Boundary Element Methods with Applications to Nonlinear Problems

This introduction to the singularly perturbed methods in the nonlinear elliptic partial differential equations emphasises the existence and local uniqueness of solutions exhibiting concentration property. The authors avoid using sophisticated estimates and explain the main techniques by thoroughly investigating two relatively simple but typical non-compact elliptic problems. Each chapter then progresses to other related problems to help the reader learn more about the general theories developed from singularly perturbed methods. Designed for PhD students and junior mathematicians intending to do their research in the area of elliptic differential equations, the text covers three main topics. The first is the compactness of the minimization sequences, or the Palais-Smale sequences, or a sequence of approximate solutions; the second is the construction of peak or bubbling solutions by using the Lyapunov-Schmidt reduction method; and the third is the local uniqueness of these solutions.

This book gives readers in-depth know-how on methods of state estimation for nonlinear control systems. It starts with an introduction to dynamic control systems and system states and a brief descript

Elementary yet rigorous, this concise treatment explores practical numerical methods for solving very general two-point boundary-value problems. The approach is directed toward students with a knowled

This book is devoted to the mathematical analysis of the numerical solution of boundary integral equations treating boundary value, transmission and contact problems arising in elasticity, acoustic an

The book covers fundamentals of the theory of optimal methods for solving ill-posed problems, as well as ways to obtain accurate and accurate-by-order error estimates for these methods. The methods de

This monograph aims to promote original mathematical methods to determine the invariant measure of two-dimensional random walks in domains with boundaries. Such processes arise in numerous application

This manual contains fully worked-out solutions to select odd-numbered exercises in the text, giving students a way to check their answers and ensure that they took the correct steps to arrive at an a

DIFFERENTIAL EQUATIONS WITH BOUNDARY-VALUE PROBLEMS, 8th Edition strikes a balance between the analytical, qualitative, and quantitative approaches to the study of differential equations. This proven

The Boundary Element Method for Engineers and Scientists: Theory and Applications, Second Edition, provides a detailed, practical guide to the principles and use of the boundary element method (BEM),

This book is devoted to the study of boundary value problems for nonlinear ordinary differential equations and focuses on questions related to the study of nonlinear interpolation. In 1967, Andrzej La

The second edition of An Introduction to Nonlinear Finite Element Analysis has the same objective as the first edition, namely, to facilitate an easy and thorough understanding of the details that are

The fast multipole method is one of the most important algorithms in computing developed in the 20th century. Along with the fast multipole method, the boundary element method (BEM) has also emerged as a powerful method for modeling large-scale problems. BEM models with millions of unknowns on the boundary can now be solved on desktop computers using the fast multipole BEM. This is the first book on the fast multipole BEM, which brings together the classical theories in BEM formulations and the recent development of the fast multipole method. Two- and three-dimensional potential, elastostatic, Stokes flow, and acoustic wave problems are covered, supplemented with exercise problems and computer source codes. Applications in modeling nanocomposite materials, bio-materials, fuel cells, acoustic waves, and image-based simulations are demonstrated to show the potential of the fast multipole BEM. Enables students, researchers, and engineers to learn the BEM and fast multipole method from a s

This text emphasizes nonlinear models for a course in time series analysis. After introducing stochastic processes, Markov chains, Poisson processes, and ARMA models, the authors cover functional auto

With parallel treatment of smooth and non-smooth problems, this text on non-linear boundary value problems and related analysis has new material on Neumann problems involving non-homogeneous different

This graduate-level textbook presents representative problems in nonlinear analysis by topological methods. The approach is elementary with simple model equations and applications, allowing students t

Here is a framework for mixed finite element methods, moving from a finite dimensional presentation, then on to formulation in Hilbert spaces and approximations, stabilized methods and eigenvalue prob

Tearing and interconnecting methods, such as FETI, FETI-DP, BETI, etc., are among the most successful domain decomposition solvers for partial differential equations. The purpose of this book is to gi

Presented in this volume are a number of new results concerning the extension theory and spectral theory of unbounded operators using the recent notions of boundary triplets and boundary relations. This approach relies on linear single-valued and multi-valued maps, isometric in a Krein space sense, and offers a basic framework for recent developments in system theory. Central to the theory are analytic tools such as Weyl functions, including Titchmarsh-Weyl m-functions and Dirichlet-to-Neumann maps. A wide range of topics is considered in this context from the abstract to the applied, including boundary value problems for ordinary and partial differential equations; infinite-dimensional perturbations; local point-interactions; boundary and passive control state/signal systems; extension theory of accretive, sectorial and symmetric operators; and Calkin's abstract boundary conditions. This accessible treatment of recent developments, written by leading researchers, will appeal to a broa

1. We describe, at first in a very formaI manner, our essential aim. n Let m be an op en subset of R , with boundary am. In m and on am we introduce, respectively, linear differential operators P and

In this book, fundamental methods of nonlinear analysis are introduced, discussed and illustrated in straightforward examples. Each method considered is motivated and explained in its general form, bu

VI SOCRATES: I think that we ought to stress that we will write only about things that we have first hand experience in, in a coherent way that will be useful to engineers and other scientists and str

This volume on some recent aspects of finite element methods and their applications is dedicated to Ulrich Langer and Arnd Meyer on the occasion of their 60th birthdays in 2012. Their work combines th

The first volume of this series dealt with the Basic Principles of Boundary Elements while the second concentrated on Time-dependent Vibration Problems and volume three on the Computational Aspects of

Die Kosten im deutschen Gesundheitssystem steigen, zugleich werden Qualitatsprobleme immer offensichtlicher – trotz aller Reformbemuhungen. Die Autoren gehen davon aus, dass nicht Kostenkontrolle, son

This series has been developed in response to the interest shown in boundary ele- ments by scientists and engineers. Whilst Volume 1 was dedicated to basic principles and applications, this book is co

This book deals with the efficient numerical solution of challenging nonlinear problems in science and engineering, both in finite dimension (algebraic systems) and in infinite dimension (ordinary and

Nonlinear stress analysis (a branch of solid mechanics) is an essential feature in the design of such diverse structures as aircraft, bridges, machines, and dams. Computational techniques have become vital tools in dealing with the complex, time-consuming problems associated with nonlinear stress analysis. Although finite element techniques are widely used, boundary element methods (BEM) offer a powerful alternative, especially in tackling problems of three-dimensional plasticity. This 2002 book describes the application of BEM in solid mechanics, beginning with basic theory and then explaining the numerical implementation of BEM in nonlinear stress analysis. The authors have also developed a BEM source code for use by the reader, which is available on the book's companion website. This book will be especially useful to stress analysts in industry, research workers in the field of computational plasticity, and postgraduate students taking courses in engineering mechanics.

The design of most modern engineering systems entails the consideration of a good trade-off between the several targets requirements to be satisfied along the system life such as high reliability, low

Divided into two parts, this book deals with the theory of elasticity and computational solution of its problems. Part A named Theoretical Elasticity describes the mathematical theory and the analyti

This work presents a thorough treatment of boundary element methods (BEM) for solving strongly elliptic boundary integral equations obtained from boundary reduction of elliptic boundary value problems

Closing a gap in the literature, this is the first comprehensive handbook on this modern and important polymer topic. Edited by highly experienced and top scientists in the field, this ready reference