Fast Matlab compatible sparse assembly on multicore computers

We develop and implement in this paper a fast sparse assembly algorithm, the fundamental operation which creates a compressed matrix from raw index data. Since it is often a quite demanding and sometimes critical operation, it is of interest to design a highly efficient implementation. We show how to do this, and moreover, we show how our implementation can be parallelized to utilize the power of modern multicore computers. Our freely available code, fully Matlab compatible, achieves about a factor of 5 times in speedup on a typical 6-core machine and 10 times on a dual-socket 16 core machine compared to the built-in serial implementation

A new generation 99 line Matlab code for compliance Topology Optimization and its extension to 3D

Compact and efficient Matlab implementations of compliance Topology Optimization (TO) for 2D and 3D continua are given, consisting of 99 and 125 lines respectively. On discretizations ranging from $3\cdot 10^{4}$ to $4.8\cdot10^{5}$ elements, the 2D version, named top99neo, shows speedups from 2.55 to 5.5 times compared to the well-known top88 code (Andreassen-etal 2011). The 3D version, named top3D125, is the most compact and efficient Matlab implementation for 3D TO to date, showing a speedup of 1.9 times compared to the code of Amir-etal 2014, on a discretization with $2.2\cdot10^{5}$ elements. For both codes, improvements are due to much more efficient procedures for the assembly and implementation of filters and shortcuts in the design update step. The use of an acceleration strategy, yielding major cuts in the overall computational time, is also discussed, stressing its easy integration within the basic codes.Comment: 17 pages, 8 Figures, 4 Table

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

PC-grade parallel processing and hardware acceleration for large-scale data analysis

Arguably, modern graphics processing units (GPU) are the first commodity, and desktop parallel processor. Although GPU programming was originated from the interactive rendering in graphical applications such as computer games, researchers in the field of general purpose computation on GPU (GPGPU) are showing that the power, ubiquity and low cost of GPUs makes them an ideal alternative platform for high-performance computing. This has resulted in the extensive exploration in using the GPU to accelerate general-purpose computations in many engineering and mathematical domains outside of graphics. However, limited to the development complexity caused by the graphics-oriented concepts and development tools for GPU-programming, GPGPU has mainly been discussed in the academic domain so far and has not yet fully fulfilled its promises in the real world. This thesis aims at exploiting GPGPU in the practical engineering domain and presented a novel contribution to GPGPU-driven linear time invariant (LTI) systems that are employed by the signal processing techniques in stylus-based or optical-based surface metrology and data processing. The core contributions that have been achieved in this project can be summarized as follow. Firstly, a thorough survey of the state-of-the-art of GPGPU applications and their development approaches has been carried out in this thesis. In addition, the category of parallel architecture pattern that the GPGPU belongs to has been specified, which formed the foundation of the GPGPU programming framework design in the thesis. Following this specification, a GPGPU programming framework is deduced as a general guideline to the various GPGPU programming models that are applied to a large diversity of algorithms in scientific computing and engineering applications. Considering the evolution of GPU’s hardware architecture, the proposed frameworks cover through the transition of graphics-originated concepts for GPGPU programming based on legacy GPUs and the abstraction of stream processing pattern represented by the compute unified device architecture (CUDA) in which GPU is considered as not only a graphics device but a streaming coprocessor of CPU. Secondly, the proposed GPGPU programming framework are applied to the practical engineering applications, namely, the surface metrological data processing and image processing, to generate the programming models that aim to carry out parallel computing for the corresponding algorithms. The acceleration performance of these models are evaluated in terms of the speed-up factor and the data accuracy, which enabled the generation of quantifiable benchmarks for evaluating consumer-grade parallel processors. It shows that the GPGPU applications outperform the CPU solutions by up to 20 times without significant loss of data accuracy and any noticeable increase in source code complexity, which further validates the effectiveness of the proposed GPGPU general programming framework. Thirdly, this thesis devised methods for carrying out result visualization directly on GPU by storing processed data in local GPU memory through making use of GPU’s rendering device features to achieve realtime interactions. The algorithms employed in this thesis included various filtering techniques, discrete wavelet transform, and the fast Fourier Transform which cover the common operations implemented in most LTI systems in spatial and frequency domains. Considering the employed GPUs’ hardware designs, especially the structure of the rendering pipelines, and the characteristics of the algorithms, the series of proposed GPGPU programming models have proven its feasibility, practicality, and robustness in real engineering applications. The developed GPGPU programming framework as well as the programming models are anticipated to be adaptable for future consumer-level computing devices and other computational demanding applications. In addition, it is envisaged that the devised principles and methods in the framework design are likely to have significant benefits outside the sphere of surface metrology.EThOS - Electronic Theses Online ServiceGBUnited Kingdo

Parallel algorithms and efficient implementation techniques for finite element approximations

In this thesis we study the efficient implementation of the finite element method for the numerical solution of partial differential equations (PDE) on modern parallel computer archi- tectures, such as Cray and IBM supercomputers. The domain-decomposition (DD) method represents the basis of parallel finite element software and is generally implemented such that the number of subdomains is equal to the number of MPI processes. We are interested in breaking this paradigm by introducing a second level of parallelism. Each subdomain is assigned to more than one processor and either MPI processes or multiple threads are used to implement the parallelism on the second level. The thesis is devoted to the study of this second level of parallelism and includes the stages described below. The algebraic additive Schwarz (AAS) domain-decomposition preconditioner is an integral part of the solution process. We seek to understand its performance on the parallel computers which we target and we introduce an improved construction approach for the parallel precon- ditioner. We examine a novel strategy for solving the AAS subdomain problems, using multiple MPI processes. At the subdomain level, this is represented by the ShyLU preconditioner. We bring improvements to its algorithm in the form of a novel inexact solver based on an incomplete QR (IQR) factorization. The performance of the new preconditioner framework is studied for Laplacian and advection-diffusion-reaction (ADR) problems and for Navier-Stokes problems, as a component within a larger framework of specialized preconditioners. The partitioning of the computational mesh comes with considerable memory limitations, when done at runtime on parallel computers, due to the low amount of available memory per processor. We describe and implement a solution to this problem, based on offloading the partitioning process to a preliminary offline stage of the simulation process. We also present the efficient implementation, based on parallel MPI collective instructions, of the routines which load the mesh parts during the simulation. We discuss an alternative parallel implementation of the finite element system assembly based on multi-threading. This new approach is used to supplement the existing one based on MPI parallelism, in situations where MPI alone can not make use of all the available parallel hardware resources. The work presented in the thesis has been done in the framework of two software projects: the Trilinos project and the LifeV parallel finite element modeling library. All the new develop- ments have been contributed back to the respective projects, to be used freely in subsequent public releases of the software

Heterogeneous multicore systems for signal processing

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

Computing Performance Benchmarks among CPU, GPU, and FPGA

In recent years, the world of high performance computing has been developing rapidly. The goal of this project was to conduct computing performance benchmarks on three major computing platforms, CPUs, GPUs, and FPGAs. A total of 66 benchmarks were evaluated. GPUs outperformed the other platforms in terms of execution time. CPUs outperformed in overall execution combined with transfer time. FPGAs outperformed for fixed algorithms using streaming. The team made several recommendations for further research in this area

Energy-momentum time integration of gradient-based models for fiber-bending stiffness in anisotropic thermo-mechanical continua

Accurate dynamic simulations of 3D fiber-reinforced materials in lightweight structures motivate our research activities. In order to accomplish this, the material reinforcement is performed by fiber rovings with a separate bending stiffness, which can be modelled by a second-order gradient of the deformation mapping (see Reference [10]). With an independent field for the gradient of the right Cauchy-Green tensor, we extend the thermoelastic Cauchy continuum for fiber-matrix composites with single fibers. In addition, we use accurate higherorder energy-momentum schemes in combination with mixed finite element methods to obtain numerically stable long-term dynamic simulations and locking free meshes. Therefore, we introduce additional independent fields of well-known as well as new mixed finite elements within a variational-based space-time finite element method and adapt it to the new material formulation. We use Cook's cantilever beam as representative numerical example. We primarily analyze the influence of the fiber bending stiffness as well as the spatial and time convergence up to cubic order, but also look at the influence of Fourier's heat conduction in the matrix and fiber families