Optimisation of a parallel ocean general circulation model

Abstract. This paper presents the development of a general-purpose parallel ocean circulation model, for use on a wide range of computer platforms, from traditional scalar machines to workstation clusters and massively parallel processors. Parallelism is provided, as a modular option, via high-level message-passing rou- tines, thus hiding the technical intricacies from the user. An initial implementation highlights that the parallel e?ciency of the model is adversely a?ected by a number of factors, for which optimisations are discussed and implemented. The resulting ocean code is portable and, in particular, allows science to be achieved on local workstations that could otherwise only be undertaken on state-of-the-art supercomputers

Parallel computations based on domain decompositions and integrated radial basis functions for fluid flow problems

The thesis reports a contribution to the development of parallel algorithms based on Domain Decomposition (DD) method and Compact Local Integrated Radial Basis Function (CLIRBF) method. This development aims to solve large scale fluid flow problems more efficiently by using parallel high performance computing (HPC). With the help of the DD method, one big problem can be separated into sub-problems and solved on parallel machines. In terms of numerical analysis, for each sub-problem, the overall condition number of the system matrix is significantly reduced. This is one of the main reasons for the stability, high accuracy and efficiency of parallel algorithms. The developed methods have been successfully applied to solve several benchmark problems with both rectangular and non-rectangular boundaries. In parallel computation, there is a challenge called Distributed Termination Detection (DTD) problem. DTD concerns the discovery whether all processes in a distributed system have finished their job. In a distributed system, this problem is not a trivial problem because there is neither a global synchronised clock nor a shared memory. Taking into account the specific requirement of parallel algorithms, a new algorithm is proposed and called the Bitmap DTD. This algorithm is designed to work with DD method for solving Partial Differential Equations (PDEs). The Bitmap DTD algorithm is inspired by the Credit/Recovery DTD class (or weight-throw). The distinguishing feature of this algorithm is the use of a bitmap to carry the snapshot of the system from process to process. The proposed algorithm possesses characteristics as follows. (i) It allows any process to detect termination (symmetry); (ii) it does not require any central control agent (decentralisation); (iii) termination detection delay is of the order of the diameter of the network; and (iv) the message complexity of the proposed algorithm is optimal. In the first attempt, the combination of the DD method and CLIRBF based collocation approach yields an effective parallel algorithm to solve PDEs. This approach has enabled not only the problem to be solved separately in each subdomain by a Central Processing Unit (CPU) but also compact local stencils to be independently treated. The present algorithm has achieved high throughput in solving large scale problems. The procedure is illustrated by several numerical examples including the benchmark lid-driven cavity flow problem. A new parallel algorithm is developed using the Control Volume Method (CVM) for the solution of PDEs. The goal is to develop an efficient parallel algorithm especially for problems with non-rectangular domains. When combined with CLIRBF approach, the resultant method can produce high-order accuracy and economical solution for problems with complex boundary. The algorithm is verified by solving two benchmark problems including the square lid-driven cavity flow and the triangular lid-driven cavity flow. In both cases, the accuracy is in great agreement with benchmark values. In terms of efficiency, the results show that the method has a very high efficiency profile and for some specific cases a super-linear speed-up is achieved. Although overlapping method yields a straightforward implementation and stable convergence, overlapping of sub-domains makes it less applicable for complex domains. The method even generates more computing overhead for each subdomain as the overlapping area grows. Hence, a parallel algorithm based on non-overlapping DD and CLIRBF has been developed for solving Navier-Stokes equations where a CLIRBF scheme is used to solve the problem in each subdomain. A relaxation factor is employed for the transmission conditions at the interface of sub-domains to ensure the convergence of the iterative method while the Bitmap DTD algorithm is used to achieve the global termination. The parallel algorithm is demonstrated through two fluid flow problems, namely the natural convection in concentric annuli (Boussinesq fluids) and the lid-driven cavity flow (viscous fluids). The results confirm the high efficiency of the present method in comparison with a sequential algorithm. A super-linear efficiency is also observed for a range of numbers of CPUs. Finally, when comparing the overlapping and non-overlapping parallel algorithms, it is found that the non-overlapping one is less stable. The numerical results show that the non-overlapping method is not able to converge for high Reynolds number while overlapping method reaches the same convergence profile as the sequential CLIRBF method. Thus, in this research when dealing with non-Newtonian fluids and large scale problems, the overlapping method is preferred to the nonoverlapping one. The flow of Oldroyd-B fluid through a planar contraction was considered as a benchmark problem. In this problem, the singularity of stress at the re-entrant corners always poses difficulty to numerical methods in obtaining stable solutions at high Weissenberg numbers. In this work, a high resolution simulation of the flow is obtained and the contour of streamline is shown to be in great agreement with other results

Software concepts and algorithms for an efficient and scalable parallel finite element method

Software packages for the numerical solution of partial differential equations (PDEs) using the finite element method are important in different fields of research. The basic data structures and algorithms change in time, as the user\'s requirements are growing and the software must efficiently use the newest highly parallel computing systems. This is the central point of this work. To make efficiently use of parallel computing systems with growing number of independent basic computing units, i.e.~CPUs, we have to combine data structures and algorithms from different areas of mathematics and computer science. Two crucial parts are a distributed mesh and parallel solver for linear systems of equations. For both there exists multiple independent approaches. In this work we argue that it is necessary to combine both of them to allow for an efficient and scalable implementation of the finite element method. First, we present concepts, data structures and algorithms for distributed meshes, which allow for local refinement. The central point of our presentation is to provide arbitrary geometrical information of the mesh and its distribution to the linear solver. A large part of the overall computing time of the finite element method is spend by the linear solver. Thus, its parallelization is of major importance. Based on the presented concept for distributed meshes, we preset several different linear solver methods. Hereby we concentrate on general purpose linear solver, which makes only little assumptions about the systems to be solver. For this, a new FETI-DP (Finite Element Tearing and Interconnect - Dual Primal) method is proposed. Those the standard FETI-DP method is quasi optimal from a mathematical point of view, its not possible to implement it efficiently for a large number of processors (> 10,000). The main reason is a relatively small but globally distributed coarse mesh problem. To circumvent this problem, we propose a new multilevel FETI-DP method which hierarchically decompose the coarse grid problem. This leads to a more local communication pattern for solver the coarse grid problem and makes it possible to scale for a large number of processors. Besides the parallelization of the finite element method, we discuss an approach to speed up serial computations of existing finite element packages. In many computations the PDE to be solved consists of more than one variable. This is especially the case in multi-physics modeling. Observation show that in many of these computation the solution structure of the variables is different. But in the standard finite element method, only one mesh is used for the discretization of all variables. We present a multi-mesh finite element method, which allows to discretize a system of PDEs with two independently refined meshes.Softwarepakete zur numerischen Lösung partieller Differentialgleichungen mit Hilfe der Finiten-Element-Methode sind in vielen Forschungsbereichen ein wichtiges Werkzeug. Die dahinter stehenden Datenstrukturen und Algorithmen unterliegen einer ständigen Neuentwicklung um den immer weiter steigenden Anforderungen der Nutzergemeinde gerecht zu werden und um neue, hochgradig parallel Rechnerarchitekturen effizient nutzen zu können. Dies ist auch der Kernpunkt dieser Arbeit. Um parallel Rechnerarchitekturen mit einer immer höher werdenden Anzahl an von einander unabhängigen Recheneinheiten, z.B.~Prozessoren, effizient Nutzen zu können, müssen Datenstrukturen und Algorithmen aus verschiedenen Teilgebieten der Mathematik und Informatik entwickelt und miteinander kombiniert werden. Im Kern sind dies zwei Bereiche: verteilte Gitter und parallele Löser für lineare Gleichungssysteme. Für jedes der beiden Teilgebiete existieren unabhängig voneinander zahlreiche Ansätze. In dieser Arbeit wird argumentiert, dass für hochskalierbare Anwendungen der Finiten-Elemente-Methode nur eine Kombination beider Teilgebiete und die Verknüpfung der darunter liegenden Datenstrukturen eine effiziente und skalierbare Implementierung ermöglicht. Zuerst stellen wir Konzepte vor, die parallele verteile Gitter mit entsprechenden Adaptionstrategien ermöglichen. Zentraler Punkt ist hier die Informationsaufbereitung für beliebige Löser linearer Gleichungssysteme. Beim Lösen partieller Differentialgleichung mit der Finiten Elemente Methode wird ein großer Teil der Rechenzeit für das Lösen der dabei anfallenden linearen Gleichungssysteme aufgebracht. Daher ist deren Parallelisierung von zentraler Bedeutung. Basierend auf dem vorgestelltem Konzept für verteilten Gitter, welches beliebige geometrische Informationen für die linearen Löser aufbereiten kann, präsentieren wir mehrere unterschiedliche Lösermethoden. Besonders Gewicht wird dabei auf allgemeine Löser gelegt, die möglichst wenig Annahmen über das zu lösende System machen. Hierfür wird die FETI-DP (Finite Element Tearing and Interconnect - Dual Primal) Methode weiterentwickelt. Obwohl die FETI-DP Methode vom mathematischen Standpunkt her als quasi-optimal bezüglich der parallelen Skalierbarkeit gilt, kann sie für große Anzahl an Prozessoren (> 10.000) nicht mehr effizient implementiert werden. Dies liegt hauptsächlich an einem verhältnismäßig kleinem aber global verteilten Grobgitterproblem. Wir stellen eine Multilevel FETI-DP Methode vor, die dieses Problem durch eine hierarchische Komposition des Grobgitterproblems löst. Dadurch wird die Kommunikation entlang des Grobgitterproblems lokalisiert und die Skalierbarkeit der FETI-DP Methode auch für große Anzahl an Prozessoren sichergestellt. Neben der Parallelisierung der Finiten-Elemente-Methode beschäftigen wir uns in dieser Arbeit mit der Ausnutzung von bestimmten Voraussetzung um auch die sequentielle Effizienz bestehender Implementierung der Finiten-Elemente-Methode zu steigern. In vielen Fällen müssen partielle Differentialgleichungen mit mehreren Variablen gelöst werden. Sehr häufig ist dabei zu beobachten, insbesondere bei der Modellierung mehrere miteinander gekoppelter physikalischer Phänomene, dass die Lösungsstruktur der unterschiedlichen Variablen entweder schwach oder vollständig voneinander entkoppelt ist. In den meisten Implementierungen wird dabei nur ein Gitter zur Diskretisierung aller Variablen des Systems genutzt. Wir stellen eine Finite-Elemente-Methode vor, bei der zwei unabhängig voneinander verfeinerte Gitter genutzt werden können um ein System partieller Differentialgleichungen zu lösen

Constrained deformation for evolutionary optimization

Sieger D. Constrained deformation for evolutionary optimization. Bielefeld: Universität Bielefeld; 2017.This thesis investigates shape deformation techniques for their use in design optimization tasks. In the first part, we introduce state-of-the-art deformation methods and evaluate them in a set of representative benchmarks. Based on these benchmarking results, we derive essential criteria and features a deformation technique should satisfy in order to be successfully applicable within design optimization. In the second part, we concentrate on the application and improvement of deformation techniques based on radial basis functions. We present and evaluate a unified framework for surface and volume mesh deformation and investigate questions of performance and scalability. In the final third part, we concentrate on the integration of additional constraints into the deformation, thereby improving the overall effectiveness of the design optimization process and fostering the creation of more feasible and producible design variations. We present a novel shape deformation technique that effectively maintains different types of geometric constraints such as planarity, circularity, or characteristic feature lines during deformation. At the same time, our method provides a unique level of modeling flexibility, quality, robustness, and scalability. Finally, we integrate techniques for automatic constraint detection directly into our deformation framework, thereby making our method more easily applicable within complex design optimization scenarios

Program Abstracts, 100th Session, Iowa Academy of Science, April 21-23, 1988

Presentation abstracts from the annual meeting of the Iowa Academy of Sciencehttps://scholarworks.uni.edu/ias_docs/1035/thumbnail.jp

Research in progress in applied mathematics, numerical analysis, fluid mechanics, and computer science

This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, fluid mechanics, and computer science during the period October 1, 1993 through March 31, 1994. The major categories of the current ICASE research program are: (1) applied and numerical mathematics, including numerical analysis and algorithm development; (2) theoretical and computational research in fluid mechanics in selected areas of interest to LaRC, including acoustics and combustion; (3) experimental research in transition and turbulence and aerodynamics involving LaRC facilities and scientists; and (4) computer science

Seventh Copper Mountain Conference on Multigrid Methods

The Seventh Copper Mountain Conference on Multigrid Methods was held on April 2-7, 1995 at Copper Mountain, Colorado. This book is a collection of many of the papers presented at the conference and so represents the conference proceedings. NASA Langley graciously provided printing of this document so that all of the papers could be presented in a single forum. Each paper was reviewed by a member of the conference organizing committee under the coordination of the editors. The vibrancy and diversity in this field are amply expressed in these important papers, and the collection clearly shows the continuing rapid growth of the use of multigrid acceleration techniques

Automated color correction for colorimetric applications using barcodes

[eng] Color-based sensor devices often offer qualitative solutions, where a material change its color from one color to another, and this is change is observed by a user who performs a manual reading. These materials change their color in response to changes in a certain physical or chemical magnitude. Nowadays, we can find colorimetric indicators with several sensing targets, such as: temperature, humidity, environmental gases, etc. The common approach to quantize these sensors is to place ad hoc electronic components, e.g., a reader device. With the rise of smartphone technology, the possibility to automatically acquire a digital image of those sensors and then compute a quantitative measure is near. By leveraging this measuring process to the smartphones, we avoid the use of ad hoc electronic components, thus reducing colorimetric application cost. However, there exists a challenge on how-to acquire the images of the colorimetric applications and how-to do it consistently, with the disparity of external factors affecting the measure, such as ambient light conditions or different camera modules. In this thesis, we tackle the challenges to digitize and quantize colorimetric applications, such as colorimetric indicators. We make a statement to use 2D barcodes, well-known computer vision patterns, as the base technology to overcome those challenges. We focus on four main challenges: (I) to capture barcodes on top of real-world challenging surfaces (bottles, food packages, etc.), which are the usual surface where colorimetric indicators are placed; (II) to define a new 2D barcode to embed colorimetric features in a back-compatible fashion; (III) to achieve image consistency when capturing images with smartphones by reviewing existent methods and proposing a new color correction method, based upon thin-plate splines mappings; and (IV) to demonstrate a specific application use case applied to a colorimetric indicator for sensing CO2 in the range of modified atmosphere packaging, MAP, one of the common food-packaging standards.[cat] Els dispositius de sensat basats en color, normalment ofereixen solucions qualitatives, en aquestes solucions un material canvia el seu color a un altre color, i aquest canvi de color és observat per un usuari que fa una mesura manual. Aquests materials canvien de color en resposta a un canvi en una magnitud física o química. Avui en dia, podem trobar indicadors colorimètrics que amb diferents objectius, per exemple: temperatura, humitat, gasos ambientals, etc. L'opció més comuna per quantitzar aquests sensors és l'ús d'electrònica addicional, és a dir, un lector. Amb l'augment de la tecnologia dels telèfons intel·ligents, la possibilitat d'automatitzar l'adquisició d'imatges digitals d'aquests sensors i després computar una mesura quantitativa és a prop. Desplaçant aquest procés de mesura als telèfons mòbils, evitem l'ús d'aquesta electrònica addicional, i així, es redueix el cost de l'aplicació colorimètrica. Tanmateix, existeixen reptes sobre com adquirir les imatges de les aplicacions colorimètriques i de com fer-ho de forma consistent, a causa de la disparitat de factors externs que afecten la mesura, com per exemple la llum ambient or les diferents càmeres utilitzades. En aquesta tesi, encarem els reptes de digitalitzar i quantitzar aplicacions colorimètriques, com els indicadors colorimètrics. Fem una proposició per utilitzar codis de barres en dues dimensions, que són coneguts patrons de visió per computador, com a base de la nostra tecnologia per superar aquests reptes. Ens focalitzem en quatre reptes principals: (I) capturar codis de barres sobre de superfícies del món real (ampolles, safates de menjar, etc.), que són les superfícies on usualment aquests indicadors colorimètrics estan situats; (II) definir un nou codi de barres en dues dimensions per encastar elements colorimètrics de forma retro-compatible; (III) aconseguir consistència en la captura d'imatges quan es capturen amb telèfons mòbils, revisant mètodes de correcció de color existents i proposant un nou mètode basat en transformacions geomètriques que utilitzen splines; i (IV) demostrar l'ús de la tecnologia en un cas específic aplicat a un indicador colorimètric per detectar CO2 en el rang per envasos amb atmosfera modificada, MAP, un dels estàndards en envasos de menjar.