter of this thesis.Los "Chip Multi-core Processors" (CMPs) son la plataforma de procesado preferida en diferentes dominios, tales como los centros de datos, sistemas de tiempo real y dispositivos móviles. En todos estos dominios, la energía puede ser el recurso más caro en el sistema de computación, concretamente, lo rápido que está creciendo. Por lo tanto, como medir el consumo energético está ganando mucha atención. Los estudios actuales se centran mayormente en cómo obtener medidas muy detalladas (finer granularity). Por ejemplo, tomar medidas de potencia en pequeños intervalos de tiempo, usando medidores de energía hardware o software. Estos estudios se centran en escenarios donde el consumo del sistema se mide bajo la suposición de que solo un programa se está ejecutando en el sistema. Aun no hay ninguna propuesta de un mecanismo a nivel de hardware para medir el consumo entre múltiples programas ejecutándose a la vez en un sistema multi-core con recursos compartidos. Por primera vez, hemos formalizado la necesidad de medir el consumo energético por-tarea en un multi-core estableciendo un concepto dual: Per-Taks Energy Metering (PTEM) y Sensible Energy Accounting (SEA). En un escenario donde varias tareas se ejecutan en paralelo en un sistema multi-core, por cada tarea, el objetivo de PTEM es estimar el consumo real energético durante tiempo de ejecución basándose en los recursos usados durante la ejecución, y SEA trata de proveer una estimación del consumo que tendría en solitario con solo una fracción concreta de los recursos del sistema. Determinar el consumo energético con precisión para cada tarea en un sistema tomara gran importancia en el futuro de los sistemas basados en multi-cores, ya que ofrecen varias ventajas tales como: (i) determinar los co-runners apropiados, (ii) mejorar la planificación de tareas teniendo en cuenta su consumo y (iii) facturación de los servicios de los data centers basada en el consumo. Hemos mostrado como estos dos conceptos pueden aplicarse a los principales componentes de un sistema de computación: el procesador y el sistema de memoria. Para empezar, hemos aplicado PTEM al procesador para registrar la actividad y la ocupación de todos los recursos por cada tarea. Luego, hemos aplicado SEA al procesador prediciendo la actividad y tiempo de ejecución por tarea cuando se ejecutan con solo una parte de los recursos del chip. Por último, hemos aplicado SEA al sistema de memoria para predecir la activada, el tiempo ejecución y cuando el sistema de memoria es invocado por cada tarea. Con todo ello, hemos alcanzado un compromiso entre el coste del hardware y la precisión en las estimaciones para obtener mecanismos implementables con un coste aceptable y una alta precisión. Durante nuestros estudios mostramos como esas técnicas pueden ser aplicadas a diferente escenarios, tales como: detectar variaciones significativas en el consumo energético por una tarea en concreto o como desarrollar políticas de planificación energéticamente más eficientes para sistemas multi-core. Los trabajos que hemos publicado durante el desarrollo de esta tesis en los IEEE/ACM journals y en varias conferencias pueden encontrarse en el capítulo de "publicaciones" de este documentoPostprint (published version

Dense and sparse parallel linear algebra algorithms on graphics processing units

Una línea de desarrollo seguida en el campo de la supercomputación es el uso de procesadores de propósito específico para acelerar determinados tipos de cálculo. En esta tesis estudiamos el uso de tarjetas gráficas como aceleradores de la computación y lo aplicamos al ámbito del álgebra lineal. En particular trabajamos con la biblioteca SLEPc para resolver problemas de cálculo de autovalores en matrices de gran dimensión, y para aplicar funciones de matrices en los cálculos de aplicaciones científicas. SLEPc es una biblioteca paralela que se basa en el estándar MPI y está desarrollada con la premisa de ser escalable, esto es, de permitir resolver problemas más grandes al aumentar las unidades de procesado. El problema lineal de autovalores, Ax = lambda x en su forma estándar, lo abordamos con el uso de técnicas iterativas, en concreto con métodos de Krylov, con los que calculamos una pequeña porción del espectro de autovalores. Este tipo de algoritmos se basa en generar un subespacio de tamaño reducido (m) en el que proyectar el problema de gran dimensión (n), siendo m << n. Una vez se ha proyectado el problema, se resuelve este mediante métodos directos, que nos proporcionan aproximaciones a los autovalores del problema inicial que queríamos resolver. Las operaciones que se utilizan en la expansión del subespacio varían en función de si los autovalores deseados están en el exterior o en el interior del espectro. En caso de buscar autovalores en el exterior del espectro, la expansión se hace mediante multiplicaciones matriz-vector. Esta operación la realizamos en la GPU, bien mediante el uso de bibliotecas o mediante la creación de funciones que aprovechan la estructura de la matriz. En caso de autovalores en el interior del espectro, la expansión requiere resolver sistemas de ecuaciones lineales. En esta tesis implementamos varios algoritmos para la resolución de sistemas de ecuaciones lineales para el caso específico de matrices con estructura tridiagonal a bloques, que se ejecutan en GPU. En el cálculo de las funciones de matrices hemos de diferenciar entre la aplicación directa de una función sobre una matriz, f(A), y la aplicación de la acción de una función de matriz sobre un vector, f(A)b. El primer caso implica un cálculo denso que limita el tamaño del problema. El segundo permite trabajar con matrices dispersas grandes, y para resolverlo también hacemos uso de métodos de Krylov. La expansión del subespacio se hace mediante multiplicaciones matriz-vector, y hacemos uso de GPUs de la misma forma que al resolver autovalores. En este caso el problema proyectado comienza siendo de tamaño m, pero se incrementa en m en cada reinicio del método. La resolución del problema proyectado se hace aplicando una función de matriz de forma directa. Nosotros hemos implementado varios algoritmos para calcular las funciones de matrices raíz cuadrada y exponencial, en las que el uso de GPUs permite acelerar el cálculo.One line of development followed in the field of supercomputing is the use of specific purpose processors to speed up certain types of computations. In this thesis we study the use of graphics processing units as computer accelerators and apply it to the field of linear algebra. In particular, we work with the SLEPc library to solve large scale eigenvalue problems, and to apply matrix functions in scientific applications. SLEPc is a parallel library based on the MPI standard and is developed with the premise of being scalable, i.e. to allow solving larger problems by increasing the processing units. We address the linear eigenvalue problem, Ax = lambda x in its standard form, using iterative techniques, in particular with Krylov's methods, with which we calculate a small portion of the eigenvalue spectrum. This type of algorithms is based on generating a subspace of reduced size (m) in which to project the large dimension problem (n), being m << n. Once the problem has been projected, it is solved by direct methods, which provide us with approximations of the eigenvalues of the initial problem we wanted to solve. The operations used in the expansion of the subspace vary depending on whether the desired eigenvalues are from the exterior or from the interior of the spectrum. In the case of searching for exterior eigenvalues, the expansion is done by matrix-vector multiplications. We do this on the GPU, either by using libraries or by creating functions that take advantage of the structure of the matrix. In the case of eigenvalues from the interior of the spectrum, the expansion requires solving linear systems of equations. In this thesis we implemented several algorithms to solve linear systems of equations for the specific case of matrices with a block-tridiagonal structure, that are run on GPU. In the computation of matrix functions we have to distinguish between the direct application of a matrix function, f(A), and the action of a matrix function on a vector, f(A)b. The first case involves a dense computation that limits the size of the problem. The second allows us to work with large sparse matrices, and to solve it we also make use of Krylov's methods. The expansion of subspace is done by matrix-vector multiplication, and we use GPUs in the same way as when solving eigenvalues. In this case the projected problem starts being of size m, but it is increased by m on each restart of the method. The solution of the projected problem is done by directly applying a matrix function. We have implemented several algorithms to compute the square root and the exponential matrix functions, in which the use of GPUs allows us to speed up the computation.Una línia de desenvolupament seguida en el camp de la supercomputació és l'ús de processadors de propòsit específic per a accelerar determinats tipus de càlcul. En aquesta tesi estudiem l'ús de targetes gràfiques com a acceleradors de la computació i ho apliquem a l'àmbit de l'àlgebra lineal. En particular treballem amb la biblioteca SLEPc per a resoldre problemes de càlcul d'autovalors en matrius de gran dimensió, i per a aplicar funcions de matrius en els càlculs d'aplicacions científiques. SLEPc és una biblioteca paral·lela que es basa en l'estàndard MPI i està desenvolupada amb la premissa de ser escalable, açò és, de permetre resoldre problemes més grans en augmentar les unitats de processament. El problema lineal d'autovalors, Ax = lambda x en la seua forma estàndard, ho abordem amb l'ús de tècniques iteratives, en concret amb mètodes de Krylov, amb els quals calculem una xicoteta porció de l'espectre d'autovalors. Aquest tipus d'algorismes es basa a generar un subespai de grandària reduïda (m) en el qual projectar el problema de gran dimensió (n), sent m << n. Una vegada s'ha projectat el problema, es resol aquest mitjançant mètodes directes, que ens proporcionen aproximacions als autovalors del problema inicial que volíem resoldre. Les operacions que s'utilitzen en l'expansió del subespai varien en funció de si els autovalors desitjats estan en l'exterior o a l'interior de l'espectre. En cas de cercar autovalors en l'exterior de l'espectre, l'expansió es fa mitjançant multiplicacions matriu-vector. Aquesta operació la realitzem en la GPU, bé mitjançant l'ús de biblioteques o mitjançant la creació de funcions que aprofiten l'estructura de la matriu. En cas d'autovalors a l'interior de l'espectre, l'expansió requereix resoldre sistemes d'equacions lineals. En aquesta tesi implementem diversos algorismes per a la resolució de sistemes d'equacions lineals per al cas específic de matrius amb estructura tridiagonal a blocs, que s'executen en GPU. En el càlcul de les funcions de matrius hem de diferenciar entre l'aplicació directa d'una funció sobre una matriu, f(A), i l'aplicació de l'acció d'una funció de matriu sobre un vector, f(A)b. El primer cas implica un càlcul dens que limita la grandària del problema. El segon permet treballar amb matrius disperses grans, i per a resoldre-ho també fem ús de mètodes de Krylov. L'expansió del subespai es fa mitjançant multiplicacions matriu-vector, i fem ús de GPUs de la mateixa forma que en resoldre autovalors. En aquest cas el problema projectat comença sent de grandària m, però s'incrementa en m en cada reinici del mètode. La resolució del problema projectat es fa aplicant una funció de matriu de forma directa. Nosaltres hem implementat diversos algorismes per a calcular les funcions de matrius arrel quadrada i exponencial, en les quals l'ús de GPUs permet accelerar el càlcul.Lamas Daviña, A. (2018). Dense and sparse parallel linear algebra algorithms on graphics processing units [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/112425TESI

Algorithms for massively parallel generic hp-adaptive finite element methods

Efficient algorithms for the numerical solution of partial differential equations are required to solve problems on an economically viable timescale. In general, this is achieved by adapting the resolution of the discretization to the investigated problem, as well as exploiting hardware specifications. For the latter category, parallelization plays a major role for modern multi-core and multi-node architectures, especially in the context of high-performance computing. Using finite element methods, solutions are approximated by discretizing the function space of the problem with piecewise polynomials. With hp-adaptive methods, the polynomial degrees of these basis functions may vary on locally refined meshes. We present algorithms and data structures required for generic hp-adaptive finite element software applicable for both continuous and discontinuous Galerkin methods on distributed memory systems. Both function space and mesh may be adapted dynamically during the solution process. We cover details concerning the unique enumeration of degrees of freedom with continuous Galerkin methods, the communication of variable size data, and load balancing. Furthermore, we present strategies to determine the type of adaptation based on error estimation and prediction as well as smoothness estimation via the decay rate of coefficients of Fourier and Legendre series expansions. Both refinement and coarsening are considered. A reference implementation in the open-source library deal.II is provided and applied to the Laplace problem on a domain with a reentrant corner which invokes a singularity. With this example, we demonstrate the benefits of the hp-adaptive methods in terms of error convergence and show that our algorithm scales up to 49,152 MPI processes.Für die numerische Lösung partieller Differentialgleichungen sind effiziente Algorithmen erforderlich, um Probleme auf einer wirtschaftlich tragbaren Zeitskala zu lösen. Im Allgemeinen ist dies durch die Anpassung der Diskretisierungsauflösung an das untersuchte Problem sowie durch die Ausnutzung der Hardwarespezifikationen möglich. Für die letztere Kategorie spielt die Parallelisierung eine große Rolle für moderne Mehrkern- und Mehrknotenarchitekturen, insbesondere im Kontext des Hochleistungsrechnens. Mit Hilfe von Finite-Elemente-Methoden werden Lösungen durch Diskretisierung des assoziierten Funktionsraums mit stückweisen Polynomen approximiert. Bei hp-adaptiven Verfahren können die Polynomgrade dieser Basisfunktionen auf lokal verfeinerten Gittern variieren. In dieser Dissertation werden Algorithmen und Datenstrukturen vorgestellt, die für generische hp-adaptive Finite-Elemente-Software benötigt werden und sowohl für kontinuierliche als auch diskontinuierliche Galerkin-Verfahren auf Systemen mit verteiltem Speicher anwendbar sind. Sowohl der Funktionsraum als auch das Gitter können während des Lösungsprozesses dynamisch angepasst werden. Im Besonderen erläutert werden die eindeutige Nummerierung von Freiheitsgraden mit kontinuierlichen Galerkin-Verfahren, die Kommunikation von Daten variabler Größe und die Lastenverteilung. Außerdem werden Strategien zur Bestimmung des Adaptierungstyps auf der Grundlage von Fehlerschätzungen und -prognosen sowie Glattheitsschätzungen vorgestellt, die über die Zerfallsrate von Koeffizienten aus Reihenentwicklungen nach Fourier und Legendre bestimmt werden. Dabei werden sowohl Verfeinerung als auch Vergröberung berücksichtigt. Eine Referenzimplementierung erfolgt in der Open-Source-Bibliothek deal.II und wird auf das Laplace-Problem auf einem Gebiet mit einer einschneidenden Ecke angewandt, die eine Singularität aufweist. Anhand dieses Beispiels werden die Vorteile der hp-adaptiven Methoden hinsichtlich der Fehlerkonvergenz und die Skalierbarkeit der präsentierten Algorithmen auf bis zu 49.152 MPI-Prozessen demonstriert

HPCCP/CAS Workshop Proceedings 1998

This publication is a collection of extended abstracts of presentations given at the HPCCP/CAS (High Performance Computing and Communications Program/Computational Aerosciences Project) Workshop held on August 24-26, 1998, at NASA Ames Research Center, Moffett Field, California. The objective of the Workshop was to bring together the aerospace high performance computing community, consisting of airframe and propulsion companies, independent software vendors, university researchers, and government scientists and engineers. The Workshop was sponsored by the HPCCP Office at NASA Ames Research Center. The Workshop consisted of over 40 presentations, including an overview of NASA's High Performance Computing and Communications Program and the Computational Aerosciences Project; ten sessions of papers representative of the high performance computing research conducted within the Program by the aerospace industry, academia, NASA, and other government laboratories; two panel sessions; and a special presentation by Mr. James Bailey