Bücher der Reihe Springer Series in Computational Mathematics

This book introduces the concepts and methodologies related to the modelling of complex phenomena occurring in materials processing, developing finite differences, finite volumes and finite elements through phase transformation, solid mechanics and fluid flow.

This is the soft cover reprint of the very popular hardcover edition. The book offers a simultaneous presentation of the theory and of the numerical treatment of elliptic problems.

This book deals with methods for solving nonstiff ordinary differential equations. The reader will benefit from many illustrations, a historical and didactic approach, and computer programs. This new edition has been rewritten and new material has been included.

This book deals with the efficient numerical solution of challenging nonlinear problems in science and engineering, both in finite and in infinite dimension. Its focus is on local and global Newton methods for direct problems or Gauss-Newton methods for inverse problems.

Multi-grid methods are the most efficient tools for solving elliptic boundary value problems. One section describes special applications (convection-diffusion equations, singular perturbation problems, eigenvalue problems, etc.).

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 and electromagnetic scattering. It serves as the mathematical foundation of the boundary element methods (BEM) both for static and dynamic problems. The book presents a systematic approach to the variational methods for boundary integral equations including the treatment with variational inequalities for contact problems. It also features adaptive BEM, hp-version BEM, coupling of finite and boundary element methods - efficient computational tools that have become extremely popular in applications.Familiarizing readers with tools like Mellin transformation and pseudodifferential operators as well as convex and nonsmooth analysis for variational inequalities, it concisely presents efficient, state-of-the-art boundary element approximations and points to up-to-date research.The authors are well known for their fundamental work on boundary elements and related topics, and this book is a major contribution to the modern theory of the BEM (especially for error controlled adaptive methods and for unilateral contact and dynamic problems) and is a valuable resource for applied mathematicians, engineers, scientists and graduate students.

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 and electromagnetic scattering. It serves as the mathematical foundation of the boundary element methods (BEM) both for static and dynamic problems. The book presents a systematic approach to the variational methods for boundary integral equations including the treatment with variational inequalities for contact problems. It also features adaptive BEM, hp-version BEM, coupling of finite and boundary element methods - efficient computational tools that have become extremely popular in applications.Familiarizing readers with tools like Mellin transformation and pseudodifferential operators as well as convex and nonsmooth analysis for variational inequalities, it concisely presents efficient, state-of-the-art boundary element approximations and points to up-to-date research.The authors are well known for their fundamental work on boundary elements and related topics, and this book is a major contribution to the modern theory of the BEM (especially for error controlled adaptive methods and for unilateral contact and dynamic problems) and is a valuable resource for applied mathematicians, engineers, scientists and graduate students.

Detailed lecture notes on six topics at the forefront of current research in numerical analysis and applied mathematics, with each set of notes presenting a self-contained guide to a current research area and supplemented by an extensive bibliography.

Detailed lecture notes on six topics at the forefront of current research in numerical analysis and applied mathematics, with each set of notes presenting a self-contained guide to a current research area and supplemented by an extensive bibliography.

- the mathematical aspect: this consists of a coherent and rigorous analy sis of convergence, with the aid of mathematical tools (these tools are mainly the use of norms for convergence proofs, the use of matrix algebra and so on).

One can identify two major types of mechanisms: the short term adaptive adjustments (defensive driving, mar keting, inventory control, etc.) that are made after making some observations of the system's parameters, and the long term anticipative actions (engineer ing design, policy setting, allocation of resources, investment strategies, etc.).

It presents and analyzes implementations aimed at applications to the computation of zero points, fixed points, nonlinear eigenvalue problems, bifurcation and turning points, and economic equilibria.

Methods for minimizing functions with discontinuous gradients are gaining in importance and the ~xperts in the computational methods of mathematical programming tend to agree that progress in the development of algorithms for minimizing nonsmooth functions is the key to the con struction of efficient techniques for solving large scale problems.

As suggested by the title of this book Numerical Toolbox for Verified Computing, we present an extensive set of sophisticated tools to solve basic numerical problems with a verification of the results.

ELLP ACK is a many faceted system for solving elliptic partial differential equations. Many people will find ELLP ACK an easy way to solve simple or moderately complex elliptic problems.

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Preliminaries . * . * . * . * * . 8 . * . Examples of Various Step-Weight Functions cp(x) . * . * . * . * . 9 . The K-Functional and the Modulus of Continuity ... 10 . The Upper Estimate, Kr.tp(f, tr)p ~ Mw;(f, t)p, Case I . 12 . 16 . 20 . A Modified K-Functional . 24 . 26 . 28 .

Research on non-standard finite element methods is evolving rapidly and in this text Brezzi and Fortin give a general framework in which the development is taking place. The presentation is built around a few classic examples: Dirichlet's problem, Stokes problem, Linear elasticity.

Designed to give a contemporary international survey of research activities in approximation theory and special functions, this book brings together the work of approximation theorists from North America, Western Europe, Asia, Russia, the Ukraine, and several other former Soviet countries.

Many mathematicians, scientists, and engineers are familiar with the Fast Fourier Transform, a method based upon the Discrete Fourier Transform. Such problems include problems over finite, semi-infinite, or infinite domains, problems with singularities, and boundary layer problems.

Overview of Numerical Quadrature The numerical evaluation of integrals is one of the oldest problems in mathematics.

The shape optimization problem for such a structure consists in finding a geometry of the structure which minimizes a given functional (e. The boundary is smooth or piecewise smooth, so boundary value problems that are defined in the domain and associated with the classical partial differential equations of mathematical physics are well posed.

This book, written by one of the leading specialists of optimization theory, sets out to provide - for a wide readership including engineers, economists and optimization specialists, from graduate student level on - a brief yet quite complete exposition of this most effective method of solution of optimization problems.