13 research outputs found

    Proceedings of the First PhD Symposium on Sustainable Ultrascale Computing Systems (NESUS PhD 2016)

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    Proceedings of the First PhD Symposium on Sustainable Ultrascale Computing Systems (NESUS PhD 2016) Timisoara, Romania. February 8-11, 2016.The PhD Symposium was a very good opportunity for the young researchers to share information and knowledge, to present their current research, and to discuss topics with other students in order to look for synergies and common research topics. The idea was very successful and the assessment made by the PhD Student was very good. It also helped to achieve one of the major goals of the NESUS Action: to establish an open European research network targeting sustainable solutions for ultrascale computing aiming at cross fertilization among HPC, large scale distributed systems, and big data management, training, contributing to glue disparate researchers working across different areas and provide a meeting ground for researchers in these separate areas to exchange ideas, to identify synergies, and to pursue common activities in research topics such as sustainable software solutions (applications and system software stack), data management, energy efficiency, and resilience.European Cooperation in Science and Technology. COS

    Sur la conception de solveurs linéaires hybrides pour les architectures parallèles modernes

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    In the context of this thesis, our focus is on numerical linear algebra, more precisely on solution of large sparse systems of linear equations. We focus on designing efficient parallel implementations of MaPHyS, an hybrid linear solver based on domain decomposition techniques. First we investigate the MPI+threads approach. In MaPHyS, the first level of parallelism arises from the independent treatment of the various subdomains. The second level is exploited thanks to the use of multi-threaded dense and sparse linear algebra kernels involved at the subdomain level. Such an hybrid implementation of an hybrid linear solver suitably matches the hierarchical structure of modern supercomputers and enables a trade-off between the numerical and parallel performances of the solver. We demonstrate the flexibility of our parallel implementation on a set of test examples. Secondly, we follow a more disruptive approach where the algorithms are described as sets of tasks with data inter-dependencies that leads to a directed acyclic graph (DAG) representation. The tasks are handled by a runtime system. We illustrate how a first task-based parallel implementation can be obtained by composing task-based parallel libraries within MPI processes throught a preliminary prototype implementation of our hybrid solver. We then show how a task-based approach fully abstracting the hardware architecture can successfully exploit a wide range of modern hardware architectures. We implemented a full task-based Conjugate Gradient algorithm and showed that the proposed approach leads to very high performance on multi-GPU, multicore and heterogeneous architectures.Dans le contexte de cette thèse, nous nous focalisons sur des algorithmes pour l’algèbre linéaire numérique, plus précisément sur la résolution de grands systèmes linéaires creux. Nous mettons au point des méthodes de parallélisation pour le solveur linéaire hybride MaPHyS. Premièrement nous considerons l'aproche MPI+threads. Dans MaPHyS, le premier niveau de parallélisme consiste au traitement indépendant des sous-domaines. Le second niveau est exploité grâce à l’utilisation de noyaux multithreadés denses et creux au sein des sous-domaines. Une telle implémentation correspond bien à la structure hiérarchique des supercalculateurs modernes et permet un compromis entre les performances numériques et parallèles du solveur. Nous démontrons la flexibilité de notre implémentation parallèle sur un ensemble de cas tests. Deuxièmement nous considérons un approche plus innovante, où les algorithmes sont décrits comme des ensembles de tâches avec des inter-dépendances, i.e., un graphe de tâches orienté sans cycle (DAG). Nous illustrons d’abord comment une première parallélisation à base de tâches peut être obtenue en composant des librairies à base de tâches au sein des processus MPI illustrer par un prototype d’implémentation préliminaire de notre solveur hybride. Nous montrons ensuite comment une approche à base de tâches abstrayant entièrement le matériel peut exploiter avec succès une large gamme d’architectures matérielles. À cet effet, nous avons implanté une version à base de tâches de l’algorithme du Gradient Conjugué et nous montrons que l’approche proposée permet d’atteindre une très haute performance sur des architectures multi-GPU, multicoeur ainsi qu’hétérogène

    High-level FPGA accelerator design for structured-mesh-based numerical solvers

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    Field Programmable Gate Arrays (FPGAs) have become highly attractive as accelerators due to their low power consumption and re-programmability. However, a key limitation is the time and know-how required to program them. Even with high-level synthesis tools, they still require significant hand-tuned/low-level customizations and design space exploration to gain good performance. The need to program FPGAs using the dataflow programming model, much less well known and practised by the high-performance computing (HPC) community, is a major barrier for adoption for HPC. The underlying motivation of this work is to bridge this gap - attaining near-optimal performance vs the ease of programming. To this end, we target the important class of applications based on structured meshes, focusing on numerical algorithms based on explicit and implicit techniques. We leverage the main characteristics of the application class, its computation-communication pattern and the hardware features. For explicit schemes, characterized by stencil computations, we unify the state-of-the-art techniques such as vectorization and unrolling with a number of new high-gain optimizations such as creating perfect data reuse data-paths, batching and tiling. A key new feature is their applicability to multiple stencil loops enabling the development of real-world workloads. For implicit schemes, we re-evaluate the characteristics of the tridiagonal system solver algorithms for FPGAs and develop a new high throughput batched multi-dimensional tridiagonal system solver library with orders of magnitude better performance than the state-of-the-art. New analytic models are developed to support the solvers, elucidating and modelling the critical path of execution and parameterizing the design. This together with the optimal designs and new library lead to a unified design work-flow for synthesis on FPGAs. The new workflow is used to implement a range of applications, from simple single stencil designs, multiple stencil loops to solvers with real-world utility. They are synthesized on the currently dominant Xilinx and Intel FPGAs. Benchmarking indicate the FPGAs matching or outperforming the best GPU implementations, the current best traditional architecture device solution. Over 30% energy saving can also be observed. The performance model demonstrates over 85% accuracy. The thesis discusses the determinants for these applications to be amenable for FPGA implementation, providing insights into the feasibility and profitability of a design. Finally we propose initial steps in automating the workflow to be used through a DSL

    Fast and accurate finite-element multigrid solvers for PDE simulations on GPU clusters

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    Der wichtigste Beitrag dieser Dissertation ist es aufzuzeigen, dass Grafikprozessoren (GPUs) als Repräsentanten der Entwicklung hin zu Vielkern-Architekturen sehr gut geeignet sind zur schnellen und genauen Lösung großer, dünn besetzter linearer Gleichungssysteme, insbesondere mit parallelen Mehrgittermethoden auf heterogenen Rechenclustern. Solche Systeme treten bspw. bei der Diskretisierung (elliptischer) partieller Differentialgleichungen mittels finiter Elemente auf. Wir demonstrieren Beschleunigungsfaktoren von mindestens einer Größenordnung gegenüber konventionellen, hochoptimierten CPU-Implementierungen, ohne Verlust von Genauigkeit und Funktionsumfang. Im Detail liefert diese Dissertation die folgenden Beiträge: Berechnungen in einfach genauer Fließkommadarstellung können für die hier betrachteten Problemklassen nicht ausreichen. Wir greifen die Methode gemischt genauer iterativer Verfeinerung (Nachiteration) wieder auf, um nicht nur die Genauigkeit von berechneten Lösungen zu verbessern, sondern vielmehr die Effizienz des Lösungsprozesses als ganzes zu steigern. Sowohl auf CPUs als auch auf GPUs demonstrieren wir eine deutliche Leistungssteigerung ohne Genauigkeitsverlust im Vergleich zur Berechnung in höherer Fliesskomma-Genauigkeit. Wir präsentieren effiziente Parallelisierungstechniken für Mehrgitter-Löser auf Grafik-Hardware, insbesondere für numerisch starke Glätter und Vorkonditionierer, die für stark anisotrope Gitter und Operatoren geeignet sind. Ein Beispiel ist die Entwicklung einer effizienten Reformulierung des Verfahrens der zyklischen Reduktion für die Lösung tridiagonaler Gleichungssysteme. Im Hinblick auf Hardware-orientierte Numerik analysieren wir sorgfältig den Kompromiss zwischen numerischer und Laufzeit-Effizienz für inexakte Parallelisierungstechniken, die einige der inhärent sequentiellen Charakteristiken solcher starker Glätter zugunsten besserer Parallelisierungseigenschaften entkoppeln. Die Reimplementierung großer, etablierter Softwarepakete zur Anpassung auf neue Hardwareplattformen ist oft inakzeptabel teuer. Wir entwickeln einen "minimalinvasiven" Zugang zur Integration von Co-Prozessoren wie GPUs in FEAST, einem exemplarischen finite Elemente Diskretisierungs- und Löserpaket. Der Hauptvorteil unserer Technik ist, dass Applikationen, die auf FEAST aufsetzen, nicht geändert werden müssen um von der Beschleunigung durch solche Co-Prozessoren zu profitieren. Wir evaluieren unseren Zugang auf großen GPU-beschleunigten Rechenclustern für klassische Benchmarkprobleme aus der linearisierten Elastizität und der Simulation stationärer laminarer Strömungsvorgänge, und beobachten gute Beschleunigungsfaktoren und gute schwache Skalierbarkeit. Die maximal erreichbare Beschleunigung wird zudem analysiert und theoretisch modelliert, um bspw. Vorhersagen treffen zu können. Weiterhin fassen wir die historische Entwicklung des Forschungsgebiets "wissenschaftliches Rechnen auf Grafikhardware" seit 2001/2002 zusammen, d.h. die Entwicklung von GPGPU als obskures Nischenthema hin zum fachübergreifenden Einsatz heute. Die Darstellung umfasst gleichermaßen die Hardware und das Programmiermodell und beinhaltet eine ausgiebige Bibliografie von Veröffentlichungen im Bereich der Simulation von PDE-Problemen auf GPUs.The main contribution of this thesis is to demonstrate that graphics processors (GPUs) as representatives of emerging many-core architectures are very well-suited for the fast and accurate solution of large sparse linear systems of equations, using parallel multigrid methods on heterogeneous compute clusters. Such systems arise for instance in the discretisation of (elliptic) partial differential equations with finite elements. We report on at least one order of magnitude speedup over highly-tuned conventional CPU implementations, without sacrificing neither accuracy nor functionality. In more detail, this thesis includes the following contributions: Single precision floating point computations may be insufficient for the class of problems considered in this thesis. We revisit mixed precision iterative refinement techniques to not only increase the accuracy of computed results, but also to increase the efficiency of the solution process. Both on CPUs and on GPUs, we demonstrate a significant performance improvement without loss of accuracy compared to computing in high precision only. We present efficient parallelisation techniques for multigrid solvers on graphics hardware, in particular for numerically strong smoothers and preconditioners that are suitable for highly anisotropic grids and operators. For instance, an efficient formulation of the cyclic reduction algorithm to solve tridiagonal systems is developed. In view of hardware-oriented numerics, we carefully analyse the trade-off between numerical and runtime performance for inexact parallelisation techniques that decouple some of the inherently sequential characteristics of strong smoothing operators. For large-scale established software frameworks, the re-implementation tailored to novel hardware platforms is often prohibitively expensive. We develop a 'minimally invasive' approach to integrate support for co-processor hardware like GPUs into FEAST, a finite element discretisation and solver toolbox. Our technique has the major advantage that applications built on top of the toolbox do not have to be changed at all to benefit from co-processor acceleration. The approach is evaluated for benchmark problems in linearised elasticity and stationary laminar flow computed on large-scale GPU-enhanced clusters. Good speedup factors and near-ideal weak scalability are observed. The achievable speedup is analysed and a theoretical speedup model is presented. Finally, we provide a historical overview of scientific computing on graphics hardware since the early beginnings in 2001/2002, when GPGPU was an obscure research topic pursued by few, to the widespread adoption nowadays. We discuss the evolution of the hardware and the programming model, and provide a comprehensive bibliography of publications related to PDE simulations on GPUs

    Polyhedral+Dataflow Graphs

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    This research presents an intermediate compiler representation that is designed for optimization, and emphasizes the temporary storage requirements and execution schedule of a given computation to guide optimization decisions. The representation is expressed as a dataflow graph that describes computational statements and data mappings within the polyhedral compilation model. The targeted applications include both the regular and irregular scientific domains. The intermediate representation can be integrated into existing compiler infrastructures. A specification language implemented as a domain specific language in C++ describes the graph components and the transformations that can be applied. The visual representation allows users to reason about optimizations. Graph variants can be translated into source code or other representation. The language, intermediate representation, and associated transformations have been applied to improve the performance of differential equation solvers, or sparse matrix operations, tensor decomposition, and structured multigrid methods

    Exploiting data locality in cache-coherent NUMA systems

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    The end of Dennard scaling has caused a stagnation of the clock frequency in computers.To overcome this issue, in the last two decades vendors have been integrating larger numbers of processing elements in the systems, interconnecting many nodes, including multiple chips in the nodes and increasing the number of cores in each chip. The speed of main memory has not evolved at the same rate as processors, it is much slower and there is a need to provide more total bandwidth to the processors, especially with the increase in the number of cores and chips. Still keeping a shared address space, where all processors can access the whole memory, solutions have come by integrating more memories: by using newer technologies like high-bandwidth memories (HBM) and non-volatile memories (NVM), by giving groups cores (like sockets, for example) faster access to some subset of the DRAM, or by combining many of these solutions. This has caused some heterogeneity in the access speed to main memory, depending on the CPU requesting access to a memory address and the actual physical location of that address, causing non-uniform memory access (NUMA) behaviours. Moreover, many of these systems are cache-coherent (ccNUMA), meaning that changes in the memory done from one CPU must be visible by the other CPUs and transparent for the programmer. These NUMA behaviours reduce the performance of applications and can pose a challenge to the programmers. To tackle this issue, this thesis proposes solutions, at the software and hardware levels, to improve the data locality in NUMA systems and, therefore, the performance of applications in these computer systems. The first contribution shows how considering hardware prefetching simultaneously with thread and data placement in NUMA systems can find configurations with better performance than considering these aspects separately. The performance results combined with performance counters are then used to build a performance model to predict, both offline and online, the best configuration for new applications not in the model. The evaluation is done using two different high performance NUMA systems, and the performance counters collected in one machine are used to predict the best configurations in the other machine. The second contribution builds on the idea that prefetching can have a strong effect in NUMA systems and proposes a NUMA-aware hardware prefetching scheme. This scheme is generic and can be applied to multiple hardware prefetchers with a low hardware cost but giving very good results. The evaluation is done using a cycle-accurate architectural simulator and provides detailed results of the performance, the data transfer reduction and the energy costs. Finally, the third and last contribution consists in scheduling algorithms for task-based programming models. These programming models help improve the programmability of applications in parallel systems and also provide useful information to the underlying runtime system. This information is used to build a task dependency graph (TDG), a directed acyclic graph that models the application where the nodes are sequential pieces of code known as tasks and the edges are the data dependencies between the different tasks. The proposed scheduling algorithms use graph partitioning techniques and provide a scheduling for the tasks in the TDG that minimises the data transfers between the different NUMA regions of the system. The results have been evaluated in real ccNUMA systems with multiple NUMA regions.La fi de la llei de Dennard ha provocat un estancament de la freqüència de rellotge dels computadors. Amb l'objectiu de superar aquest fet, durant les darreres dues dècades els fabricants han integrat més quantitat d'unitats de còmput als sistemes mitjançant la interconnexió de nodes diferents, la inclusió de múltiples xips als nodes i l'increment de nuclis de processador a cada xip. La rapidesa de la memòria principal no ha evolucionat amb el mateix factor que els processadors; és molt més lenta i hi ha la necessitat de proporcionar més ample de banda als processadors, especialment amb l'increment del nombre de nuclis i xips. Tot mantenint un adreçament compartit en el qual tots els processadors poden accedir a la memòria sencera, les solucions han estat al voltant de la integració de més memòries: amb tecnologies modernes com HBM (high-bandwidth memories) i NVM (non-volatile memories), fent que grups de nuclis (com sòcols sencers) tinguin accés més ràpid a una part de la DRAM o amb la combinació de solucions. Això ha provocat una heterogeneïtat en la velocitat d'accés a la memòria principal, en funció del nucli que sol·licita l'accés a una adreça en particular i la seva localització física, fet que provoca uns comportaments no uniformes en l'accés a la memòria (non-uniform memory access, NUMA). A més, sovint tenen memòries cau coherents (cache-coherent NUMA, ccNUMA), que implica que qualsevol canvi fet a la memòria des d'un nucli d'un processador ha de ser visible la resta de manera transparent. Aquests comportaments redueixen el rendiment de les aplicacions i suposen un repte. Per abordar el problema, a la tesi s'hi proposen solucions, a nivell de programari i maquinari, que milloren la localitat de dades als sistemes NUMA i, en conseqüència, el rendiment de les aplicacions en aquests sistemes. La primera contribució mostra que, quan es tenen en compte alhora la precàrrega d'adreces de memòria amb maquinari (hardware prefetching) i les decisions d'ubicació dels fils d'execució i les dades als sistemes NUMA, es poden trobar millors configuracions que quan es condieren per separat. Una combinació dels resultats de rendiment i dels comptadors disponibles al sistema s'utilitza per construir un model de rendiment per fer la predicció, tant per avançat com també en temps d'execució, de la millor configuració per aplicacions que no es troben al model. L'avaluació es du a terme a dos sistemes NUMA d'alt rendiment, i els comptadors mesurats en un sistema s'usen per predir les millors configuracions a l'altre sistema. La segona contribució es basa en la idea que el prefetching pot tenir un efecte considerable als sistemes NUMA i proposa un esquema de precàrrega a nivell de maquinari que té en compte els efectes NUMA. L'esquema és genèric i es pot aplicar als algorismes de precàrrega existents amb un cost de maquinari molt baix però amb molt bons resultats. S'avalua amb un simulador arquitectural acurat a nivell de cicle i proporciona resultats detallats del rendiment, la reducció de les comunicacions de dades i els costos energètics. La tercera i darrera contribució consisteix en algorismes de planificació per models de programació basats en tasques. Aquests simplifiquen la programabilitat de les aplicacions paral·leles i proveeixen informació molt útil al sistema en temps d'execució (runtime system) que en controla el funcionament. Amb aquesta informació es construeix un graf de dependències entre tasques (task dependency graph, TDG), un graf dirigit i acíclic que modela l'aplicació i en el qual els nodes són fragments de codi seqüencial (o tasques) i els arcs són les dependències de dades entre les tasques. Els algorismes de planificació proposats fan servir tècniques de particionat de grafs i proporcionen una planificació de les tasques del TDG que minimitza la comunicació de dades entre les diferents regions NUMA del sistema. Els resultats han estat avaluats en sistemes ccNUMA reals amb múltiples regions NUMA.El final de la ley de Dennard ha provocado un estancamiento de la frecuencia de reloj de los computadores. Con el objetivo de superar este problema, durante las últimas dos décadas los fabricantes han integrado más unidades de cómputo en los sistemas mediante la interconexión de nodos diferentes, la inclusión de múltiples chips en los nodos y el incremento de núcleos de procesador en cada chip. La rapidez de la memoria principal no ha evolucionado con el mismo factor que los procesadores; es mucho más lenta y hay la necesidad de proporcionar más ancho de banda a los procesadores, especialmente con el incremento del número de núcleos y chips. Aun manteniendo un sistema de direccionamiento compartido en el que todos los procesadores pueden acceder al conjunto de la memoria, las soluciones han oscilado alrededor de la integración de más memorias: usando tecnologías modernas como las memorias de alto ancho de banda (highbandwidth memories, HBM) y memorias no volátiles (non-volatile memories, NVM), haciendo que grupos de núcleos (como zócalos completos) tengan acceso más veloz a un subconjunto de la DRAM, o con la combinación de soluciones. Esto ha provocado una heterogeneidad en la velocidad de acceso a la memoria principal, en función del núcleo que solicita el acceso a una dirección de memoria en particular y la ubicación física de esta dirección, lo que provoca unos comportamientos no uniformes en el acceso a la memoria (non-uniform memory access, NUMA). Además, muchos de estos sistemas tienen memorias caché coherentes (cache-coherent NUMA, ccNUMA), lo que implica que cualquier cambio hecho en la memoria desde un núcleo de un procesador debe ser visible por el resto de procesadores de forma transparente para los programadores. Estos comportamientos NUMA reducen el rendimiento de las aplicaciones y pueden suponer un reto para los programadores. Para abordar dicho problema, en esta tesis se proponen soluciones, a nivel de software y hardware, que mejoran la localidad de datos en los sistemas NUMA y, en consecuencia, el rendimiento de las aplicaciones en estos sistemas informáticos. La primera contribución muestra que, cuando se tienen en cuenta a la vez la precarga de direcciones de memoria mediante hardware (o hardware prefetching ) y las decisiones de la ubicación de los hilos de ejecución y los datos en los sistemas NUMA, se pueden hallar mejores configuraciones que cuando se consideran ambos aspectos por separado. Con una combinación de los resultados de rendimiento y de los contadores disponibles en el sistema se construye un modelo de rendimiento, tanto por avanzado como en en tiempo de ejecución, de la mejor configuración para aplicaciones que no están incluidas en el modelo. La evaluación se realiza en dos sistemas NUMA de alto rendimiento, y los contadores medidos en uno de los sistemas se usan para predecir las mejores configuraciones en el otro sistema. La segunda contribución se basa en la idea de que el prefetching puede tener un efecto considerable en los sistemas NUMA y propone un esquema de precarga a nivel hardware que tiene en cuenta los efectos NUMA. Este esquema es genérico y se puede aplicar a diferentes algoritmos de precarga existentes con un coste de hardware muy bajo pero que proporciona muy buenos resultados. Dichos resultados se obtienen y evalúan mediante un simulador arquitectural preciso a nivel de ciclo y proporciona resultados detallados del rendimiento, la reducción de las comunicaciones de datos y los costes energéticos. Finalmente, la tercera y última contribución consiste en algoritmos de planificación para modelos de programación basados en tareas. Estos modelos simplifican la programabilidad de las aplicaciones paralelas y proveen información muy útil al sistema en tiempo de ejecución (runtime system) que controla su funcionamiento. Esta información se utiliza para construir un grafo de dependencias entre tareas (task dependency graph, TDG), un grafo dirigido y acíclico que modela la aplicación y en el ue los nodos son fragmentos de código secuencial, conocidos como tareas, y los arcos son las dependencias de datos entre las distintas tareas. Los algoritmos de planificación que se proponen usan técnicas e particionado de grafos y proporcionan una planificación de las tareas del TDG que minimiza la comunicación de datos entre las distintas regiones NUMA del sistema. Los resultados se han evaluado en sistemas ccNUMA reales con múltiples regiones NUMA.Postprint (published version

    Generalized averaged Gaussian quadrature and applications

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    A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

    MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

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    Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

    Parallel Overlapping Schwarz Preconditioners and Multiscale Discretizations with Applications to Fluid-Structure Interaction and Highly Heterogeneous Problems

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    Accurate simulations of transmural wall stresses in artherosclerotic coronary arteries may help to predict plaque rupture. Therefore, a robust and efficient numerical framework for Fluid-Structure Interaction (FSI) of the blood flow and the arterial wall has to be set up, and suitable material laws for the modeling of the fluid and the structural response have to be incorporated. In this thesis, monolithic coupling algorithms and corresponding monolithic preconditioners are used to simulate FSI using highly nonlinear anisotropic polyconvex hyperelastic and anisotropic viscoelastic material models for the arterial wall. An MPI-parallel FSI software from the LifeV library is coupled to the software FEAP in order to enable access to the structural material models implemented in FEAP. To define a benchmark test for highly nonlinear material models in FSI, a simple geometry corresponding to a section of an idealized coronary artery, suitable boundary conditions, and material parameters adapted to experimental data are used. In particular, the geometry is chosen to be nonsymmetric to make effects due to the anisotropy of the structure visible. An initialization phase and several heartbeats are simulated, and systematical studies with meshes of increasing refinement and different space discretizations are carried out. The results indicate that, for the highly nonlinear material models, piecewise quadratic or F-bar element discretizations lead to significantly better results than piecewise linear shape functions. The results using piecewise linear shape functions are less accurate with respect to the displacements and, in particular, to the approximation of the stresses. To improve the performance of the FSI simulations, a more robust preconditioner for the highly nonlinear structural material models has to be used. Therefore, a parallel implementation of the GDSW (Generalized Dryja-Smith-Widlund) preconditioner, which is a geometric two-level overlapping Schwarz preconditioner with energy-minimizing coarse space, is presented. The implementation, which is based on the software library Trilinos, is held flexible to make further extensions of the preconditioner possible. Even though the dimension of its coarse space is comparably large, parallel scalability for two and three dimensional scalar elliptic and linear elastic problems for thousands of cores is demonstrated. Also for unstructured domain decompositions and for a hybrid version of the preconditioner, convincing scalability is presented. When used as a preconditioner for the structure block in FSI simulations, the GDSW preconditioner shows excellent performance as well: scalability for up to 512 cores and a significant reduction of the simulation time and of the number of iterations with respect to the previously used preconditioner, IFPACK, are observed. IFPACK is an algebraic one-level overlapping Schwarz preconditioner. Finally, highly heterogeneous (multiscale) problems are investigated. Since the GDSW coarse space is not robust for general problems of this type, spaces based on Approximate Component Mode Synthesis (ACMS) are considered. On the basis of the ACMS space, coarse spaces for overlapping Schwarz methods are constructed, and a parallel implementation of a special finite element method is presented. For the coarse spaces, preliminary results indicating numerical scalability and robustness are discussed. For the parallel implementation of the special finite element method, very good parallel weak scalability is observed with respect to the construction of the basis functions and to the solution of the resulting linear system using the FETI-DP (Finite Element Tearing and Interconnecting - Dual Primal) method
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