الصفحة 1
الصفحة 1
Numerical Continuation Methods for Dynamical Systems : Path following and boundary value problems
The book opens with a foreword by Herbert B. Keller and lecture notes by Sebius Doedel himself that introduce the basic concepts of numerical bifurcation analysis. The other chapters by leading experts discuss continuation for various types of systems and objects and showcase examples of how numerical bifurcation analysis can be used in concrete applications. Topics that are treated include: interactive continuation tools, higher-dimensional continuation, the computation of invariant manifolds, and continuation techniques for slow-fast systems, for symmetric Hamiltonian systems, for spatially extended systems and for systems with delay. Three chapters review physical applications: the dynamics of a SQUID, global bifurcations in laser systems, and dynamics and bifurcations in electronic circuits.
Numerical Approximation Methods for Elliptic Boundary Value Problems : Finite and Boundary Elements
Although the aim of this book is to give a unified introduction into finite and boundary element methods, the main focus is on the numerical analysis of boundary integral and boundary element methods. Starting from the variational formulation of elliptic boundary value problems boundary integral operators and associated boundary integral equations are introduced and analyzed. By using finite and boundary elements corresponding numerical approximation schemes are considered.
Modeling of Creep for Structural Analysis
"Creep Modeling for Structural Analysis" develops methods to simulate and analyze the time-dependent changes of stress and strain states in engineering structures up to the critical stage of creep rupture. The principal subjects of creep mechanics are the formulation of constitutive equations for creep in structural materials under multi-axial stress states; the application of structural mechanics models of beams, plates, shells and three-dimensional solids and the utilization of procedures for the solution of non-linear initial-boundary value problems. The objective of this book is to review some of the classical and recently proposed approaches to the modeling of creep for structural analysis applications as well as to extend the collection of available solutions of creep problems by new, more sophisticated examples.
Methods of nonlinear analysis : Applications to differential equations
In this book, fundamental methods of nonlinear analysis are introduced, discussed and illustrated in straightforward examples. Every method considered is motivated and explained in its general form, but presented in an abstract framework as comprehensively as possible. Applications and generalizations are shown. In particular, a large number of methods is applied to boundary value problems for partial differential equations.
Homogenization of Partial Differential Equations
Homogenization is a method for modeling processes in microinhomogeneous media, which are encountered in radiophysics, filtration theory, rheology, elasticity theory, and other domains of mechanics, physics, and technology. These processes are described by PDEs with rapidly oscillating coefficients or boundary value problems in domains with complex microstructure. From the technical point of view, given the complexity of these processes, the best techniques to solve a wide variety of problems involve constructing appropriate macroscopic (homogenized) models. The present monograph is a comprehensive study of homogenized problems, based on the asymptotic analysis of boundary value problems as the characteristic scales of the microstructure decrease to zero. The work focuses on the construction of nonstandard models: non-local models, multicomponent models, and models with memory.
High Order Difference Methods for Time Dependent PDE
Many books have been written on ?nite difference methods (FDM), but there are good reasons to write still another one. The main reason is that even if higher order methods have been known for a long time, the analysis of stability, accuracy and effectiveness is missing to a large extent. For example, the de?nition of the formal high order accuracy is based on the assumption that the true solution is smooth, or expressed differently, that the grid is ?ne enough such that all variations in the solution are well resolved. In many applications, this assumption is not ful?lled, and then it is interesting to know if a high order method is still effective. Another problem that needs thorough analysis is the construction of boundary conditions such that both accuracy and stability is upheld. And ?nally, there has been quite a strongdevelopmentduringthe last years, inparticularwhenit comesto verygeneral and stable difference operators for application on initial–boundary value problems.
Hierarchical Matrices : A Means to Efficiently Solve Elliptic Boundary Value Problems
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 problems. In addition to storing such matrices, approximations of the usual matrix operations can be computed with logarithmic-linear complexity, which can be exploited to setup approximate preconditioners in an efficient and convenient way. Besides the algorithmic aspects of hierarchical matrices, the main aim of this book is to present their theoretical background. The book contains the existing approximation theory for elliptic problems including partial differential operators with nonsmooth coefficients.
Experimental Unsaturated Soil Mechanics
These proceedings are a continuation of the series of International Conferences in Germany entitled "Mechanics of Unsaturated Soils." The primary objective is to discuss and understand unsaturated soil behaviour such that engineered activities are made better with times in terms of judgement and quality. We all realise by now that in addition to the knowledge on the classical concepts, it becomes an enormous challenging task to adapt convincing new concepts and present them in such a way that it could be used in engineering practices. The experimental studies reported primarily focus on the role of microstructure and fabric for the complex coupled hydro-mechanical behaviour of cohesive frictional materials. Several papers consider the relevance of temperature affecting the constitutive behaviour of clays. Common features of state of the art theoretical and numerical approaches, including theory of porous media and mixture theory, intend to describe the complex multi-field problems of fully coupled thermo-hydraulic-mechanical-chemical initial - boundary value problems.
Evolutionary Equations : Picard's Theorem for Partial Differential Equations, and Applications
This book provides a solution theory for time-dependent partial differential equations, which classically have not been accessible by a unified method. Instead of using sophisticated techniques and methods, the approach is elementary in the sense that only Hilbert space methods and some basic theory of complex analysis are required. Nevertheless, key properties of solutions can be recovered in an elegant manner.
Elliptic and Parabolic Problems : A Special Tribute to the Work of Haim Brezis
This volume contains contributions by former students and collaborators of Haim Brezis given in honor of his 60th anniversary at a conference in Gaeta. H. Brezis has made significant contributions in the fields of partial differential equations and functional analysis. He is an inspiring teacher and counselor of many mathematicians in the front ranks. The collection of papers presented here grew out from his deep insight of analysis. In addition it reflects Brezis's elegant way of creative thinking
Computational Contact Mechanics
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.
Mathematical Methods in Engineering
This book contains some of the contributions that have been carefully selected and peer-reviewed, which were presented at the International Symposium MME06 Mathematical Methods in Engineering, held in Cankaya University, Ankara, April 2006. The Symposium provided a setting for discussing recent developments in Fractional Mathematics, Neutrices and Generalized Functions, Boundary Value Problems, Applications of Wavelets, Dynamical Systems and Control Theory.
Mathematical Foundation of Geodesy : Selected Papers of Torben Krarup
This volume contains selected papers by Torben Krarup, one of the most important geodesists of the 20th century. His writings are mathematically well founded and scientifically relevant. In this impressive collection of papers he demonstrates his rare innovative ability to present significant topics and concepts. Modern students of geodesy can learn a lot from his selection of mathematical tools for solving actual problems. The collection contains the famous booklet "A Contribution to the Mathematical Foundation of Physical Geodesy" from 1969, the unpublished "Molodenskij letters" from 1973, the final version of "Integrated Geodesy" from 1978, "Foundation of a Theory of Elasticity for Geodetic Networks" from 1974, as well as numerous trend setting papers on the theory of adjustment.
Boundary value problems, Weyl Functions, and differential operators
This book presents a comprehensive survey of modern operator techniques for boundary value problems and spectral theory, employing abstract boundary mappings and Weyl functions.
An introduction to differential geometry with applications to elasticity
Interestingly, notions that pertain to di?erential geometry per se,suchas covariant derivatives of tensor ?elds, are also introduced in Chapters 3 and 4, where they appear most naturally in the derivation of the basic boundary value problems of three-dimensional elasticity and shell theory.
A Posteriori Error Analysis Via Duality Theory : With Applications in Modeling and Numerical Approximations
This volume provides a posteriori error analysis for mathematical idealizations in modeling boundary value problems, especially those arising in mechanical applications, and for numerical approximations of numerous nonlinear variational problems. The author avoids giving the results in the most general, abstract form so that it is easier for the reader to understand more clearly the essential ideas involved. Many examples are included to show the usefulness of the derived error estimates.
