Error Control and Adaptivity in Scientific Computing

Author: Haydar Bulgak,Christoph Zenger

Publisher: Springer Science & Business Media

ISBN: 9401146470

Category: Mathematics

Page: 354

View: 5408

One of the main ways by which we can understand complex processes is to create computerised numerical simulation models of them. Modern simulation tools are not used only by experts, however, and reliability has therefore become an important issue, meaning that it is not sufficient for a simulation package merely to print out some numbers, claiming them to be the desired results. An estimate of the associated error is also needed. The errors may derive from many sources: errors in the model, errors in discretization, rounding errors, etc. Unfortunately, this situation does not obtain for current packages and there is a great deal of room for improvement. Only if the error can be estimated is it possible to do something to reduce it. The contributions in this book cover many aspects of the subject, the main topics being error estimates and error control in numerical linear algebra algorithms (closely related to the concept of condition numbers), interval arithmetic and adaptivity for continuous models.

Numerical Algebra, Matrix Theory, Differential-Algebraic Equations and Control Theory

Festschrift in Honor of Volker Mehrmann

Author: Peter Benner,Matthias Bollhöfer,Daniel Kressner,Christian Mehl,Tatjana Stykel

Publisher: Springer

ISBN: 3319152602

Category: Mathematics

Page: 608

View: 9782

This edited volume highlights the scientific contributions of Volker Mehrmann, a leading expert in the area of numerical (linear) algebra, matrix theory, differential-algebraic equations and control theory. These mathematical research areas are strongly related and often occur in the same real-world applications. The main areas where such applications emerge are computational engineering and sciences, but increasingly also social sciences and economics. This book also reflects some of Volker Mehrmann's major career stages. Starting out working in the areas of numerical linear algebra (his first full professorship at TU Chemnitz was in "Numerical Algebra," hence the title of the book) and matrix theory, Volker Mehrmann has made significant contributions to these areas ever since. The highlights of these are discussed in Parts I and II of the present book. Often the development of new algorithms in numerical linear algebra is motivated by problems in system and control theory. These and his later major work on differential-algebraic equations, to which he together with Peter Kunkel made many groundbreaking contributions, are the topic of the chapters in Part III. Besides providing a scientific discussion of Volker Mehrmann's work and its impact on the development of several areas of applied mathematics, the individual chapters stand on their own as reference works for selected topics in the fields of numerical (linear) algebra, matrix theory, differential-algebraic equations and control theory.

Multigrid

Author: Ulrich Trottenberg,Cornelius W. Oosterlee,Anton Schuller

Publisher: Academic Press

ISBN: 9780127010700

Category: Mathematics

Page: 631

View: 7408

Mathematics of Computing -- Numerical Analysis.

Error-controlled adaptive finite elements in solid mechanics

Author: Erwin Stein,E. Ramm

Publisher: Wiley

ISBN: 9780471496502

Category: Mathematics

Page: 410

View: 5027

Finite Element Methods are used for numerous engineering applications where numerical solutions of partial differential equations are needed. As computers can now deal with the millions of parameters used in these methods, automatic error estimation and automatic adaptation of the utilised method (according to this error estimation), has become a hot research topic. This text offers comprehensive coverage of this new field of automatic adaptation and error estimation, bringing together the work of eight outstanding researchers in this field who have completed a six year national research project within the German Science Foundation. The result is a state-of-the-art work in true reference style. Each chapter is self-contained and covers theoretical, algorithmic and software presentations as well as solved problems. A main feature consists of several carefully elaborated benchmarks of 2D- and 3D- applications. * First book to go beyond the Finite Element Method in itself * Covers material from a new research area * Presents benchmarks of 2D- and 3D- applications * Fits with the new trend for genetic strategies in engineering

BPR

Author: N.A

Publisher: N.A

ISBN: N.A

Category: American literature

Page: N.A

View: 3460


Boekblad

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Netherlands

Page: N.A

View: 6632


Choice

Publication of the Association of College and Research Libraries, a Division of the American Library Association

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Academic libraries

Page: N.A

View: 5017


Materialien und Systeme

Author: Uwe Hartmann

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3486855425

Category: Science

Page: 581

View: 1715

Volume 2 of this four-part textbook is devoted to the full range of materials relevant to nanostructural research and nanotechnology. These materials encompass soft condensed matter, including biological matter, along with nano-scale building blocks in the form of monolayer films, nanotubes, clusters, and biological machines.

Minimax models in the theory of numerical methods

Author: Alekseĭ Grigorʹevich Sukharev

Publisher: Kluwer Academic Pub

ISBN: 9780792318217

Category: Business & Economics

Page: 256

View: 9138

The efficiency of computational methods and the choice of the most efficient methods for solving a specific problem or a specific class of problems have always played an important role in numerical analysis. Optimization of the computerized solution process is now a major problem of applied mathematics, which stimulates the search for new computational methods and ways to implement them. In Minimax Models in the Theory of Numerical Methods, methods for estimating the efficiency of computational algorithms and problems of their optimality are studied within the framework of a general computation model. The subjects dealt with in this important book are very different from the traditional subjects of computational methods. Close attention is paid to adaptive (sequential) computational algorithms, the process of computation being regarded as a controlled process and the algorithm as a control strategy. This approach allows methods of game theory and othermethods of operations research and systems analysis to be widely used for constructing optimal algorithms. The goal underlying the study of the various computation models dealt with in this title is the construction of concrete numerical algorithms admitting program implementation. The central role belongs to the concept of a sequentially optimal algorithm, which in many cases reflects the characteristics of real-life computational processes more fully than the traditional optimality concepts.