Edited by J.R. Whiteman ,
BICOM, Institute of Computational Mathematics, Department of Mathematical Sciences, Brunel University,

The Mathematics of Finite Elements and Applications X
Proceedings of the Tenth Conference on The Mathematics of Finite Elements and Applications
(MAFELAP 1999), Middlesex, UK, 22-25 June 1999

Description

The tenth conference on The Mathematics of Finite Elements and Applications, MAFELAP 1999, was held at Brunel University during the period 22-25 June, 1999. This book seeks to highlight certain aspects of the state-of-the-art theory and applications of finite element methods of that time.

This latest conference, in the MAFELAP series, followed the well established MAFELAP pattern of bringing together mathematicians, engineers and others interested in the field to discuss finite element techniques.
In the MAFELAP context finite elements have always been interpreted in a broad and inclusive manner, including techniques such as finite difference, finite volume and boundary element methods as well as actual finite element methods. Twenty-six papers were carefully selected for this book out of the 180 presentations made at the conference, and all of these reflect this style and approach to finite elements. The increasing importance of modelling, in addition to numerical discretization, error estimation and adaptivity was also studied in MAFELAP 1999.

Contents

Preface.
Fictitious domain methods for particulate flow in two and three dimensions (R. Glowinski et al.).
Locally conservative algorithms for flow (B. Rivi鑽e, M.F. Wheeler).
Recent advances in adaptive modelling of heterogeneous media (J. Tinsley Oden, K. Vemaganti).
Modelling and finite element analysis of applied polymer viscoelasticity problems (S. Shaw et al.).
A viscoelastic hybrid shell finite element (A.R. Johnson).
The dual-weighted-residual method for error control and mesh adaptation in finite element methods (R. Rannacher).
h-adaptive finite element methods for contact problems (P. Wriggers et al.).
hp-finite element methods for hyperbolic problems (E. S・i et al.).
What do we want and what do we have in a posteriori estimates in the FEM (I. Babuska et al.).
Solving short wave problems using special finite elements - towards an adaptive approach (O. Laghrouche, P. Bettess).
Finite element methods for fluid-structure vibration problems (A. Berm�dez et al.).
Coupling different numerical algorithms for two phase fluid flow (M. Peszynska et al.).
Analysis and numerics of strongly degenerate convection-diffusion problems modelling sedimentation-consolidation processes (R. B・ger, K.H. Karlsen).
Some extensions of the local discontinuous galerkin method for convection-diffusion equations in multidimensions (B. Cockburn, C. Dawson).
Scientific computing tools for 3D magnetic field problems (M. Kuhn et al.).
Duality based domain decomposition with adaptive natural coarse grid projectors for contact problems (Z. Dost疝 et al.).
A multi-well problem for phase transformations (M.S. Kuczma).
Advanced boundary element algorithms (C. Lage, C. Schwab).
H-matrix approximation on graded meshes (W. Hackbusch, B.N. Khoromskij).
Boundary integral formulations for stokes flows in deforming regions (L.C. Wrobel et al.).
Semi-Lagrangian finite volume methods for viscoelastic flow problems (T.N. Phillips, A.J. Williams).
A finite volume method for viscous compressible flows in low and high speed applications (J. Vierendeels et al.).
On finite element methods for coupling eigenvalue problems (H. De Schepper, R. Van Keer).
Mesh shape and anisotropic elements: theory and practice (T. Apel et al.).
On the treatment of propagating mode-1 cracks by variational inequalities (M. Bach).
Recent trends in the computational modelling of continua and multi-fracturing solids (D.R.J. Owen et al.).

Bibliographic and Ordering Information

For information about conditions of sale, ordering procedures, and links to our regional sales offices, please read through our ordering information.
2000

Hardbound

ISBN: 0-08-043568-8
450 pages

Pablo Pedregal

Variational Methods in Nonlinear Elasticity

In less than 100 pages, this book covers the main vector variational methods developed to solve nonlinear elasticity problems. Presenting a general framework with a tight focus, the author provides a comprehensive exposition of a technically difficult, yet rapidly developing area of modern applied mathematics. The book includes the classical existence theory as well as a brief incursion into problems where nonexistence is fundamental. It also provides self-contained, concise accounts of quasi convexity, polyconvexity, and rank-one convexity, which are used in nonlinear elasticity.

Pedregal introduces the reader to Young measures as an important tool in solving vector variational techniques. Readers are encouraged to pursue nonlinear elasticity as one of the best means to apply these techniques. Although there are other books devoted to nonlinear elasticity or variational methods, none are concerned with Young measures as a tool for proving existence results in nonlinear elasticity.

In addition, many valuable references are included to direct the reader to other important research.

Audience
This book will be of interest to mechanical and aeronautical engineers, applied physicists, material scientists, applied mathematicians, and applied analysts interested in applications of calculus of variations to nonlinear elasticity and problems with microstructure.

Contents

Preface; Chapter 1: Elastic Materials and Variational Principles; Chapter 2: Quasi Convexity and Young Measures; Chapter 3: Polyconvexity and Existence Theorems; Chapter 4: Rank-one Convexity and Microstructure; Chapter 5: Technical Remarks; Bibliographical Comments; Bibliography; Index.

2000 / xii + 99 pages / Softcover / ISBN 0-89871-452-4

Andreas Griewank

Evaluating Derivatives
Principles and Techniques of Algorithmic Differentiation

Frontiers in Applied Mathematics 19

Algorithmic, or automatic, differentiation (AD) is concerned with the accurate and efficient evaluation of derivatives for functions defined by computer programs. No truncation errors are incurred, and the resulting numerical derivative values can be used for all scientific computations that are based on linear, quadratic, or even higher order approximations to nonlinear scalar or vector functions. In particular, AD has been applied to optimization, parameter identification, equation solving, the numerical integration of differential equations, and combinations thereof. Apart from quantifying sensitivities numerically, AD techniques can also provide structural information, e.g., sparsity pattern and generic rank of Jacobian matrices.

This first comprehensive treatment of AD describes all chainrule-based techniques for evaluating derivatives of composite functions with particular emphasis on the reverse, or adjoint, mode. The corresponding complexity analysis shows that gradients are always relatively cheap, while the cost of evaluating Jacobian and Hessian matrices is found to be strongly dependent on problem structure and its efficient exploitation. Attempts to minimize operations count and/or memory requirement lead to hard combinatorial optimization problems in the case of Jacobians and a well-defined trade-off curve between spatial and temporal complexity for gradient evaluations.

The book is divided into three parts: a stand-alone introduction to the fundamentals of AD and its software, a thorough treatment of methods for sparse problems, and final chapters on higher derivatives, nonsmooth problems, and program reversal schedules. Each of the chapters concludes with examples and exercises suitable for students with a basic understanding of differential calculus, procedural programming, and numerical linear algebra.

Audience

This volume will be valuable for designers and users of algorithms and software for nonlinear computational problems. It opens up an exciting opportunity to develop new algorithms that reflect the availability of accurate derivatives and their true cost to achieve improvements in speed and reliability. Some familiarity with modern approaches to the seemingly straightforward task of evaluating derivatives will benefit any mathematician, scientist or engineer.

Contents (partial)

Preface; Prologue; Introduction; Part I: Tangents and Gradients. A Framework for Evaluating Functions; Fundamentals of Forward and Reverse; Repeating and Extending Reverse; Implementation and Software; Part II: Jacobians and Hessians. Sparse Forward and Reverse; Exploiting Sparsity by Compression; Going Beyond Forward and Reverse; Observations on Efficiency; Part III: Advances and Reversals. Taylor and Tensor Coefficients; Differentiation without Differentiability; Serial and Parallel Reversal Schedules; Bibliography; Index.

2000 / xxiv + 369 pages / Softcover / ISBN 0-89871-451-6

Dockner, E.J., University of Vienna, Austria
Hartl, R.F., University of Vienna, Austria
Luptacik, M., Vienna University of Economics and Business Administration, Vienna, Austria
Sorger, G., Queen Mary & Westfield College, London, UK
(Eds.)

Optimization, Dynamics and Economic Analysis
Essays in Honor of Gustav Feichtinger

2000. X, 428 pp. 75 figs., 18 tabs.
3-7908-1295-1
Recommended List Price

This book includes a collection of articles that present recent developments in the fields of optimization and dynamic game theory, economic dynamics, dynamic theory of the firm, and population dynamics and non standard applications of optimal control theory. The authors of the articles are well respected authorities in their fields and are known for their high quality research in the fields of optimization and economic dynamics.

Keywords: Optimization, Dynamic Game Theory, Economic Dynamics, Dynamic Theory of the Firm, Population Dynamics

Contents: Optimization and Dynamic Games: I.M. Bomze: Copositivity Aspects of Standard Quadratic Optimization Problems.- D. Augustin, H. Maurer: Computational Sensitivity Analysis of State Constrained Contol Problems.- H.X. Phu, H.G. Bock, S. Pickenhain: Rough Stability of Solutions to Nonconvex Optimzation Problems.- M. Luptacik: Data Envelopment Analysis as a Tool for Measurement of Eco-Efficiency.- M. Sommersgute-Reichmann, A. Stephan: Evaluating the New Activity-based Hospital-financing-systems in Austria.- D.A. Behrens, R. Neck: Similarities Between Solutions of Discrete-time (Non-)Linear-quadratic Games.- W. Krabs, S. Pickl, J. Scheffran: Optimization of an N-Person Game under Linear Side Conditions.- Economic Dynamics: C. Chiarella, X.Z. He: The Dynamics of the Cobweb When Producers are Risk Averse Learners.- C. Chiarella, P. Flaschel, G. Groh, W. Semmler: AS-AD Disequilibrium Dynamics and Economic
Growth.- H. Dawid, M. Kopel: Market Takeovers in Medieval Trade.- C. Hommes: Cobweb Dynamics Under Bounded Rationality.- A. Luhmer: A Principle-agent Problem in Continuous Time.- A.J. Novak: A Note on Investment Credit and Endogenous Cycles.- S. Rinaldi, F. Amigoni: The Role of Extrinsic Motivation in the Dynamics of Creative Professions.- G. Sorger: Income Distribution and Endogenous Growth.- H. Takahasi: A Turnpike Theorem with Public Theorem.- F. Wirl: Wage Bargaining and Incentive Compatibility: Is Unemployment Optimal After All?- Theory of the Firm: E.J. Dockner, K. Nishimura: Dynamic Investment Games.- R.F. Hartl, P.M. Kort: Optimal Investments with Increasing Returns to Scale: A Further Analyis.- S. J�rgensen: A Note on Dynamic Transfer Price Bargaining.- K.P. Kistner, I. Dobos: Optimal Production-inventory
Strategies for a Reverse Logistics System.- E. Presman, S.P. Sethi, H. Zhang: Optimal Production Planning in General Stochastic Jobshops with Long-run Average Cost.- C. Schneeweiﾟ: On an Extension of Classical Production and Cost Theory.- G. Tragler: Optimal Controls in Spatial Advertising Diffusion Models.- Population Dynamics: C. H�hn: All About e60.- W. Lutz, S. Scherbov: Quantifying Vicious Circle Dynamics: The PEDA Model for Population, Environment Development and Agriculture in African Countries.- A. Prskawetz, A. Gragnani: The Complexity of the Malthusian Trap and Potential Routes of Escape.- G. Steinmann, A. Prskawetz: Natural Resources Standards of Living and the Demographic Transition.- J.W. Vaupel, V. Canudas Romo: How Mortality Improvement Increases Population Growth.- Miscellaneous Applications: J.P. Caulkins: The Evolution of Drug Initiation: From Social Networks to Public Markets.- M. Deistler, M. Wagner: On the Structure of Cointegration.- W. Eichhorn, U. Leopold-Wildburger: Model an Reality - The Principle of Simplicity within the Empirical Sciences.- H. Kozumi, W. Polasek: A Bayesian Semiparametric Analysis of ARCH Models.- G. Leitmann: Screeming Policies for Control of an Infectious Disease.- A. Mehlmann: Der Herr des Chaos.- Personal Data and Publications of H. Feichtinger.

Kuncheva, L.I., University of Wales, Bangor, UK

Fuzzy Classifier Design

2000. X, 315 pp. 113 figs., 81 tabs.
3-7908-1298-6
Recommended List Price

This book about fuzzy classifier design briefly introduces the fundamentals of supervised pattern recognition and fuzzy set theory. Fuzzy if-then classifiers are defined and some theoretical properties thereof are studied. Popular training algorithms are detailed. Non if-then fuzzy classifiers include relational, k-nearest neighbor, prototype-based designs, etc. A chapter on multiple classifier combination discusses fuzzy and non-fuzzy models for fusion and selection.

Keywords: Fuzzy Logic, Fuzzy Classifier Design, Pattern Recognition

Contents: Introduction: What are fuzzy classifiers?- The data sets used in this book.- Notations and acronyms.- Organization of the book.- Acknowledgements.- Statistical Pattern Recognition: Class, feature, feature space.- Classifier, discriminant functions, classification regions.- Clustering.- Prior probabilities, class-conditional probability density functions, posterior probabilities.- Minimum error and minimum risk classification. Loss matrix.- Performance estimation.- Experimental comparison of classifiers.- A taxonomy of classifier design methods.- Statistical Classifiers: Parametric classifiers.- Nonparametric classifiers.- Finding k-nn prototypes.- Neural networks.- Fuzzy Sets: Fuzzy logic, an oxymoron?- Basic definitions.- Operations on fuzzy sets.- Determining membership functions.- Fuzzy If-then Classifiers: Fuzzy if-then systems.- Function
approximation with fuzzy if-then systems.- Fuzzy if-then classifiers.- Universal approximation and equivalences of fuzzy if-then classifiers.- Training of Fuzzy If-then Classifiers: Expert opinion or data analysis.- Tuning the consequents.- Tuning the antecedents.- Tuning antecedents and consequents using clustering.- Genetic algorithms for tuning fuzzy if-then classifiers.- Fuzzy classifiers and neural networks: hybridization or identity?- Forget interpretability and choose a model.- Non if-then Fuzzy Models: Early ideas.- Fuzzy k-nearest neighbors (k-nn) designs.- Generalized nearest prototype classifier (GNPC).- Combinations of Multiple Classifiers Using Fuzzy Sets: Combining classifiers: the variety of paradigms.- Classifier Selection.- Classifier Fusion.- Experimental results.- Conclusions: What to Choose.

Series: Studies in Fuzziness and Soft Computing. VOL. 49

Hardle, W., Humboldt-Universitat zu Berlin, Germany
Liang, H., Texas A&M University, College Station, TX, USA
Gao, J., Queensland University of Technology, Brisbane, Australia

Partially Linear Models

2000. X, 203 pp. 17 figs., 11 tabs.
3-7908-1300-1

Recommended List Price

In the last ten years, there has been increasing interest and activity in the general area of partially linear regression smoothing in statistics. Many methods and techniques have been proposed and studied. This monograph hopes to bring an up-to-date presentation of the state of the art of partially linear regression techniques. The emphasis is on methodologies rather than on the theory, with a particular focus on applications of partially linear regression techniques to various statistical problems. These problems include least squares regression, asymptotically efficient estimation, bootstrap resampling, censored data analysis, linear measurement error models, nonlinear measurement models, nonlinear and nonparametric time series models.

Keywords: Partially Linear Models, Partially Linear Regression Techniques

Contents: Symbols and Notation.- Introduction: Background, History and Practical Examples.- The Least Squares Estimators.- Assumptions and Remarks.- The Scope of the Monograph.- The Structure of the Monograoh.- Estimation of the Parametric Component: Estimation with Heteroscedastic Errors.- Estimation with Censored Data.- Bootstrap Approximations.- Estimation of the Nonparametric Component: Introduction.- Consistency Results.- Asymptotic Normality.- Simulated and Real Examples.- Appendix.- Estimation with Measurement Errors: Linear Variables with Measurement Errors.- Nonlinear Variables with Measurement Errors.- Some Related Theoretic Topics: The Laws of the Iterated Logarithm.- The Berry-Esseen Bounds.- Asymptotically Efficient Estimation.- Bahadur Asymptotic Efficiency.- Second Order Asymptotic Efficiency.- Estimation of the Error Distribution.- Partially Linear Time Series Models: Introduction.- Adaptive Parametric and Nonparametric Tests.- Optimum Linear Subset Selection.-
Optimum Bandwidth Selection.- Other Related Developments.- The Assumptions and the Proofs of
Theorems.- Appendix: Basic Lemmas.

Series: Contributions to Statistics.