Despite the ample number of articles on parallel-vector computational algorithms published over the last 20 years, there is a lack of texts in the field customized for senior undergraduate and graduate engineering research. Parallel-Vector Equation Solvers for Finite Element Engineering Applications aims to fill this gap, detailing both the theoretical development and important implementations of equation-solution algorithms. The mathematical background necessary to understand their inception balances well with descriptions of their practical uses. Illustrated with a number of state-of-the-art FORTRAN codes developed as examples for the book, Dr. Nguyen's text is a perfect choice for instructors and researchers alike.

This book presents numerical methods and computational aspects for linear integral equations. Such equations occur in various areas of applied mathematics, physics, and engineering. The material covered in this book, though not exhaustive, offers useful techniques for solving a variety of problems. Historical information cover­ ing the nineteenth and twentieth centuries is available in fragments in Kantorovich and Krylov (1958), Anselone (1964), Mikhlin (1967), Lonseth (1977), Atkinson (1976), Baker (1978), Kondo (1991), and Brunner (1997). Integral equations are encountered in a variety of applications in many fields including continuum mechanics, potential theory, geophysics, electricity and mag­ netism, kinetic theory of gases, hereditary phenomena in physics and biology, renewal theory, quantum mechanics, radiation, optimization, optimal control sys­ tems, communication theory, mathematical economics, population genetics, queue­ ing theory, and medicine. Most of the boundary value problems involving differ­ ential equations can be converted into problems in integral equations, but there are certain problems which can be formulated only in terms of integral equations. A computational approach to the solution of integral equations is, therefore, an essential branch of scientific inquiry.

This is the fifth book of the Kluwer's series Advances in Robot Kine­ matics. The book presents the most recent research advances in the theory, design, control and application of robotic systems, which are intended for a variety of purposes such as manipulation, manufactur­ ing, automation, surgery, locomotion and biomechanics. The issues addressed are fundamentally kinematic in nature, including synthesis, calibration, redundancy, force control, dexterity, inverse and forward kinematics, kinematic singularities, as well as over-constrained systems. Methods used include line geometry, quaternion algebra, screw alge­ bra, and linear algebra. These methods are applied to both parallel and serial multi-degree-of-freedom systems. The results should interest researchers, teachers and students, in fields of engineering and mathe­ matics related to robot theory, design, control and application. Each contribution in this book had been rigorously reviewed by two or three independent reviewers and 53 articles had been recommended for publication. We are happy to observe that Advances in Robot Kine­ matics has always attracted the most outstanding authors and has de­ veloped a remarkable scientific community in the area. Many important and original scientific results were for the first time reported and dis­ cussed in these books. All articles in this book were also reported at the eight international symposium on Advances in Robot Kinematics that was organised in June 2002 in Caldes de Malavella in Spain.

This volume contains refereed papers based on the lectures presented at the XIV International Conference on Mathematical Programming held at Matrahaza, Hungary, between 27-31 March 1999. This conference was organized by the Laboratory of Operations Research and Deci­ sion Systems at the Computer and Automation Institute, Hungarian Academy of Sciences. The editors hope this volume will contribute to the theory and applications of mathematical programming. As a tradition of these events, the main purpose of the confer­ ence was to review and discuss recent advances and promising research trends concerning theory, algorithms and applications in different fields of Optimization Theory and related areas such as Convex Analysis, Complementarity Systems and Variational Inequalities. The conference is traditionally held in the Matra Mountains, and housed by the resort house of the Hungarian Academy of Sciences. This was the 14th event of the long lasting series of conferences started in 1973. The organizers wish to express their thanks to the authors for their contributions in this volume, and the anonymous referees for their valu­ able comments. Special thanks are directed to our sponsors, the Hun­ garian Academy of Sciences, the National Committee for Technological Development, the Hungarian National Science Foundation, and last but not least, the Hungarian Operational Research Society. We would like to thank John Martindale from Kluwer Academic Publishers for helping us produce this volume, Eva Nora Nagy for cor­ rections and proof-readings, and Peter Dombi for his excellent work on typesetting and editing the manuscript.

In a rapidly evolving field such as computational physics, six years is an eternity. Even though many of the elementary techniques described here are of venerable age, their assembly into sophisticated combined methods and their intensive application to ever new problems is an ongoing and exciting process. After six years, a new the new vistas edition of this textbook must therefore take into account some of that have opened up recently. Apart from these additions and some didactic improvements, the general struc­ ture of the book holds good. The first three chapters are devoted to a thorough, if concise, treatment of the main ingredients from numerical mathematics: finite differences, linear algebra, and stochastics. This exercise will prove valuable when we proceed, in chapters 4 and 5, to combine these elementary tools into powerful instruments for the integration of differential equations. The final chapters are devoted to a number of applications in selected fields: statistical physics, quantum mechanics, and hydrodynamics. I will gradually augment this text by web-resident sample programs. These will be written in JAVA and will be accompanied by short explanations and references to this text. Thus it may prove worthwhile to pay an occasional visit to my web-site www.ap.univie.ac.at/users/Franz.Vesely/ to see if any new applets have sprung up.

Th e variational spline theory which originates f rom th e well-known paper by J.e. Holliday (1957) is today a well-developed field in approxi- mat ion theory. The gene ra l definition of splines in the Hilbert space, ex- istence, uniqueness, and characterization theorems were obt ained about 35 years ago by M. Atteia, P.J. L aur ent, and P.M. Anselone, but in rec ent years impor tant new results have been obtained in th e abst ract variational spline theory. Th ese concern the convergence in th e Hilb ert spaces, general techniques for error es tim ation of abs trac t splines includ- ing multi-dimensional splines on scatt ered meshes, new kinds of charac- teriz ation th eorems based on reproducing kernels and m appin gs, and the theory and algorithms for the splines on subspaces (finite element me th od for complic at ed non-polynomial splines). New variatio na l for- mulations arose for vec tor splines, rational splines, te nsor and blending splines, trac es of splines on the smooth manifold, discontinuous splines, etc. Optim al approxi mat ions of linear functionals and ope rat ors are also developed from th ese concepts.

This book is intended to be an easy, concise, but rather complete, introduc­ the ISO/ANSI C++ programming language with special empha­ tion to sis on object-oriented numeric computation for students and professionals in science and engineering. The description of the language is platform­ independent. Thus it applies to different operating systems such as UNIX, Linux, MacOS, Windows, and DOS, as long as a standard C++ compiler is equipped. The prerequisite of this book is elementary knowledge of cal­ culus and linear algebra. However, this prerequisite is hardly necessary if this book is going to be used as a textbook for teaching C++ and all the sections on numeric methods are skipped. Programming experience in an­ other language such as FORTRAN, C, Ada, Pascal, Maple, or Matlab will certainly help, but is not presumed. All C++ features are introduced in an easy way through concepts such as functions, complex numbers, vectors, matrices, and integrals, which are familiar to every student and professional in science and engineering.

Deals with the most basic notion of linear algebra, to bring emphasis on approaches to the topic serving at the elementary level and more broadly.

In 19 articles presented by leading experts in the field of geometric modelling the state-of-the-art on representing, modeling, and analyzing curves, surfaces as well as other 3-dimensional geometry is given. The range of applications include CAD/CAM-systems, computer graphics, scientific visualization, virtual reality, simulation and medical imaging. The content of this book is based on selected lectures given at a workshop held at IBFI Schloss Dagstuhl, Germany. Topics treated are: – curve and surface modelling – non-manifold modelling in CAD – multiresolution analysis of complex geometric models – surface reconstruction – variational design – computational geometry of curves and surfaces – 3D meshing – geometric modelling for scientific visualization – geometric models for biomedical applications.

Continuous System Simulation describes systematically and methodically how mathematical models of dynamic systems, usually described by sets of either ordinary or partial differential equations possibly coupled with algebraic equations, can be simulated on a digital computer.

Interest in constrained optimization originated with the simple linear pro­ gramming model since it was practical and perhaps the only computationally tractable model at the time. Constrained linear optimization models were soon adopted in numerous application areas and are perhaps the most widely used mathematical models in operations research and management science at the time of this writing. Modelers have, however, found the assumption of linearity to be overly restrictive in expressing the real-world phenomena and problems in economics, finance, business, communication, engineering design, computational biology, and other areas that frequently demand the use of nonlinear expressions and discrete variables in optimization models.

The microcomputer has put a vast amount of computational power in the hands of the practicing chemical engineer. However, a microcomputer is of little use unless there are programs available to solve chemical engineer­ ing problems; In this book, I have put together a collection of BASIC pro­ grams that w~ll help the practicing engineer be more productive and able to solve complex problems that are normally handled on mainframe com­ puters. The plant engineer will find the book particularly useful. The plant en­ gineer is calle~ upon to investigate problems that range from simple trouble shooting to tQe detailed design of complex chemical plants. The larger proj­ ects are usually add-on jobs to the regular duties of keeping a chemical plant running. In t~day's business climate, answers to problems must be obtained quickly and ~ccurately. The computer is capable of testing hypothesis, thereby allo~ing engineers to evaluate alternative solutions to problems quickly and provide answers to management's questions that invariably shift like the sand~ in a desert.

This state-of-the-art survey features topics related to the impact of multicore, manycore, and coprocessor technologies in science and for large-scale applications in an interdisciplinary environment. The papers cover issues of current research in mathematical modeling, design of parallel algorithms, aspects of microprocessor architecture, parallel programming languages, hardware-aware computing, heterogeneous platforms, manycore technologies, performance tuning, and requirements for large-scale applications. The contributions presented in this volume offer a survey on the state of the art, the concepts and perspectives for future developments. They are an outcome of an inspiring conference conceived and organized by the editors at the Karlsruhe Institute Technology (KIT) in September 2011. The twelve revised full papers presented together with two contributed papers focus on combination of new aspects of microprocessor technologies, parallel applications, numerical simulation, and software development; thus they clearly show the potential of emerging technologies in the area of multicore and manycore processors that are paving the way towards personal supercomputing and very likely towards exascale computing.

The purpose of this book is to place a resource in the hands of experimental mechanics researchers to enable them to understand and to obtain a working familiarity with certain of the numerical methods particularly useful to the field. The book is organized to permit readers to study the methods and to observe their application in experimental problems. It is also intended to encourage readers to directly apply the methods to the same problems or to similar problems of their choosing. To this end, computer programs are available electronically, together with data, for easy application. Program listings are given in the appendix. There are four chapters which make up the central coverage of the text. The first of these deals with least-square methods of problem solution, both for curve fitting and for general solution of overdetermined problems. Nonlinear least-squares methods are included. Secondly, splines; specifically smoothed splines, are covered, including specification of boundary conditions for the latter. Use for differentiation is emphasized with attention to control of possible excesses in smoothing.

Developed from the authors’ introductory combinatorics course, this book focuses on a branch of mathematics which plays a crucial role in computer science. Combinatorial methods provide many analytical tools used for determining the expected performance of computer algorithms. Elementary subjects such as combinations and permutations, and mathematical tools such as generating functions and Pólya’s Theory of Counting, are covered, as are analyses of specific problems such as Ramsey Theory, matchings, and Hamiltonian and Eulerian paths.