Numerisk analyse

Looking back at the years that have passed since the realization of the very first electronic, multi-purpose computers, one observes a tremendous growth in hardware and software performance. Today, researchers and engi- neers have access to computing power and software that can solve numerical problems which are not fully understood in terms of existing mathemati- cal theory. Thus, computational sciences must in many respects be viewed as experimental disciplines. As a consequence, there is a demand for high- quality, flexible software that allows, and even encourages, experimentation with alternative numerical strategies and mathematical models. Extensibil- ity is then a key issue; the software must provide an efficient environment for incorporation of new methods and models that will be required in fu- ture problem scenarios. The development of such kind of flexible software is a challenging and expensive task. One way to achieve these goals is to in- vest much work in the design and implementation of generic software tools which can be used in a wide range of application fields. In order to provide a forum where researchers could present and discuss their contributions to the described development, an International Work- shop on Modern Software Tools for Scientific Computing was arranged in Oslo, Norway, September 16-18, 1996. This workshop, informally referred to as Sci Tools '96, was a collaboration between SINTEF Applied Mathe- matics and the Departments of Informatics and Mathematics at the Uni- versity of Oslo.

Comment poser et résoudre les équations de Maxwell ? On présente ici les outils nécessaires : formulations faibles, éléments d¿arêtes, méthodes intégrales, en insistant sur la modélisation, c¿est-à-dire la « mise en équations » de situations concrètes : il y a en effet, pour chaque catégorie de problèmes en électrotechnique (chauffage par induction, machines et moteurs électriques, cavités résonnantes, etc.), un modèle mathématique approprié, qüil faut savoir dériver des équations fondamentales. Pour chacun des modèles étudiés dans ce livre (« Maxwell complet », « conduction », « ondes en milieu borné », etc.) on donne la formulation appropriée et la version « discrétisée », c¿est-à-dire exploitable sur un ordinateur, que la méthode des éléments finis permet d¿en déduire.Depuis sa rédaction, ce cours a été enseigné dans plusieurs formations doctorales européennes, destinées à des ingénieurs en électrotechnique et à des étudiants en analyse numérique. La présente réédition a été revue et corrigée en fonction de cette expérience, avec une bibliographie complétée. Bagage mathématique requis: algèbre et analyse numérique linéaire, et quelque familiarité avec la méthode des éléments finis. On ne suppose pas de connaissances préalables en électricité.

This book is primarily intended as a research monograph that could also be used in graduate courses for the design of parallel algorithms in matrix computations.It assumes general but not extensive knowledge of numerical linear algebra, parallel architectures, and parallel programming paradigms. The book consists of four parts: (I) Basics; (II) Dense and Special Matrix Computations; (III) Sparse Matrix Computations; and (IV) Matrix functions and characteristics. Part I deals with parallel programming paradigms and fundamental kernels, including reordering schemes for sparse matrices. Part II is devoted to dense matrix computations such as parallel algorithms for solving linear systems, linear least squares, the symmetric algebraic eigenvalue problem, and the singular-value decomposition. It also deals with the development of parallel algorithms for special linear systems such as banded ,Vandermonde ,Toeplitz ,and block Toeplitz systems. Part III addresses sparse matrix computations: (a) the development of parallel iterative linear system solvers with emphasis on scalable preconditioners, (b) parallel schemes for obtaining a few of the extreme eigenpairs or those contained in a given interval in the spectrum of a standard or generalized symmetric eigenvalue problem, and (c) parallel methods for computing a few of the extreme singular triplets. Part IV focuses on the development of parallel algorithms for matrix functions and special characteristics such as the matrix pseudospectrum and the determinant. The book also reviews the theoretical and practical background necessary when designing these algorithms and includes an extensive bibliography that will be useful to researchers and students alike. The book brings together many existing algorithms for the fundamental matrix computations that have a proven track record of efficient implementation in terms of data locality and data transfer on state-of-the-art systems, as well as several algorithms that are presented for the first time, focusing on the opportunities for parallelism and algorithm robustness.

This book introduces, in an accessible way, the basic elements of Numerical PDE-Constrained Optimization, from the derivation of optimality conditions to the design of solution algorithms. Numerical optimization methods in function-spaces and their application to PDE-constrained problems are carefully presented. The developed results are illustrated with several examples, including linear and nonlinear ones. In addition, MATLAB codes, for representative problems, are included. Furthermore, recent results in the emerging field of nonsmooth numerical PDE constrained optimization are also covered. The book provides an overview on the derivation of optimality conditions and on some solution algorithms for problems involving bound constraints, state-constraints, sparse cost functionals and variational inequality constraints.

This book constitutes the refereed proceedings of the 7th International Conference on Similarity Search and Applications, SISAP 2014, held in A Coruña, Spain, in October 2014. The 21 full papers and 6 short papers presented were carefully reviewed and selected from 45 submissions. The papers are organized in topical sections on Improving Similarity Search Methods and Techniques; Indexing and Applications; Metrics and Evaluation; New Scenarios and Approaches; Applications and Specific Domains.

The two-volume set of LNCS 10941 and 10942 constitutes the proceedings of the 9th International Conference on Advances in Swarm Intelligence, ICSI 2018, held in Shanghai, China, in June 2018. The total of 113 papers presented in these volumes was carefully reviewed and selected from 197 submissions. The papers were organized in topical sections namely: multi-agent systems; swarm robotics; fuzzy logic approaches; planning and routing problems; recommendation in social media; predication; classification; finding patterns; image enhancement; deep learning; theories and models of swarm intelligence; ant colony optimization; particle swarm optimization; artificial bee colony algorithms; genetic algorithms; differential evolution; fireworks algorithm; bacterial foraging optimization; artificial immune system; hydrologic cycle optimization; other swarm-based optimization algorithms; hybrid optimization algorithms; multi-objective optimization; large-scale global optimization.

This highly multidisciplinary volume contains contributions from leading researchers in STEAM-H disciplines (Science, Technology, Engineering, Agriculture, Mathematics and Health). The volume explores new frontiers in multidisciplinary research, including: the mathematics of cardiac arrhythmia; brain research on working memory; penalized ordinal regression to classify melanoma skin samples; forecasting of time series data; dynamics of niche models; analysis of chemical moieties as anticancer agents; study of gene locus control regions; qualitative mathematical modelling; convex quadrics and group circle systems; remanufacturing planning and control; complexity reduction of functional differential equations; computation of viscous interfacial motion; and differentiation in human pluripotent stem cells. An extension of a seminar series at Virginia State University, the collection is intended to foster student interest and participation in interdisciplinary research and to stimulate new research. The content will be of interest to a broad spectrum of scientists, mathematicians and research students working in interdisciplinary fields including the biosciences, mathematics, engineering, neurosciences and behavioral sciences.

These proceedings contain lectures presented at the NATO-NSF-ARO sponsored Advanced Study I~stitute on "Computer Aided Analysis and Optimization of Mechanical System Dynamics" held in Iowa City, Iowa, 1-12 August, 1983. Lectures were presented by free world leaders in the field of machine dynamics and optimization. Participants in the Institute were specialists from throughout NATO, many of whom presented contributed papers during the Institute and all of whom participated actively in discussions on technical aspects of the subject. The proceedings are organized into five parts, each addressing a technical aspect of the field of computational methods in dynamic analysis and design of mechanical systems. The introductory paper presented first in the text outlines some of the numerous technical considerations that must be given to organizing effective and efficient computational methods and computer codes to serve engineers in dynamic analysis and design of mechanical systems. Two substantially different approaches to the field are identified in this introduction and are given attention throughout the text. The first and most classical approach uses a minimal set of Lagrangian generalized coordinates to formulate equations of motion with a small number of constraints. The second method uses a maximal set of cartesian coordinates and leads to a large number of differential and algebraic constraint equations of rather simple form. These fundamentally different approaches and associated methods of symbolic computation, numerical integration, and use of computer graphics are addressed throughout the proceedings.

This book assesses the state-of-the-art in computational fluid dynamics (CFD) applied to ship hydrodynamics and provides guidelines for the future developments in the field based on the Gothenburg 2010 Workshop. It presents ship hull test cases, experimental data and submitted computational methods, conditions, grids and results.  Analysis is made of errors for global (resistance, sinkage and trim and self-propulsion) and local flow (wave elevations and mean velocities and turbulence) variables, including standard deviations for global variables and propeller modeling for self-propulsion. The effects of grid size and turbulence models are evaluated for both global and local flow variables. Detailed analysis is made of turbulence modeling capabilities for capturing local flow physics. Errors are also analyzed for head-wave seakeeping and forward speed diffraction, and calm-water forward speed-roll decay. Resistance submissions are used to evaluate the error and uncertainty by means of a systematic verification and validation (V&V) study along with statistical investigations.  Post-workshop experimental and computational studies are conducted and analyzed for evaluation of facility biases and to draw more concrete conclusions regarding the most reliable turbulence model, appropriate numerical methods and grid resolution requirements, respectively.

Walter Gautschi has written extensively on topics ranging from special functions, quadrature and orthogonal polynomials to difference and differential equations, software implementations, and the history of mathematics. He is world renowned for his pioneering work in numerical analysis and constructive orthogonal polynomials, including a definitive textbook in the former, and a monograph in the latter area. This three-volume set, Walter Gautschi: Selected Works with Commentaries, is a compilation of Gautschi's most influential papers and includes commentaries by leading experts. The work begins with a detailed biographical section and ends with a section commemorating Walter's prematurely deceased twin brother. This title will appeal to graduate students and researchers in numerical analysis, as well as to historians of science. Selected Works with Commentaries, Vol. 1Numerical ConditioningSpecial FunctionsInterpolation and Approximation Selected Works with Commentaries, Vol. 2Orthogonal Polynomials on the Real LineOrthogonal Polynomials on the SemicircleChebyshev QuadratureKronrod and Other QuadraturesGauss-type Quadrature Selected Works with Commentaries, Vol. 3Linear Difference EquationsOrdinary Differential EquationsSoftwareHistory and BiographyMiscellaneaWorks of Werner Gautschi

This book constitutes the refereed proceedings of the 5th International Conference on Combinatorial Optimization and Applications, COCOA 2011, held in Zhangjiajie, China, in August 2011. The 43 revised full papers were carefully reviewed and selected from 65 submissions. The papers cover a broad range of topics in combinatorial optimization and applications focussing on experimental and applied research of general algorithmic interest and research motivated by real-world problems.

This book presents numerical and other approximation techniques for solving various types of mathematical problems that cannot be solved analytically. In addition to well known methods, it contains some non-standard approximation techniques that are now formally collected as well as original methods developed by the author that do not appear in the literature.This book contains an extensive treatment of approximate solutions to various types of integral equations, a topic that is not often discussed in detail. There are detailed analyses of ordinary and partial differential equations and descriptions of methods for estimating the values of integrals that are presented in a level of detail that will suggest techniques that will be useful for developing methods for approximating solutions to problems outside of this text.The book is intended for researchers who must approximate solutions to problems that cannot be solved analytically. It is also appropriate for students taking courses in numerical approximation techniques.

This is the second edition of the valuable reference source for numerical simulations of contact mechanics suitable for many fields like civil engineering, car design, aeronautics, metal forming, or biomechanics.Boundary value problems involving contact are of great importance in industrial applications in engineering such as bearings, metal forming processes, rubber seals, drilling problems, crash analysis of cars, rolling contact between car tires and the road, cooling of electronic devices... Other applications are related to biomechanical engineering design where human joints, implants or teeth are of consideration. Due to this variety, contact problems are today combined either with large elastic or inelastic deformations including time dependent responses. Thermal coupling also might have to be considered. Even stability behaviour has to be linked to contact.The topic of computational contact is described in depth providing an up-to-date treatment of different formulations, algorithms and discretisation techniques for contact problems which are established in the geometrically linear and nonlinear range. This book provides the necessary continuum mechanics background which includes the derivation of the contact constraints. Constitutive equations stemming from tribology which are valid at the contact interface are discussed in detail. Discretization schemes for small and finite deformations are discussed in depth. Solid and beam contact is considered as well as contact of unstable systems and thermomechanical contact. The algorithmic side covers a broad range of solution methods. Additionally adaptive discretisation techniques for contact analysis are presented as a modern tool for engineering design simulations. The present text book is written for graduate, Masters and PhD students, but also for engineers in industry, who have to simulate contact problems in practical application and wish to understand the theoretical and algorithmic background of contact treatment in modern finite element systems.For this second edition, illustrative simplified examples and new discretisation schemes as well as adaptive procedures for coupled problems are added.

Dieses Buch behandelt stochastische Integrale bezüglich der Brownschen Bewegung (Itô-Integrale), den daraus resultierenden Itôschen Differentialkalkül und einige Anwendungen. Das Buch zeichnet sich durch zwei Besonderheiten aus: Zum Einen sind die mathematischen Voraussetzungen minimiert, und zum Anderen wird der Itô-Kalkül in einem ersten Schritt völlig ohne Martingale entwickelt. Dies erleichtert (insbesondere für Anwender) den Einstieg in die Theorie, da tiefer liegende stochastische Methoden zunächst nicht benötigt werden. Erst in einem zweiten Schritt werden die engen Beziehungen zur Martingaltheorie und zur Browschen Bewegung entwickelt (Darstellungssätze, Sätze von Lévy, Girsanov, etc.). Anwendungen auf stochastische Differentialgleichungen und Optionspreistheorie runden den Text ab.

The natural mission of Computational Science is to tackle all sorts of human problems and to work out intelligent automata aimed at alleviating the b- den of working out suitable tools for solving complex problems. For this reason ComputationalScience,thoughoriginatingfromtheneedtosolvethemostch- lenging problems in science and engineering (computational science is the key player in the ?ght to gain fundamental advances in astronomy, biology, che- stry, environmental science, physics and several other scienti?c and engineering disciplines) is increasingly turning its attention to all ?elds of human activity. In all activities, in fact, intensive computation, information handling, kn- ledge synthesis, the use of ad-hoc devices, etc. increasingly need to be exploited and coordinated regardless of the location of both the users and the (various and heterogeneous) computing platforms. As a result the key to understanding the explosive growth of this discipline lies in two adjectives that more and more appropriately refer to Computational Science and its applications: interoperable and ubiquitous. Numerous examples of ubiquitous and interoperable tools and applicationsaregiveninthepresentfourLNCSvolumescontainingthecontri- tions delivered at the 2004 International Conference on Computational Science and its Applications (ICCSA 2004) held in Assisi, Italy, May 14-17, 2004.

The natural mission of Computational Science is to tackle all sorts of human problems and to work out intelligent automata aimed at alleviating the b- den of working out suitable tools for solving complex problems. For this reason ComputationalScience,thoughoriginatingfromtheneedtosolvethemostch- lenging problems in science and engineering (computational science is the key player in the ?ght to gain fundamental advances in astronomy, biology, che- stry, environmental science, physics and several other scienti?c and engineering disciplines) is increasingly turning its attention to all ?elds of human activity. In all activities, in fact, intensive computation, information handling, kn- ledge synthesis, the use of ad-hoc devices, etc. increasingly need to be exploited and coordinated regardless of the location of both the users and the (various and heterogeneous) computing platforms. As a result the key to understanding the explosive growth of this discipline lies in two adjectives that more and more appropriately refer to Computational Science and its applications: interoperable and ubiquitous. Numerous examples of ubiquitous and interoperable tools and applicationsaregiveninthepresentfourLNCSvolumescontainingthecontri- tions delivered at the 2004 International Conference on Computational Science and its Applications (ICCSA 2004) held in Assisi, Italy, May 14-17, 2004.

This book serves as a set of lecture notes for a senior undergraduate level course on the introduction to numerical computation, which was developed through 4 semesters of teaching the course over 10 years. The book requires minimum background knowledge from the students, including only a three-semester of calculus, and a bit on matrices.

Quasi-Monte Carlo methods have become an increasingly popular alternative to Monte Carlo methods over the last two decades. This book presents all of the essential tools for using quasi-Monte Carlo sampling on practical problems, especially in finance.