Numerical Methods For Differential Equations Optimization And Technological Problems

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Numerical Methods for Differential Equations, Optimization, and Technological Problems

Sergey Repin,Timo Tiihonen,Tero Tuovinen
Numerical Methods for Differential Equations Optimization and Technological Problems Book PDF

Author : Sergey Repin,Timo Tiihonen,Tero Tuovinen
Publisher : Springer Science & Business Media
Page : 446 pages
File Size : 44,5 Mb
Release : 2012-10-13
Category : Technology & Engineering
ISBN : 9789400752870

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Numerical Methods for Differential Equations, Optimization, and Technological Problems by Sergey Repin,Timo Tiihonen,Tero Tuovinen Pdf

This book contains the results in numerical analysis and optimization presented at the ECCOMAS thematic conference “Computational Analysis and Optimization” (CAO 2011) held in Jyväskylä, Finland, June 9–11, 2011. Both the conference and this volume are dedicated to Professor Pekka Neittaanmäki on the occasion of his sixtieth birthday. It consists of five parts that are closely related to his scientific activities and interests: Numerical Methods for Nonlinear Problems; Reliable Methods for Computer Simulation; Analysis of Noised and Uncertain Data; Optimization Methods; Mathematical Models Generated by Modern Technological Problems. The book also includes a short biography of Professor Neittaanmäki.

Numerical Methods for Energy Applications

Naser Mahdavi Tabatabaei,Nicu Bizon
Numerical Methods for Energy Applications Book PDF

Author : Naser Mahdavi Tabatabaei,Nicu Bizon
Publisher : Springer Nature
Page : 1033 pages
File Size : 52,7 Mb
Release : 2021-03-22
Category : Technology & Engineering
ISBN : 9783030621919

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Numerical Methods for Energy Applications by Naser Mahdavi Tabatabaei,Nicu Bizon Pdf

This book provides a thorough guide to the use of numerical methods in energy systems and applications. It presents methods for analysing engineering applications for energy systems, discussing finite difference, finite element, and other advanced numerical methods. Solutions to technical problems relating the application of these methods to energy systems are also thoroughly explored. Readers will discover diverse perspectives of the contributing authors and extensive discussions of issues including: • a wide variety of numerical methods concepts and related energy systems applications;• systems equations and optimization, partial differential equations, and finite difference method;• methods for solving nonlinear equations, special methods, and their mathematical implementation in multi-energy sources;• numerical investigations of electrochemical fields and devices; and• issues related to numerical approaches and optimal integration of energy consumption. This is a highly informative and carefully presented book, providing scientific and academic insight for readers with an interest in numerical methods and energy systems.

Matrix, Numerical, and Optimization Methods in Science and Engineering

Kevin W. Cassel
Matrix Numerical and Optimization Methods in Science and Engineering Book PDF

Author : Kevin W. Cassel
Publisher : Cambridge University Press
Page : 727 pages
File Size : 52,6 Mb
Release : 2021-03-04
Category : Mathematics
ISBN : 9781108479097

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Matrix, Numerical, and Optimization Methods in Science and Engineering by Kevin W. Cassel Pdf

Vector and matrix algebra -- Algebraic eigenproblems and their applications -- Differential eigenproblems and their applications -- Vector and matrix calculus -- Analysis of discrete dynamical systems -- Computational linear algebra -- Numerical methods for differential equations -- Finite-difference methods for boundary-value problems -- Finite-difference methods for initial-value problems -- Least-squares methods -- Data analysis : curve fitting and interpolation -- Optimization and root finding of algebraic systems -- Data-driven methods and reduced-order modeling.

Mathematical Analysis and Numerical Methods for Science and Technology

Robert Dautray,Jacques-Louis Lions
Mathematical Analysis and Numerical Methods for Science and Technology Book PDF

Author : Robert Dautray,Jacques-Louis Lions
Publisher : Springer
Page : 604 pages
File Size : 54,6 Mb
Release : 2015-03-20
Category : Mathematics
ISBN : 9783642615665

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Mathematical Analysis and Numerical Methods for Science and Technology by Robert Dautray,Jacques-Louis Lions Pdf

These 6 volumes - the result of a 10 year collaboration between the authors, two of France's leading scientists and both distinguished international figures - compile the mathematical knowledge required by researchers in mechanics, physics, engineering, chemistry and other branches of application of mathematics for the theoretical and numerical resolution of physical models on computers. Since the publication in 1924 of the "Methoden der mathematischen Physik" by Courant and Hilbert, there has been no other comprehensive and up-to-date publication presenting the mathematical tools needed in applications of mathematics in directly implementable form. The advent of large computers has in the meantime revolutionised methods of computation and made this gap in the literature intolerable: the objective of the present work is to fill just this gap. Many phenomena in physical mathematics may be modeled by a system of partial differential equations in distributed systems: a model here means a set of equations, which together with given boundary data and, if the phenomenon is evolving in time, initial data, defines the system. The advent of high-speed computers has made it possible for the first time to calculate values from models accurately and rapidly. Researchers and engineers thus have a crucial means of using numerical results to modify and adapt arguments and experiments along the way. Every facet of technical and industrial activity has been affected by these developments. Modeling by distributed systems now also supports work in many areas of physics (plasmas, new materials, astrophysics, geophysics), chemistry and mechanics and is finding increasing use in the life sciences.

Partial Differential Equations

Mark S. Gockenbach
Partial Differential Equations Book PDF

Author : Mark S. Gockenbach
Publisher : SIAM
Page : 665 pages
File Size : 47,9 Mb
Release : 2010-12-02
Category : Mathematics
ISBN : 9780898719352

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Partial Differential Equations by Mark S. Gockenbach Pdf

A fresh, forward-looking undergraduate textbook that treats the finite element method and classical Fourier series method with equal emphasis.

Introduction to Nonsmooth Optimization

Adil Bagirov,Napsu Karmitsa,Marko M. Mäkelä
Introduction to Nonsmooth Optimization Book PDF

Author : Adil Bagirov,Napsu Karmitsa,Marko M. Mäkelä
Publisher : Springer
Page : 372 pages
File Size : 50,6 Mb
Release : 2014-08-12
Category : Business & Economics
ISBN : 9783319081144

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Introduction to Nonsmooth Optimization by Adil Bagirov,Napsu Karmitsa,Marko M. Mäkelä Pdf

This book is the first easy-to-read text on nonsmooth optimization (NSO, not necessarily differentiable optimization). Solving these kinds of problems plays a critical role in many industrial applications and real-world modeling systems, for example in the context of image denoising, optimal control, neural network training, data mining, economics and computational chemistry and physics. The book covers both the theory and the numerical methods used in NSO and provide an overview of different problems arising in the field. It is organized into three parts: 1. convex and nonconvex analysis and the theory of NSO; 2. test problems and practical applications; 3. a guide to NSO software. The book is ideal for anyone teaching or attending NSO courses. As an accessible introduction to the field, it is also well suited as an independent learning guide for practitioners already familiar with the basics of optimization.

Computer-Aided Analysis of Difference Schemes for Partial Differential Equations

Victor G. Ganzha,E. V. Vorozhtsov
Computer Aided Analysis of Difference Schemes for Partial Differential Equations Book PDF

Author : Victor G. Ganzha,E. V. Vorozhtsov
Publisher : John Wiley & Sons
Page : 458 pages
File Size : 48,5 Mb
Release : 2011-03-01
Category : Science
ISBN : 9781118030851

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Computer-Aided Analysis of Difference Schemes for Partial Differential Equations by Victor G. Ganzha,E. V. Vorozhtsov Pdf

Advances in computer technology have conveniently coincided withtrends in numerical analysis toward increased complexity ofcomputational algorithms based on finite difference methods. It isno longer feasible to perform stability investigation of thesemethods manually--and no longer necessary. As this book shows,modern computer algebra tools can be combined with methods fromnumerical analysis to generate programs that will do the jobautomatically. Comprehensive, timely, and accessible--this is the definitivereference on the application of computerized symbolic manipulationsfor analyzing the stability of a wide range of difference schemes.In particular, it deals with those schemes that are used to solvecomplex physical problems in areas such as gas dynamics, heat andmass transfer, catastrophe theory, elasticity, shallow watertheory, and more. Introducing many new applications, methods, and concepts,Computer-Aided Analysis of Difference Schemes for PartialDifferential Equations * Shows how computational algebra expedites the task of stabilityanalysis--whatever the approach to stability investigation * Covers ten different approaches for each stability method * Deals with the specific characteristics of each method and itsapplication to problems commonly encountered by numerical modelers * Describes all basic mathematical formulas that are necessary toimplement each algorithm * Provides each formula in several global algebraic symboliclanguages, such as MAPLE, MATHEMATICA, and REDUCE * Includes numerous illustrations and thought-provoking examplesthroughout the text For mathematicians, physicists, and engineers, as well as forpostgraduate students, and for anyone involved with numericsolutions for real-world physical problems, this book provides avaluable resource, a helpful guide, and a head start ondevelopments for the twenty-first century.

Optimal Shape Design for Elliptic Systems

O. Pironneau
Optimal Shape Design for Elliptic Systems Book PDF

Author : O. Pironneau
Publisher : Springer Science & Business Media
Page : 179 pages
File Size : 54,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642877223

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Optimal Shape Design for Elliptic Systems by O. Pironneau Pdf

The study of optimal shape design can be arrived at by asking the following question: "What is the best shape for a physical system?" This book is an applications-oriented study of such physical systems; in particular, those which can be described by an elliptic partial differential equation and where the shape is found by the minimum of a single criterion function. There are many problems of this type in high-technology industries. In fact, most numerical simulations of physical systems are solved not to gain better understanding of the phenomena but to obtain better control and design. Problems of this type are described in Chapter 2. Traditionally, optimal shape design has been treated as a branch of the calculus of variations and more specifically of optimal control. This subject interfaces with no less than four fields: optimization, optimal control, partial differential equations (PDEs), and their numerical solutions-this is the most difficult aspect of the subject. Each of these fields is reviewed briefly: PDEs (Chapter 1), optimization (Chapter 4), optimal control (Chapter 5), and numerical methods (Chapters 1 and 4).

An Introduction to Neural Network Methods for Differential Equations

Neha Yadav,Anupam Yadav,Manoj Kumar
An Introduction to Neural Network Methods for Differential Equations Book PDF

Author : Neha Yadav,Anupam Yadav,Manoj Kumar
Publisher : Springer
Page : 114 pages
File Size : 48,5 Mb
Release : 2015-02-26
Category : Mathematics
ISBN : 9789401798167

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An Introduction to Neural Network Methods for Differential Equations by Neha Yadav,Anupam Yadav,Manoj Kumar Pdf

This book introduces a variety of neural network methods for solving differential equations arising in science and engineering. The emphasis is placed on a deep understanding of the neural network techniques, which has been presented in a mostly heuristic and intuitive manner. This approach will enable the reader to understand the working, efficiency and shortcomings of each neural network technique for solving differential equations. The objective of this book is to provide the reader with a sound understanding of the foundations of neural networks and a comprehensive introduction to neural network methods for solving differential equations together with recent developments in the techniques and their applications. The book comprises four major sections. Section I consists of a brief overview of differential equations and the relevant physical problems arising in science and engineering. Section II illustrates the history of neural networks starting from their beginnings in the 1940s through to the renewed interest of the 1980s. A general introduction to neural networks and learning technologies is presented in Section III. This section also includes the description of the multilayer perceptron and its learning methods. In Section IV, the different neural network methods for solving differential equations are introduced, including discussion of the most recent developments in the field. Advanced students and researchers in mathematics, computer science and various disciplines in science and engineering will find this book a valuable reference source.

Advances in Optimization and Numerical Analysis

S. Gomez,J.P. Hennart
Advances in Optimization and Numerical Analysis Book PDF

Author : S. Gomez,J.P. Hennart
Publisher : Springer Science & Business Media
Page : 285 pages
File Size : 48,6 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9789401583305

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Advances in Optimization and Numerical Analysis by S. Gomez,J.P. Hennart Pdf

In January 1992, the Sixth Workshop on Optimization and Numerical Analysis was held in the heart of the Mixteco-Zapoteca region, in the city of Oaxaca, Mexico, a beautiful and culturally rich site in ancient, colonial and modern Mexican civiliza tion. The Workshop was organized by the Numerical Analysis Department at the Institute of Research in Applied Mathematics of the National University of Mexico in collaboration with the Mathematical Sciences Department at Rice University, as were the previous ones in 1978, 1979, 1981, 1984 and 1989. As were the third, fourth, and fifth workshops, this one was supported by a grant from the Mexican National Council for Science and Technology, and the US National Science Foundation, as part of the joint Scientific and Technical Cooperation Program existing between these two countries. The participation of many of the leading figures in the field resulted in a good representation of the state of the art in Continuous Optimization, and in an over view of several topics including Numerical Methods for Diffusion-Advection PDE problems as well as some Numerical Linear Algebraic Methods to solve related pro blems. This book collects some of the papers given at this Workshop.

Large-Scale PDE-Constrained Optimization

Lorenz T. Biegler,Omar Ghattas,Matthias Heinkenschloss,Bart van Bloemen Waanders
Large Scale PDE Constrained Optimization Book PDF

Author : Lorenz T. Biegler,Omar Ghattas,Matthias Heinkenschloss,Bart van Bloemen Waanders
Publisher : Springer Science & Business Media
Page : 347 pages
File Size : 48,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642555084

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Large-Scale PDE-Constrained Optimization by Lorenz T. Biegler,Omar Ghattas,Matthias Heinkenschloss,Bart van Bloemen Waanders Pdf

Optimal design, optimal control, and parameter estimation of systems governed by partial differential equations (PDEs) give rise to a class of problems known as PDE-constrained optimization. The size and complexity of the discretized PDEs often pose significant challenges for contemporary optimization methods. With the maturing of technology for PDE simulation, interest has now increased in PDE-based optimization. The chapters in this volume collectively assess the state of the art in PDE-constrained optimization, identify challenges to optimization presented by modern highly parallel PDE simulation codes, and discuss promising algorithmic and software approaches for addressing them. These contributions represent current research of two strong scientific computing communities, in optimization and PDE simulation. This volume merges perspectives in these two different areas and identifies interesting open questions for further research.

Computational Optimization of Systems Governed by Partial Differential Equations

Alfio Borzi,Volker Schulz
Computational Optimization of Systems Governed by Partial Differential Equations Book PDF

Author : Alfio Borzi,Volker Schulz
Publisher : SIAM
Page : 295 pages
File Size : 47,5 Mb
Release : 2012-01-26
Category : Mathematics
ISBN : 9781611972047

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Computational Optimization of Systems Governed by Partial Differential Equations by Alfio Borzi,Volker Schulz Pdf

This book provides a bridge between continuous optimization and PDE modelling and focuses on the numerical solution of the corresponding problems. Intended for graduate students in PDE-constrained optimization, it is also suitable as an introduction for researchers in scientific computing or optimization.

Computing Methods in Optimization Problems

A. V. Balakrishnan,Lucien W. Neustadt
Computing Methods in Optimization Problems Book PDF

Author : A. V. Balakrishnan,Lucien W. Neustadt
Publisher : Academic Press
Page : 338 pages
File Size : 50,8 Mb
Release : 2014-05-12
Category : Mathematics
ISBN : 9781483223155

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Computing Methods in Optimization Problems by A. V. Balakrishnan,Lucien W. Neustadt Pdf

Computing Methods in Optimization Problems deals with hybrid computing methods and optimization techniques using computers. One paper discusses different numerical approaches to optimizing trajectories, including the gradient method, the second variation method, and a generalized Newton-Raphson method. The paper cites the advantages and disadvantages of each method, and compares the second variation method (a direct method) with the generalized Newton-Raphson method (an indirect method). An example problem illustrates the application of the three methods in minimizing the transfer time of a low-thrust ion rocket between the orbits of Earth and Mars. Another paper discusses an iterative process for steepest-ascent optimization of orbit transfer trajectories to minimize storage requirements such as in reduced memory space utilized in guidance computers. By eliminating state variable storage and control schedule storage, the investigator can achieve reduced memory requirements. Other papers discuss dynamic programming, invariant imbedding, quasilinearization, Hilbert space, and the computational aspects of a time-optimal control problem. The collection is suitable for computer programmers, engineers, designers of industrial processes, and researchers involved in aviation or control systems technology.

Advances in Mathematical Modeling, Optimization and Optimal Control

Jean-Baptiste Hiriart-Urruty,Adam Korytowski,Helmut Maurer,Maciej Szymkat
Advances in Mathematical Modeling Optimization and Optimal Control Book PDF

Author : Jean-Baptiste Hiriart-Urruty,Adam Korytowski,Helmut Maurer,Maciej Szymkat
Publisher : Springer
Page : 205 pages
File Size : 51,8 Mb
Release : 2016-05-19
Category : Mathematics
ISBN : 9783319307855

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Advances in Mathematical Modeling, Optimization and Optimal Control by Jean-Baptiste Hiriart-Urruty,Adam Korytowski,Helmut Maurer,Maciej Szymkat Pdf

This book contains extended, in-depth presentations of the plenary talks from the 16th French-German-Polish Conference on Optimization, held in Kraków, Poland in 2013. Each chapter in this book exhibits a comprehensive look at new theoretical and/or application-oriented results in mathematical modeling, optimization, and optimal control. Students and researchers involved in image processing, partial differential inclusions, shape optimization, or optimal control theory and its applications to medical and rehabilitation technology, will find this book valuable. The first chapter by Martin Burger provides an overview of recent developments related to Bregman distances, which is an important tool in inverse problems and image processing. The chapter by Piotr Kalita studies the operator version of a first order in time partial differential inclusion and its time discretization. In the chapter by Günter Leugering, Jan Sokołowski and Antoni Żochowski, nonsmooth shape optimization problems for variational inequalities are considered. The next chapter, by Katja Mombaur is devoted to applications of optimal control and inverse optimal control in the field of medical and rehabilitation technology, in particular in human movement analysis, therapy and improvement by means of medical devices. The final chapter, by Nikolai Osmolovskii and Helmut Maurer provides a survey on no-gap second order optimality conditions in the calculus of variations and optimal control, and a discussion of their further development.

Numerical Methods for Unconstrained Optimization and Nonlinear Equations

J. E. Dennis, Jr.,Robert B. Schnabel
Numerical Methods for Unconstrained Optimization and Nonlinear Equations Book PDF

Author : J. E. Dennis, Jr.,Robert B. Schnabel
Publisher : SIAM
Page : 394 pages
File Size : 45,7 Mb
Release : 1996-12-01
Category : Mathematics
ISBN : 1611971209

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Numerical Methods for Unconstrained Optimization and Nonlinear Equations by J. E. Dennis, Jr.,Robert B. Schnabel Pdf

This book has become the standard for a complete, state-of-the-art description of the methods for unconstrained optimization and systems of nonlinear equations. Originally published in 1983, it provides information needed to understand both the theory and the practice of these methods and provides pseudocode for the problems. The algorithms covered are all based on Newton's method or "quasi-Newton" methods, and the heart of the book is the material on computational methods for multidimensional unconstrained optimization and nonlinear equation problems. The republication of this book by SIAM is driven by a continuing demand for specific and sound advice on how to solve real problems. The level of presentation is consistent throughout, with a good mix of examples and theory, making it a valuable text at both the graduate and undergraduate level. It has been praised as excellent for courses with approximately the same name as the book title and would also be useful as a supplemental text for a nonlinear programming or a numerical analysis course. Many exercises are provided to illustrate and develop the ideas in the text. A large appendix provides a mechanism for class projects and a reference for readers who want the details of the algorithms. Practitioners may use this book for self-study and reference. For complete understanding, readers should have a background in calculus and linear algebra. The book does contain background material in multivariable calculus and numerical linear algebra.