Error Control and Adaptivity in Scientific Computing

Author: Haydar Bulgak,Christoph Zenger

Publisher: Springer Science & Business Media

ISBN: 9401146470

Category: Mathematics

Page: 354

View: 5894

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: 2351

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: 2491

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: 3457

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

Numerical integration

recent developments, software, and applications

Author: Terje O. Espelid,North Atlantic Treaty Organization. Scientific Affairs Division

Publisher: Kluwer Academic Pub

ISBN: N.A

Category: Computers

Page: 367

View: 9921

This volume contains the proceedings of the NATO Advanced Research Workshop on Numerical Integration that took place in Bergen, Norway, in June 1991. It includes papers for all invited talks and a selection of contributed talks. The papers are organized into four parts: numerical integration rules, numerical integration error analysis, numerical integration applications and numerical integration algorithms and software; many papers are relevant to more than one category. The workshop studied the state of the art in numerical integration (both single and multidimensional). The book contains a number of survey papers by experts on themes such as: numerical solution of integral equations, cubature formulae construction, handling singularities in finite elements, statistical applications, lattice rules, error estimates, error bounds and software.

Resilience and Risk

Methods and Application in Environment, Cyber and Social Domains

Author: Igor Linkov,José Manuel Palma-Oliveira

Publisher: Springer

ISBN: 9402411232

Category: Computers

Page: 580

View: 6567

This volume addresses the challenges associated with methodology and application of risk and resilience science and practice to address emerging threats in environmental, cyber, infrastructure and other domains. The book utilizes the collective expertise of scholars and experts in industry, government and academia in the new and emerging field of resilience in order to provide a more comprehensive and universal understanding of how resilience methodology can be applied in various disciplines and applications. This book advocates for a systems-driven view of resilience in applications ranging from cyber security to ecology to social action, and addresses resilience-based management in infrastructure, cyber, social domains and methodology and tools. Risk and Resilience has been written to open up a transparent dialog on resilience management for scientists and practitioners in all relevant academic disciplines and can be used as supplement in teaching risk assessment and management courses.

Error Estimation and Adaptive Discretization Methods in Computational Fluid Dynamics

Author: Timothy J Barth,Herman Deconinck

Publisher: Springer Science & Business Media

ISBN: 3662051893

Category: Mathematics

Page: 349

View: 7218

As computational fluid dynamics (CFD) is applied to ever more demanding fluid flow problems, the ability to compute numerical fluid flow solutions to a user specified tolerance as well as the ability to quantify the accuracy of an existing numerical solution are seen as essential ingredients in robust numerical simulation. Although the task of accurate error estimation for the nonlinear equations of CFD seems a daunting problem, considerable effort has centered on this challenge in recent years with notable progress being made by the use of advanced error estimation techniques and adaptive discretization methods. To address this important topic, a special course wasjointly organized by the NATO Research and Technology Office (RTO), the von Karman Insti tute for Fluid Dynamics, and the NASA Ames Research Center. The NATO RTO sponsored course entitled "Error Estimation and Solution Adaptive Discretization in CFD" was held September 10-14, 2002 at the NASA Ames Research Center and October 15-19, 2002 at the von Karman Institute in Belgium. During the special course, a series of comprehensive lectures by leading experts discussed recent advances and technical progress in the area of numerical error estimation and adaptive discretization methods with spe cific emphasis on computational fluid dynamics. The lecture notes provided in this volume are derived from the special course material. The volume con sists of 6 articles prepared by the special course lecturers.

BPR

Author: N.A

Publisher: N.A

ISBN: N.A

Category: American literature

Page: N.A

View: 9299


Boekblad

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Netherlands

Page: N.A

View: 6442


Real Time Computing

Author: Alexander D. Stoyenko

Publisher: Springer Science & Business Media

ISBN: 3642880495

Category: Computers

Page: 766

View: 7146

NATO's Division of Scientific and Environmental Affairs sponsored this Advan ced Study Institute because it was felt to be timely to cover this important and challengjng subject for the first time in the framework of NATO's ASI programme. The significance of real-time systems in everyones' life is rapidly growing. The vast spectrum of these systems can be characterised by just a few examples of increasing complexity: controllers in washing machines, air traffic control systems, control and safety systems of nuclear power plants and, finally, future military systems like the Strategic Defense Initiative (SDI). The import ance of such systems for the well-being of people requires considerable efforts in research and development of highly reliable real-time systems. Furthermore, the competitiveness and prosperity of entire nations now depend on the early app lication and efficient utilisation of computer integrated manufacturing systems (CIM), of which real-time systems are an essential and decisive part. Owing to its key significance in computerised defence systems, real-time computing has also a special importance for the Alliance. The early research and development activities in this field in the 1960s and 1970s aimed towards improving the then unsatisfactory software situation. Thus, the first high-level real-time languages were defined and developed: RTL/2, Coral 66, Procol, LTR, and PEARL. In close connection with these language develop ments and with the utilisation of special purpose process control peripherals, the research on real-time operating systems advanced considerably.

Nonlinear Stochastic Problems

Author: S. Bucy,J.M.F Moura

Publisher: Springer Science & Business Media

ISBN: 9789027715906

Category: Mathematics

Page: 623

View: 5004

This volume corresponds to the invited lectures and advanced research papers presented at the NATD Advanced Study Institute on Nonlinear Stochastic Problems with emphasis on Identification, Signal Processing, Control and Nonlinear Filtering held in Algarve (Portugal), on May 1982. The book is a blend of theoretical issues, algorithmic implementation aspects, and application examples. In many areas of science and engineering, there are problems which are intrinsically nonlinear 3nd stochastic in nature. Clear examples arise in identification and mOdeling, signal processing, nonlinear filtering, stochastic and adaptive conLrol. The meeting was organized because it was felt that there is a need for discussion of the methods and philosophy underlying these different areas, and in order to communicate those approaches that have proven to be effective. As the computational technology progresses, more general approaches to a number of problems which have been treated previously by linearization and perturbation methods become feasible and rewarding.

Computer and Information Science Applications in Bioprocess Engineering

Author: Antonio R. Moreira,Kimberlee K. Wallace

Publisher: Springer Science & Business Media

ISBN: 9780792338659

Category: Science

Page: 477

View: 7882

Biotechnology has been labelled as one of the key technologies of the last two decades of the 20th century, offering solutions to problems ranging from food and agricultural production to pharmaceutical and medical applications, as well as environmental and bioremediation problems. Biological processes, however, are complex and the prevailing mechanisms are either unknown or poorly understood. This means that adequate techniques for data acquisition and analysis, leading to appropriate modelling and simulation packages that can be superimposed on the engineering principles, need to be routine tools for future biotechnologists. This volume presents a summary of the most recent work in the field, covering: instrumentation systems; enzyme technology; environmental biotechnology; food applications; and metabolic engineering.