Advances in Iterative Methods for Nonlinear Equations

Author: Sergio Amat,Sonia Busquier

Publisher: Springer

ISBN: 331939228X

Category: Mathematics

Page: 286

View: 1088

This book focuses on the approximation of nonlinear equations using iterative methods. Nine contributions are presented on the construction and analysis of these methods, the coverage encompassing convergence, efficiency, robustness, dynamics, and applications. Many problems are stated in the form of nonlinear equations, using mathematical modeling. In particular, a wide range of problems in Applied Mathematics and in Engineering can be solved by finding the solutions to these equations. The book reveals the importance of studying convergence aspects in iterative methods and shows that selection of the most efficient and robust iterative method for a given problem is crucial to guaranteeing a good approximation. A number of sample criteria for selecting the optimal method are presented, including those regarding the order of convergence, the computational cost, and the stability, including the dynamics. This book will appeal to researchers whose field of interest is related to nonlinear problems and equations, and their approximation.

Advances in Numerical Analysis: Nonlinear partial differential equations and dynamical systems

Author: William Allan Light,Science and Engineering Research Council (Great Britain)

Publisher: Oxford University Press, USA

ISBN: 9780198534389

Category: Mathematics

Page: 288

View: 8722

The aim of this volume is to present research workers and graduate students in numerical analysis with a state-of-the-art survey of some of the most active areas of numerical analysis. This, and a companion volume, arise from a Summer School intended to cover recent trends in the subject. The chapters are written by the main lecturers at the School. Each is an internationally renowned expert in his respective field. This volume covers research in the numerical analysis of nonlinear phenomena: evolution equations, free boundary problems, spectral methods, and numerical methods for dynamical systems, nonlinear stability, and differential equations on manifolds.

Recent Advances in Computational and Applied Mathematics

Author: Theodore E. Simos

Publisher: Springer Science & Business Media

ISBN: 9789048199815

Category: Mathematics

Page: 310

View: 2534

This multi-author contributed proceedings volume contains recent advances in several areas of Computational and Applied Mathematics. Each review is written by well known leaders of Computational and Applied Mathematics. The book gives a comprehensive account of a variety of topics including – Efficient Global Methods for the Numerical Solution of Nonlinear Systems of Two point Boundary Value Problems; Advances on collocation based numerical methods for Ordinary Differential Equations and Volterra Integral Equations; Basic Methods for Computing Special Functions, Melt Spinning: Optimal Control and Stability Issues; Brief survey on the CP methods for the Schrödinger equation; Symplectic Partitioned Runge-Kutta methods for the numerical integration of periodic and oscillatory problems. Recent Advances in Computational and Applied Mathematics is aimed at advanced undergraduates and researchers who are working in these fast moving fields.

Advances in Numerical Simulation of Nonlinear Water Waves

Author: Qingwei Ma

Publisher: World Scientific

ISBN: 9812836500

Category: Mathematics

Page: 700

View: 2223

Most of the Earth''s surface is covered by water. Our everyday lives and activities are affected by water waves in oceans, such as the tsunami that occurred in the Indian Ocean on 26 December 2004. This indicates how important it is for us to fully understand water waves, in particular the very large ones. One way to do so is to perform numerical simulation based on the nonlinear theory. Considerable research advances have been made in this area over the past decade by developing various numerical methods and applying them to emerging problems; however, until now there has been no comprehensive book to reflect these advances. This unique volume aims to bridge this gap. This book contains 18 self-contained chapters written by more than 50 authors from 12 different countries, many of whom are world-leading experts in the field. Each chapter is based mainly on the pioneering work of the authors and their research teams over the past decades.The chapters altogether deal with almost all numerical methods that have so far been employed to simulate nonlinear water waves and cover many important and very interesting applications, such as overturning waves, breaking waves, waves generated by landslides, freak waves, solitary waves, tsunamis, sloshing waves, interaction of extreme waves with beaches, interaction with fixed structures, and interaction with free-response floating structures. Therefore, this book provides a comprehensive overview of the state-of-the-art research and key achievements in numerical modeling of nonlinear water waves, and serves as a unique reference for postgraduates, researchers and senior engineers working in industry.

Control and Dynamic Systems V32: Advances in Aerospace Systems Dynamics and Control Systems Part 2 of 3

Advances in Theory and Applications

Author: C.T. Leonides

Publisher: Academic Press

ISBN: 0323162436

Category: Technology & Engineering

Page: 294

View: 6671

Control and Dynamic Systems: Advances in Theory in Applications, Volume 32: Advances in Aerospace Systems Dynamics and Control Systems, Part 2 of 3 deals with significant advances in technologies which support the development of aerospace systems. It also presents several algorithms and computational techniques used in complex aerospace systems. After discussing flight management systems (FMS), this volume presents techniques for treating complex aerospace systems models. These techniques include parameter identification, asymptotic perturbation method, reliability techniques, constrained optimization techniques, and computation methods for decoy discrimination and optimal targeting. This book is an excellent reference for research and professional workers in the field who want a comprehensive source of techniques with significant applied implications.

Advances in Neural Information Processing Systems 19

Proceedings of the 2006 Conference

Author: Bernhard Schölkopf,John Platt,Thomas Hofmann

Publisher: MIT Press

ISBN: 0262195682

Category: Computers

Page: 1643

View: 6841

The annual conference on NIPS is the flagship conference on neural computation. It draws top academic researchers from around the world & is considered to be a showcase conference for new developments in network algorithms & architectures. This volume contains all of the papers presented at NIPS 2006.

Numerical Methods for Differential Systems

Recent Developments in Algorithms, Software, and Applications

Author: L. Lapidus,W. E. Schiesser

Publisher: Elsevier

ISBN: 148326985X

Category: Mathematics

Page: 304

View: 2315

Numerical Methods for Differential Systems: Recent Developments in Algorithms, Software, and Applications reviews developments in algorithms, software, and applications of numerical methods for differential systems. Topics covered include numerical algorithms for ordinary and partial differential equations (ODE/PDEs); theoretical approaches to the solution of nonlinear algebraic and boundary value problems via associated differential systems; integration algorithms for initial-value ODEs with particular emphasis on stiff systems; finite difference algorithms; and general- and special-purpose computer codes for ODE/PDEs. Comprised of 15 chapters, this book begins with an introduction to high-order A-stable averaging algorithms for stiff differential systems, followed by a discussion on second derivative multistep formulas based on g-splines; numerical integration of linearized stiff ODEs; and numerical solution of large systems of stiff ODEs in a modular simulation framework. Subsequent chapters focus on numerical methods for mass action kinetics; a systematized collection of codes for solving two-point boundary value problems; general software for PDEs; and the choice of algorithms in automated method of lines solution of PDEs. The final chapter is devoted to quality software for ODEs. This monograph should be of interest to mathematicians, chemists, and chemical engineers.

Numerical Methods for Hyperbolic and Kinetic Problems

CEMRACS 2003, Summer Research Center in Mathematics and Advances in Scientific Computing, July 21- August 29, 2003, CIRM, Marseille, France

Author: Stéphane Cordier

Publisher: European Mathematical Society

ISBN: 9783037190128

Category: Differential equations, Hyperbolic

Page: 359

View: 5974

Hyperbolic and kinetic equations arise in a large variety of industrial problems. For this reason, the Summer Mathematical Research Center on Scientific Computing and its Applications (CEMRACS), held at the Center of International Research in Mathematics (CIRM) in Luminy, was devoted to this topic. During a six-week period, junior and senior researchers worked full time on several projects proposed by industry and academia. Most of this work was completed later on, and the present book reflects these results. The articles address modelling issues as well as the development and comparisons of numerical methods in different situations. The applications include multi-phase flows, plasma physics, quantum particle dynamics, radiative transfer, sprays, and aeroacoustics. The text is aimed at researchers and engineers interested in applications arising from modelling and numerical simulation of hyperbolic and kinetic problems.

Advances in computer methods for partial differential equations-V

proceedings of the fifth IMACS International Symposium on Computer Methods for Partial Differential Equations, held at Lehigh University, Bethlehem, Pennsylvania, U.S.A., June 19-June 21, 1984

Author: International Association for Mathematics and Computers in Simulation,United States. Office of Naval Research

Publisher: N.A

ISBN: N.A

Category: Differential equations, Partial

Page: 558

View: 5837


Advances in Numerical Heat Transfer

Author: W. J. Minkowycz

Publisher: CRC Press

ISBN: 9781420095227

Category: Science

Page: 400

View: 833

Definitive Treatment of the Numerical Simulation of Bioheat Transfer and Fluid Flow Motivated by the upwelling of current interest in subjects critical to human health, Advances in Numerical Heat Transfer, Volume 3 presents the latest information on bioheat and biofluid flow. Like its predecessors, this volume assembles a team of renowned international researchers who cover both fundamentals and applications. It explores ingenious modeling techniques and innovative numerical simulation for solving problems in biomedical engineering. The text begins with the modeling of thermal transport by perfusion within the framework of the porous-media theory. It goes on to review other perfusion models, different forms of the bioheat equation for several thermal therapies, and thermal transport in individual blood vessels. The book then describes thermal methods of tumor detection and treatment as well as issues of blood heating and cooling during lengthy surgeries. It also discusses how the enhancement of heat conduction in tumor tissue by intruded nanoparticles improves the efficacy of thermal destruction of the tumor. The final chapters focus on whole-body thermal models, issues concerning the thermal treatment of cancer, and a case study on the thermal ablation of an enlarged prostate.

Advances in Scattering and Biomedical Engineering

Proceedings of the Sixth International Workshop, Tsepelovo, Greece, 18-21 September 2003

Author: Dimitrios Ioannou Fotiadis,Christos Massalas

Publisher: World Scientific

ISBN: 9789812702593

Category: Biological models

Page: 648

View: 7959

This volume consists of the papers presented at the 6th International Workshop on Scattering Theory and Biomedical Engineering. Organized every two years, this workshop provides an overview of the hot topics in scattering theory and biomedical technology, and brings together young researchers and senior scientists, creating a forum for the exchange of new scientific ideas. At the sixth meeting, all the invited speakers, who are recognized as being eminent in their field and, more important, as being stimulating speakers, presented their latest achievements. The proceedings have been selected for coverage in: . OCo Index to Scientific & Technical Proceedings- (ISTP- / ISI Proceedings). OCo Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings). OCo CC Proceedings OCo Biomedical, Biological & Agricultural Sciences. Contents: Scattering Theory: On the Elastic Scattering Problem from Cubic Anisotropic Inclusions (K A Anagnostopoulos & A Charalambopoulos); On the Scattering of Spherical Electromagnetic Waves by a Penetrable Chiral Obstacle (C Athanasiadis et al.); A Factorization Methods for Maxwell''s Equations (A Kirsch); Acoustic Scattering by an Impenetrable Spheroid (J A Roumeliotis et al.); Applied Mathematics: Wave Dispersion Phenomena in Concrete (D G Aggelis & D Polyzos); Homogenization of Maxwell''s Equations in Dissipative Bianisotropic Media (G Barbatis & I G Stratis); Moment''s Method for Inverse Boundary Value Problems (Y Kurylev); Cleaning Astronomical Databases Using Hough Transforms and Renewal Strings (C K I Williams et al.); Mesh Modeling and its Applications in Image Processing (Y Yang); Biomedical Engineering: Autoregressive Spectral Analysis of Phrenic Neurogram Before and After Vagotomy in the Piglet (S Agner & M Akay); Classifying Patterns Relating to the Early Development of Posttraumatic Stress Disorder Using Principal Components Analysis (B Knorr et al.); Fingerprint Verification Based on Image Processing Segmentation Using an Onion Algorithm of Computational Geometry (M Poulos et al.); and other papers. Readership: Graduate students, academics and researchers in biomedical engineering, bioinformatics and mathematical biology."

Recent Developments in Discontinuous Galerkin Finite Element Methods for Partial Differential Equations

2012 John H Barrett Memorial Lectures

Author: Xiaobing Feng,Ohannes Karakashian,Yulong Xing

Publisher: Springer Science & Business Media

ISBN: 3319018183

Category: Mathematics

Page: 279

View: 2853

The field of discontinuous Galerkin finite element methods has attracted considerable recent attention from scholars in the applied sciences and engineering. This volume brings together scholars working in this area, each representing a particular theme or direction of current research. Derived from the 2012 Barrett Lectures at the University of Tennessee, the papers reflect the state of the field today and point toward possibilities for future inquiry. The longer survey lectures, delivered by Franco Brezzi and Chi-Wang Shu, respectively, focus on theoretical aspects of discontinuous Galerkin methods for elliptic and evolution problems. Other papers apply DG methods to cases involving radiative transport equations, error estimates, and time-discrete higher order ALE functions, among other areas. Combining focused case studies with longer sections of expository discussion, this book will be an indispensable reference for researchers and students working with discontinuous Galerkin finite element methods and its applications.

Recent Advances in Fracture Mechanics

Honoring Mel and Max Williams

Author: Wolfgang Knauss,R.A. Schapery

Publisher: Springer Science & Business Media

ISBN: 9780792358244

Category: Science

Page: 431

View: 1117

The papers in this volume represent a considerable cross-section of the field of fracture mechanics, a testimony to the breadth of interest that Mel and Max Williams' friends share with them. Several are expanded versions of papers that were given in special sessions honoring them at the 1997 Ninth International Conference on Fracture Mechanics in Sydney, Australia. The subjects treated in this volume can be classified as follows: dynamic fracture problems as viewed primarily from a classical continuum point of view; analysis of relatively general crack geometrics; fracture problems of polymers and other relatively ductile materials; scaling rules that allow extension of results obtained at one size to be translated into behavior at different size scales; problems dealing with interactions that produce complex stress fields; fracture problems directly appropriate to composite materials; analysis of stress concentrations in anisotropic, elastic solids; and the problem of cracks in thin plates bending. This volume will be of interest to engineers and scientists working on all aspects of the physics and mechanics of fracture.

Advances in Multiuser Detection

Author: Michael L. Honig

Publisher: John Wiley & Sons

ISBN: 9780470473801

Category: Technology & Engineering

Page: 512

View: 3102

A Timely Exploration of Multiuser Detection in Wireless Networks During the past decade, the design and development of current and emerging wireless systems have motivated many important advances in multiuser detection. This book fills an important need by providing a comprehensive overview of crucial recent developments that have occurred in this active research area. Each chapter is contributed by noted experts and is meant to serve as a self-contained treatment of the topic. Coverage includes: Linear and decision feedback methods Iterative multiuser detection and decoding Multiuser detection in the presence of channel impairments Performance analysis with random signatures and channels Joint detection methods for MIMO channels Interference avoidance methods at the transmitter Transmitter precoding methods for the MIMO downlink This book is an ideal entry point for exploring ongoing research in multiuser detection and for learning about the field's existing unsolved problems and issues. It is a valuable resource for researchers, engineers, and graduate students who are involved in the area of digital communications.

Modern Advances in Software and Solution Algorithms for Reservoir Simulation

Author: N.A

Publisher: Stanford University

ISBN: N.A

Category:

Page: N.A

View: 1528

As conventional hydrocarbon resources dwindle, and environmentally-driven markets start to form and mature, investments are expected to shift into the development of novel emerging subsurface process technologies. While these processes are characterized by a high commercial potential, they are also typically associated with high technical risk. The time-to-market along comparable development pipelines, such as for Enhanced Oil Recovery (EOR) methods in the Oil and Gas sector, is on the order of tens of years. It is anticipated that in the near future, there will be much value in developing simulation tools that can shorten time-to-market cycles, making investment shifts more attractive. There are two forces however that may debilitate us from delivering simulation as a scientific discovery tool. The first force is the growing nonlinearity of the problem base. The second force is the flip-side of a double edged sword; a rapidly evolving computer architecture scene. The first part of this work concerns the formulation and linearization of nonlinear simultaneous equations; the archetypal inflexible component of all large scale simulators. The proposed solution is an algorithmic framework and library of data-types called the Automatically Differentiable Expression Templates Library (ADETL). The ADETL provides generic representations of variables and discretized expressions on a simulation grid, and the data-types provide algorithms employed behind the scenes to automatically compute the sparse analytical Jacobian. Using the library, large-scale simulators can be developed rapidly by simply writing the residual equations, and without any hand differentiation, hand crafted performance tuning loops, or any other low-level constructs. A key challenge that is addressed is in enabling this level of abstraction and programming ease while making it easy to develop code that runs fast. Faster than any of several existing automatic differentiation packages, faster than any purely Object Oriented implementation, and at least in the order of the execution speed of code delivered by a development team with hand-optimized residuals, analytical derivatives, and Jacobian assembly routines. A second challenge is in providing a generic multi-layered software framework that incorporates plug-in low-level constructs tuned to emerging architectures. The inception of the ADETL spurred an effort to develop the new generation AD-GPRS simulator, which we use to demonstrate the powers of the ADETL. We conclude with a thought towards a future where simulators can write themselves. The second part of this work develops nonlinear methods that can exploit the nature of the underlying physics to deal with the current and upcoming challenges in physical nonlinearity. The Fully Implicit Method offers unconditional stability of the discrete approximations. This stability comes at the expense of transferring the inherent physical stiffness onto the coupled nonlinear residual equations that are solved at each timestep. Current reservoir simulators apply safe-guarded variants of Newton's method that can neither guarantee convergence, nor provide estimates of the relation between convergence rate and timestep size. In practice, timestep chops become necessary, and they are guided heuristically. With growing complexity, convergence difficulties can lead to substantial losses in computational effort and prohibitively small timesteps. We establish an alternate class of nonlinear iteration that converges and that associates a timestep to each iteration. Moreover, the linear solution process within each iteration is performed locally. Several challenging examples are presented, and the results demonstrate the robustness and computational efficiency of the proposed class of methods. We conclude with thoughts to unify timestepping and iterative nonlinear methods.

Advances in Mathematics Research

Author: Gabriel Oyibo

Publisher: Nova Publishers

ISBN: 9781590334300

Category: Mathematics

Page: 211

View: 5720

Mathematics has been behind many of humanity's most significant advances in fields as varied as genome sequencing, medical science, space exploration, and computer technology. But those breakthroughs were yesterday. Where will mathematicians lead us tomorrow and can we help shape that destiny? This book assembles carefully selected articles highlighting and explaining cutting-edge research and scholarship in mathematics.

Advances in Computer Science, Intelligent Systems and Environment

Author: David Jin,Sally Lin

Publisher: Springer Science & Business Media

ISBN: 3642237568

Category: Computers

Page: 776

View: 6651

CSISE2011 is an integrated conference concentrating its focus upon Computer Science,Intelligent System and Environment. In the proceeding, you can learn much more knowledge about Computer Science, Intelligent System and Environment of researchers all around the world. The international conference will provide a forum for engineers, scientist, teachers and all researchers to discuss their latest research achievements and their future research plan. The main role of the proceeding is to be used as an exchange pillar for researchers who are working in the mentioned field. In order to meet high standard of Springer ́s Advances in Intelligent and Soft Computing ,the organization committee has made their efforts to do the following things. Firstly, poor quality paper has been refused after reviewing course by anonymous referee experts. Secondly, periodically review meetings have been held around the reviewers about five times for exchanging reviewing suggestions. Finally, the conference organization had several preliminary sessions before the conference. Through efforts of different people and departments, the conference will be successful and fruitful. We hope that you can get much more knowledges from our CSISE2011, and we also hope that you can give us good suggestions to improve our work in the future.