Boundary Element Methods with Applications to Nonlinear Problems

The parallel developments of the Finite Element Methods in the 1950’s and the engineering applications of stochastic processes in the 1940’s provided a combined numerical analysis tool for the studies

Intended for advanced undergraduate and graduate students, the first four chapters of this book are devoted to the introduction of the finite element concept. The focus then covers two essential areas - heat transfer and fluid mechanics: topics with different finite element formulations. Heat transfer applications begin with the classical one-dimensional thin-rod problem, followed by the two-dimensional heat transfer problem including a variety of boundary conditions. Finally, a complicated-geometry three-dimensional problem, involving a cooled radial turbine rotor, is presented, with the cooling passages treated as 'heat sinks' in the finite element analysis. For fluid mechanics, the concept of 'nodeless' degrees of freedom is introduced, with real-life fluid-flow applications. The time-dependent finite-element analysis topic is addressed through the problem of unsteady stator/rotor flow interaction within a turbomachinery stage. Finally, the concept of 'virtually-deformable finite el

The book gives a comprehensive coverage of most classical nonparametric statistical tests as well as nonparametric techniques in regression and generalized regression, time-to-event analysis, density

"A practical, professional guide to MATLAB applications, numerical techniques, and scientific computing MATLAB Numerical Methods with Chemical Engineering Applications shows how to use MATLAB to mode

Networked and Distributed Predictive Control presents rigorous, yet practical, methods for the design of networked and distributed predictive control systems – the first book to do so. The design of m

Suitable for statisticians, mathematicians, actuaries, and students interested in the problems of insurance and analysis of lifetimes, Statistical Methods with Applications to Demography and Life Insu

This book is the first on the topic and explains the most cutting-edge methods needed for precise calculations and explores the development of powerful algorithms to solve research problems. Multipoin

This book provides researchers and engineers in the imaging field with the skills they need to effectively deal with nonlinear inverse problems associated with different imaging modalities, including

This second edition with about 25% updated and new content offers wide-ranging coverage of fundamental rotordynamics in order to provide engineers with the necessary knowledge to eliminate various vib

This overview of some of the main results and recent developments in nonlinear water waves presents fundamental aspects of the field and discusses several important topics of current research interest

"Computer methods continue to be critical in the analysis, simulation, design and optimization of engineering processes and systems. Computational approaches are needed to solve the complex mathematic

While the finite element method (FEM) has become the standard technique used to solve static and dynamic problems associated with structures and machines, ANSYS software has developed into the enginee

This self-contained textbook provides the basic, abstract?tools?used in?nonlinear analysis?and their applications to semilinear elliptic boundary value problems and displays how various?approaches?can

Multicriteria Analysis and LCA Techniques introduces the reader to the basic principles of multicriteria analysis (MCA) and life cycle assessment (LCA) techniques. The use of these tools is rapidly be

Applications of Finite Element Methods for Reliability Studies on ULSI Interconnections provides a detailed description of the application of finite element methods (FEMs) to the study of ULSI interco

Published by McGraw-Hill since its first edition in 1941, this classic text is an introduction to Fourier series and their applications to boundary value problems in partial differential equations of

Offers an introduction to Fourier series and their applications to boundary value problems in partial differential equations of engineering and physics. This title also introduces the concept of ortho

This advanced graduate-level text examines variational methods in partial differential equations and illustrates their applications to a number of free-boundary problems. Detailed statements of the s

Nonlinear resonance analysis is a unique mathematical tool that can be used to study resonances in relation to, but independently of, any single area of application. This is the first book to present the theory of nonlinear resonances as a new scientific field, with its own theory, computational methods, applications and open questions. The book includes several worked examples, mostly taken from fluid dynamics, to explain the concepts discussed. Each chapter demonstrates how nonlinear resonance analysis can be applied to real systems, including large-scale phenomena in the Earth's atmosphere and novel wave turbulent regimes, and explains a range of laboratory experiments. The book also contains a detailed description of the latest computer software in the field. It is suitable for graduate students and researchers in nonlinear science and wave turbulence, along with fluid mechanics and number theory. Colour versions of a selection of the figures are available at www.cambridge.org/9780

This book deals with the application of spectral methods to problems of uncertainty propagation and quanti?cation in model-based computations. It speci?cally focuses on computational and algorithmic f

This text emphasizes the general area of nonlinear engineering models with an in-depth discussion of computer algorithms for solving nonlinear problems coupled with appropriate examples of such nonli

Hierarchical matrices are an efficient framework for large-scale fully populated matrices arising, e.g., from the finite element discretization of solution operators of elliptic boundary value problem

This volume introduces Fourier and transform methods for solutions to boundary value problems associated with natural phenomena. Unlike most treatments, it emphasizes basic concepts and techniques rat

This book examines the theory of boundary value problems for elliptic systems of partial differential equations, a theory which has many applications in mathematics and the physical sciences. The aim is to 'algebraize' the index theory by means of pseudo-differential operators and methods in the spectral theory of matrix polynomials. This latter theory provides important tools that will enable the student to work efficiently with the principal symbols of the elliptic and boundary operators on the boundary. This book is ideal for use in graduate-level courses on partial differential equations, elliptic systems, pseudo-differential operators and matrix analysis. Since many new methods and results are introduced and used throughout the book, all the theorems are proved in detail, and the methods are well illustrated through numerous examples and exercises.

Many problems in science and engineering are described by nonlinear differential equations, which can be notoriously difficult to solve. Through the interplay of topological and variational ideas, methods of nonlinear analysis are able to tackle such fundamental problems. This graduate text explains some of the key techniques in a way that will be appreciated by mathematicians, physicists and engineers. Starting from elementary tools of bifurcation theory and analysis, the authors cover a number of more modern topics from critical point theory to elliptic partial differential equations. A series of Appendices give convenient accounts of a variety of advanced topics that will introduce the reader to areas of current research. The book is amply illustrated and many chapters are rounded off with a set of exercises.

This book offers a systematic presentation of up-to-date material scattered throughout the literature from the methodology point of view. It reviews the basic theories and methods, with many interesti

Perturbation theory is a fascinating and fundamental topic in mathematics and its applications to the natural and engineering sciences. In this workbook, each explicit example is studied and methods i

Why another book on the finite element method? There are currently more than 200 books in print with "Finite Element Method" in their titles. Many are devoted to special topics or emphasize error anal

MacCluer (mathematics, Michigan State U.) examines numerical methods and symbolic manipulation based on modern Sobolev methods. Working on an advanced undergraduate level, MacCluer starts with steady

This book provides a comprehensive and in-depth treatment of one of the most important control problems: the nonlinear output regulation problem. It contains up-to-date research results and algorithms

Despite the continued rapid advance in computing speed and memory the increase in the complexity of models used by engineers persists in outpacing them. Even where there is access to the latest hardwa

This book includes a self-contained theory of inequality problems and their applications to unilateral mechanics. Fundamental theoretical results and related methods of analysis are discussed on vario

Nonlinear elasticity is concerned with nonlinear effects associated with deformations of elastic bodies subjected to external forces or temperature variations. It has important applications in many areas, including the aerospace and rubber industries, and biomechanics. This book, written by a group of leading researchers invited especially for the purpose, provides an up-to-date and concise account of the fundamentals of the theory of nonlinear elasticity and a comprehensive review of several major current research directions in this important field. It combines the characteristics of coherence and detail found in standard treatises with the strength and freshness of research articles. The emphasis is placed firmly on coverage of modern topics and recent developments rather than on the very theoretical approach often found. The book will be an excellent reference source for both beginners and specialists in engineering, applied mathematics and physics. It is also ideally suited for gra

Providing an easy introduction to the boundary element method, this book is ideal for any reader wishing to work in this field or use this method for the solution of engineering problems. From the beg

This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples and geome

Covers major vector variational methods developed to solve nonlinear elasticity problems. Discusses the classical existence theory, makes a brief incursion into problems where nonexistence is fundamen

Group sequential methods answer the needs of clinical trial monitoring committees who must assess the data available at an interim analysis. These interim results may provide grounds for terminating t

The boundary element method is more appropriate than the finite element method to tackle linear, wave propagation, infinite domain, mobile boundaries and unknown boundaries problems. In some engineeri

This book deals with such important subjects as variational methods, the continuity method, parabolic equations on fiber bundles, ideas concerning points of concentration, blowing-up technique, geomet

This book deals with such important subjects as variational methods, the continuity method, parabolic equations on fiber bundles, ideas concerning points of concentration, blowing-up technique, geomet