Numerical Time Dependent Partial Differential Equations for Scientists and Engineers

Numerical Time Dependent Partial Differential Equations for Scientists and Engineers
Author: Moysey Brio,Gary M. Webb,Aramais R. Zakharian
Publsiher: Academic Press
Total Pages: 312
Release: 2010-09-21
ISBN: 9780080917047
Category: Mathematics
Language: EN, FR, DE, ES & NL

Numerical Time Dependent Partial Differential Equations for Scientists and Engineers Book Excerpt:

It is the first text that in addition to standard convergence theory treats other necessary ingredients for successful numerical simulations of physical systems encountered by every practitioner. The book is aimed at users with interests ranging from application modeling to numerical analysis and scientific software development. It is strongly influenced by the authors research in in space physics, electrical and optical engineering, applied mathematics, numerical analysis and professional software development. The material is based on a year-long graduate course taught at the University of Arizona since 1989. The book covers the first two-semesters of a three semester series. The second semester is based on a semester-long project, while the third semester requirement consists of a particular methods course in specific disciplines like computational fluid dynamics, finite element method in mechanical engineering, computational physics, biology, chemistry, photonics, etc. The first three chapters focus on basic properties of partial differential equations, including analysis of the dispersion relation, symmetries, particular solutions and instabilities of the PDEs; methods of discretization and convergence theory for initial value problems. The goal is to progress from observations of simple numerical artifacts like diffusion, damping, dispersion, and anisotropies to their analysis and management technique, as it is not always possible to completely eliminate them. In the second part of the book we cover topics for which there are only sporadic theoretical results, while they are an integral part and often the most important part for successful numerical simulation. We adopt a more heuristic and practical approach using numerical methods of investigation and validation. The aim is teach students subtle key issues in order to separate physics from numerics. The following topics are addressed: Implementation of transparent and absorbing boundary conditions; Practical stability analysis in the presence of the boundaries and interfaces; Treatment of problems with different temporal/spatial scales either explicit or implicit; preservation of symmetries and additional constraints; physical regularization of singularities; resolution enhancement using adaptive mesh refinement and moving meshes. Self contained presentation of key issues in successful numerical simulation Accessible to scientists and engineers with diverse background Provides analysis of the dispersion relation, symmetries, particular solutions and instabilities of the partial differential equations

Numerical Partial Differential Equations for Environmental Scientists and Engineers

Numerical Partial Differential Equations for Environmental Scientists and Engineers
Author: Daniel R. Lynch
Publsiher: Springer Science & Business Media
Total Pages: 388
Release: 2004-12-15
ISBN: 0387236198
Category: Science
Language: EN, FR, DE, ES & NL

Numerical Partial Differential Equations for Environmental Scientists and Engineers Book Excerpt:

For readers with some competence in PDE solution properties, this book offers an interdisciplinary approach to problems occurring in natural environmental media: the hydrosphere, atmosphere, cryosphere, lithosphere, biosphere and ionosphere. It presents two major discretization methods: Finite Difference and Finite Element, plus a section on practical approaches to ill-posed problems. The blend of theory, analysis, and implementation practicality supports solving and understanding complicated problems.

Continuum Theory and Modeling of Thermoelectric Elements

Continuum Theory and Modeling of Thermoelectric Elements
Author: Christophe Goupil
Publsiher: John Wiley & Sons
Total Pages: 360
Release: 2016-02-23
ISBN: 3527413375
Category: MATHEMATICS
Language: EN, FR, DE, ES & NL

Continuum Theory and Modeling of Thermoelectric Elements Book Excerpt:

This volume presents the latest research results in the thermodynamics and design of thermoelectric devices, providing a solid foundation for thermoelectric element and module design in the technical development process, and a valuable tool for any application development.

High dimensional Partial Differential Equations in Science and Engineering

High dimensional Partial Differential Equations in Science and Engineering
Author: André D. Bandrauk,Michel C. Delfour,Claude Le Bris
Publsiher: American Mathematical Soc.
Total Pages: 194
Release: 2007-01-01
ISBN: 9780821870372
Category: Mathematics
Language: EN, FR, DE, ES & NL

High dimensional Partial Differential Equations in Science and Engineering Book Excerpt:

High-dimensional spatio-temporal partial differential equations are a major challenge to scientific computing of the future. Up to now deemed prohibitive, they have recently become manageable by combining recent developments in numerical techniques, appropriate computer implementations, and the use of computers with parallel and even massively parallel architectures. This opens new perspectives in many fields of applications. Kinetic plasma physics equations, the many body Schrodinger equation, Dirac and Maxwell equations for molecular electronic structures and nuclear dynamic computations, options pricing equations in mathematical finance, as well as Fokker-Planck and fluid dynamics equations for complex fluids, are examples of equations that can now be handled. The objective of this volume is to bring together contributions by experts of international stature in that broad spectrum of areas to confront their approaches and possibly bring out common problem formulations and research directions in the numerical solutions of high-dimensional partial differential equations in various fields of science and engineering with special emphasis on chemistry and physics. Information for our distributors: Titles in this series are co-published with the Centre de Recherches Mathematiques.

Numerical Solution of Partial Differential Equations in Science and Engineering

Numerical Solution of Partial Differential Equations in Science and Engineering
Author: Leon Lapidus,George F. Pinder
Publsiher: John Wiley & Sons
Total Pages: 677
Release: 1982
ISBN: 9780471098669
Category: Mathematics
Language: EN, FR, DE, ES & NL

Numerical Solution of Partial Differential Equations in Science and Engineering Book Excerpt:

"This book was written to provide a text for graduate and undergraduate students who took our courses in numerical methods. It incorporates the essential elements of all the numerical methods currently used extensively in the solution of partial differential equations encountered regularly in science and engineering. Because our courses were typically populated by students from varied backgrounds and with diverse interests, we attempted to eliminate jargon or nomenclature that would render the work unintelligible to any student. Moreover, in response to student needs, we incorporated not only classical (and not so classical) finite-difference methods but also finite-element, collocation, and boundary-element procedures. After an introduction to the various numerical schemes, each equation type--parabolic, elliptic, and hyperbolic--is allocated a separate chapter. Within each of these chapters the material is presented by numerical method. Thus one can read the book either by equation-type or numerical approach."--Preface, page [v].

Drying Phenomena

Drying Phenomena
Author: Ibrahim Dincer,Calin Zamfirescu
Publsiher: John Wiley & Sons
Total Pages: 512
Release: 2016-01-19
ISBN: 1119975867
Category: Science
Language: EN, FR, DE, ES & NL

Drying Phenomena Book Excerpt:

Comprehensively covers conventional and novel drying systems and applications, while keeping a focus on the fundamentals of drying phenomena. Presents detailed thermodynamic and heat/mass transfer analyses in a reader-friendly and easy-to-follow approach Includes case studies, illustrative examples and problems Presents experimental and computational approaches Includes comprehensive information identifying the roles of flow and heat transfer mechanisms on the drying phenomena Considers industrial applications, corresponding criterion, complications, prospects, etc. Discusses novel drying technologies, the corresponding research platforms and potential solutions

Moving Finite Element Method

Moving Finite Element Method
Author: Maria do Carmo Coimbra,Alirio Egidio Rodrigues,Jaime Duarte Rodrigues,Rui Jorge Mendes Robalo,Rui Manuel Pires Almeida
Publsiher: CRC Press
Total Pages: 248
Release: 2016-11-30
ISBN: 1498723896
Category: Mathematics
Language: EN, FR, DE, ES & NL

Moving Finite Element Method Book Excerpt:

This book focuses on process simulation in chemical engineering with a numerical algorithm based on the moving finite element method (MFEM). It offers new tools and approaches for modeling and simulating time-dependent problems with moving fronts and with moving boundaries described by time-dependent convection-reaction-diffusion partial differential equations in one or two-dimensional space domains. It provides a comprehensive account of the development of the moving finite element method, describing and analyzing the theoretical and practical aspects of the MFEM for models in 1D, 1D+1d, and 2D space domains. Mathematical models are universal, and the book reviews successful applications of MFEM to solve engineering problems. It covers a broad range of application algorithm to engineering problems, namely on separation and reaction processes presenting and discussing relevant numerical applications of the moving finite element method derived from real-world process simulations.

Proper Orthogonal Decomposition Methods for Partial Differential Equations

Proper Orthogonal Decomposition Methods for Partial Differential Equations
Author: Zhendong Luo,Goong Chen
Publsiher: Academic Press
Total Pages: 278
Release: 2018-11-26
ISBN: 0128167998
Category: Mathematics
Language: EN, FR, DE, ES & NL

Proper Orthogonal Decomposition Methods for Partial Differential Equations Book Excerpt:

Proper Orthogonal Decomposition Methods for Partial Differential Equations evaluates the potential applications of POD reduced-order numerical methods in increasing computational efficiency, decreasing calculating load and alleviating the accumulation of truncation error in the computational process. Introduces the foundations of finite-differences, finite-elements and finite-volume-elements. Models of time-dependent PDEs are presented, with detailed numerical procedures, implementation and error analysis. Output numerical data are plotted in graphics and compared using standard traditional methods. These models contain parabolic, hyperbolic and nonlinear systems of PDEs, suitable for the user to learn and adapt methods to their own R&D problems. Explains ways to reduce order for PDEs by means of the POD method so that reduced-order models have few unknowns Helps readers speed up computation and reduce computation load and memory requirements while numerically capturing system characteristics Enables readers to apply and adapt the methods to solve similar problems for PDEs of hyperbolic, parabolic and nonlinear types

Implementing Spectral Methods for Partial Differential Equations

Implementing Spectral Methods for Partial Differential Equations
Author: David A. Kopriva
Publsiher: Springer Science & Business Media
Total Pages: 397
Release: 2009-05-27
ISBN: 9048122619
Category: Mathematics
Language: EN, FR, DE, ES & NL

Implementing Spectral Methods for Partial Differential Equations Book Excerpt:

This book explains how to solve partial differential equations numerically using single and multidomain spectral methods. It shows how only a few fundamental algorithms form the building blocks of any spectral code, even for problems with complex geometries.

Introduction to Numerical Methods for Time Dependent Differential Equations

Introduction to Numerical Methods for Time Dependent Differential Equations
Author: Heinz-Otto Kreiss,Omar Eduardo Ortiz
Publsiher: John Wiley & Sons
Total Pages: 192
Release: 2014-04-24
ISBN: 1118838912
Category: Mathematics
Language: EN, FR, DE, ES & NL

Introduction to Numerical Methods for Time Dependent Differential Equations Book Excerpt:

Introduces both the fundamentals of time dependent differential equations and their numerical solutions Introduction to Numerical Methods for Time Dependent Differential Equations delves into the underlying mathematical theory needed to solve time dependent differential equations numerically. Written as a self-contained introduction, the book is divided into two parts to emphasize both ordinary differential equations (ODEs) and partial differential equations (PDEs). Beginning with ODEs and their approximations, the authors provide a crucial presentation of fundamental notions, such as the theory of scalar equations, finite difference approximations, and the Explicit Euler method. Next, a discussion on higher order approximations, implicit methods, multistep methods, Fourier interpolation, PDEs in one space dimension as well as their related systems is provided. Introduction to Numerical Methods for Time Dependent Differential Equations features: A step-by-step discussion of the procedures needed to prove the stability of difference approximations Multiple exercises throughout with select answers, providing readers with a practical guide to understanding the approximations of differential equations A simplified approach in a one space dimension Analytical theory for difference approximations that is particularly useful to clarify procedures Introduction to Numerical Methods for Time Dependent Differential Equations is an excellent textbook for upper-undergraduate courses in applied mathematics, engineering, and physics as well as a useful reference for physical scientists, engineers, numerical analysts, and mathematical modelers who use numerical experiments to test designs or predict and investigate phenomena from many disciplines.

Simulation of ODE PDE Models with MATLAB OCTAVE and SCILAB

Simulation of ODE PDE Models with MATLAB    OCTAVE and SCILAB
Author: Alain Vande Wouwer,Philippe Saucez,Carlos Vilas
Publsiher: Springer
Total Pages: 406
Release: 2014-06-07
ISBN: 3319067907
Category: Technology & Engineering
Language: EN, FR, DE, ES & NL

Simulation of ODE PDE Models with MATLAB OCTAVE and SCILAB Book Excerpt:

Simulation of ODE/PDE Models with MATLAB®, OCTAVE and SCILAB shows the reader how to exploit a fuller array of numerical methods for the analysis of complex scientific and engineering systems than is conventionally employed. The book is dedicated to numerical simulation of distributed parameter systems described by mixed systems of algebraic equations, ordinary differential equations (ODEs) and partial differential equations (PDEs). Special attention is paid to the numerical method of lines (MOL), a popular approach to the solution of time-dependent PDEs, which proceeds in two basic steps: spatial discretization and time integration. Besides conventional finite-difference and element techniques, more advanced spatial-approximation methods are examined in some detail, including nonoscillatory schemes and adaptive-grid approaches. A MOL toolbox has been developed within MATLAB®/OCTAVE/SCILAB. In addition to a set of spatial approximations and time integrators, this toolbox includes a collection of application examples, in specific areas, which can serve as templates for developing new programs. Simulation of ODE/PDE Models with MATLAB®, OCTAVE and SCILAB provides a practical introduction to some advanced computational techniques for dynamic system simulation, supported by many worked examples in the text, and a collection of codes available for download from the book’s page at www.springer.com. This text is suitable for self-study by practicing scientists and engineers and as a final-year undergraduate course or at the graduate level.

Numerical Methods and Methods of Approximation in Science and Engineering

Numerical Methods and Methods of Approximation in Science and Engineering
Author: Karan S. Surana
Publsiher: CRC Press
Total Pages: 478
Release: 2018-10-31
ISBN: 0429647867
Category: Mathematics
Language: EN, FR, DE, ES & NL

Numerical Methods and Methods of Approximation in Science and Engineering Book Excerpt:

Numerical Methods and Methods of Approximation in Science and Engineering prepares students and other readers for advanced studies involving applied numerical and computational analysis. Focused on building a sound theoretical foundation, it uses a clear and simple approach backed by numerous worked examples to facilitate understanding of numerical methods and their application. Readers will learn to structure a sequence of operations into a program, using the programming language of their choice; this approach leads to a deeper understanding of the methods and their limitations. Features: Provides a strong theoretical foundation for learning and applying numerical methods Takes a generic approach to engineering analysis, rather than using a specific programming language Built around a consistent, understandable model for conducting engineering analysis Prepares students for advanced coursework, and use of tools such as FEA and CFD Presents numerous detailed examples and problems, and a Solutions Manual for instructors

Time Dependent Problems and Difference Methods

Time Dependent Problems and Difference Methods
Author: Bertil Gustafsson,Heinz-Otto Kreiss,Joseph Oliger
Publsiher: John Wiley & Sons
Total Pages: 528
Release: 2013-07-18
ISBN: 1118548523
Category: Mathematics
Language: EN, FR, DE, ES & NL

Time Dependent Problems and Difference Methods Book Excerpt:

Praise for the First Edition ". . . fills a considerable gap in the numerical analysisliterature by providing a self-contained treatment . . . this is animportant work written in a clear style . . . warmly recommended toany graduate student or researcher in the field of the numericalsolution of partial differential equations." —SIAM Review Time-Dependent Problems and Difference Methods, SecondEdition continues to provide guidance for the analysis ofdifference methods for computing approximate solutions to partialdifferential equations for time-dependent problems. The book treatsdifferential equations and difference methods with a paralleldevelopment, thus achieving a more useful analysis of numericalmethods. The Second Edition presents hyperbolic equations in greatdetail as well as new coverage on second-order systems of waveequations including acoustic waves, elastic waves, and Einsteinequations. Compared to first-order hyperbolic systems,initial-boundary value problems for such systems contain newproperties that must be taken into account when analyzingstability. Featuring the latest material in partial differentialequations with new theorems, examples, andillustrations,Time-Dependent Problems and Difference Methods,Second Edition also includes: High order methods on staggered grids Extended treatment of Summation By Parts operators and theirapplication to second-order derivatives Simplified presentation of certain parts and proofs Time-Dependent Problems and Difference Methods, SecondEdition is an ideal reference for physical scientists,engineers, numerical analysts, and mathematical modelers who usenumerical experiments to test designs and to predict andinvestigate physical phenomena. The book is also excellent forgraduate-level courses in applied mathematics and scientificcomputations.

Using R for Numerical Analysis in Science and Engineering

Using R for Numerical Analysis in Science and Engineering
Author: Victor A. Bloomfield
Publsiher: CRC Press
Total Pages: 359
Release: 2018-09-03
ISBN: 1315360497
Category: Mathematics
Language: EN, FR, DE, ES & NL

Using R for Numerical Analysis in Science and Engineering Book Excerpt:

Instead of presenting the standard theoretical treatments that underlie the various numerical methods used by scientists and engineers, Using R for Numerical Analysis in Science and Engineering shows how to use R and its add-on packages to obtain numerical solutions to the complex mathematical problems commonly faced by scientists and engineers. This practical guide to the capabilities of R demonstrates Monte Carlo, stochastic, deterministic, and other numerical methods through an abundance of worked examples and code, covering the solution of systems of linear algebraic equations and nonlinear equations as well as ordinary differential equations and partial differential equations. It not only shows how to use R’s powerful graphic tools to construct the types of plots most useful in scientific and engineering work, but also: Explains how to statistically analyze and fit data to linear and nonlinear models Explores numerical differentiation, integration, and optimization Describes how to find eigenvalues and eigenfunctions Discusses interpolation and curve fitting Considers the analysis of time series Using R for Numerical Analysis in Science and Engineering provides a solid introduction to the most useful numerical methods for scientific and engineering data analysis using R.

Matrix Numerical and Optimization Methods in Science and Engineering

Matrix  Numerical  and Optimization Methods in Science and Engineering
Author: Kevin W. Cassel
Publsiher: Cambridge University Press
Total Pages: 600
Release: 2021-01-31
ISBN: 110847909X
Category: Mathematics
Language: EN, FR, DE, ES & NL

Matrix Numerical and Optimization Methods in Science and Engineering Book Excerpt:

Address vector and matrix methods necessary in numerical methods and optimization of linear systems in engineering with this unified text. Treats the mathematical models that describe and predict the evolution of our processes and systems, and the numerical methods required to obtain approximate solutions. Explores the dynamical systems theory used to describe and characterize system behaviour, alongside the techniques used to optimize their performance. Integrates and unifies matrix and eigenfunction methods with their applications in numerical and optimization methods. Consolidating, generalizing, and unifying these topics into a single coherent subject, this practical resource is suitable for advanced undergraduate students and graduate students in engineering, physical sciences, and applied mathematics.

Domain Decomposition Methods in Science and Engineering XVI

Domain Decomposition Methods in Science and Engineering XVI
Author: Olof B. Widlund,David E. Keyes
Publsiher: Springer Science & Business Media
Total Pages: 778
Release: 2007-01-19
ISBN: 3540344683
Category: Computers
Language: EN, FR, DE, ES & NL

Domain Decomposition Methods in Science and Engineering XVI Book Excerpt:

Domain decomposition is an active research area concerned with the development, analysis, and implementation of coupling and decoupling strategies in mathematical and computational models of natural and engineered systems. The present volume sets forth new contributions in areas of numerical analysis, computer science, scientific and industrial applications, and software development.

Numerical Methods for Evolutionary Differential Equations

Numerical Methods for Evolutionary Differential Equations
Author: Uri M. Ascher
Publsiher: SIAM
Total Pages: 395
Release: 2008
ISBN: 0898718910
Category: Evolution equations
Language: EN, FR, DE, ES & NL

Numerical Methods for Evolutionary Differential Equations Book Excerpt:

Methods for the numerical simulation of dynamic mathematical models have been the focus of intensive research for well over 60 years, and the demand for better and more efficient methods has grown as the range of applications has increased. Mathematical models involving evolutionary partial differential equations (PDEs) as well as ordinary differential equations (ODEs) arise in diverse applications such as fluid flow, image processing and computer vision, physics-based animation, mechanical systems, relativity, earth sciences, and mathematical finance. This textbook develops, analyzes, and applies numerical methods for evolutionary, or time-dependent, differential problems. Both PDEs and ODEs are discussed from a unified viewpoint. The author emphasizes finite difference and finite volume methods, specifically their principled derivation, stability, accuracy, efficient implementation, and practical performance in various fields of science and engineering. Smooth and nonsmooth solutions for hyperbolic PDEs, parabolic-type PDEs, and initial value ODEs are treated, and a practical introduction to geometric integration methods is included as well. Audience: suitable for researchers and graduate students from a variety of fields including computer science, applied mathematics, physics, earth and ocean sciences, and various engineering disciplines. Researchers who simulate processes that are modeled by evolutionary differential equations will find material on the principles underlying the appropriate method to use and the pitfalls that accompany each method.

Reduced Order Methods for Modeling and Computational Reduction

Reduced Order Methods for Modeling and Computational Reduction
Author: Alfio Quarteroni,Gianluigi Rozza
Publsiher: Springer
Total Pages: 334
Release: 2014-06-05
ISBN: 3319020900
Category: Mathematics
Language: EN, FR, DE, ES & NL

Reduced Order Methods for Modeling and Computational Reduction Book Excerpt:

This monograph addresses the state of the art of reduced order methods for modeling and computational reduction of complex parametrized systems, governed by ordinary and/or partial differential equations, with a special emphasis on real time computing techniques and applications in computational mechanics, bioengineering and computer graphics. Several topics are covered, including: design, optimization, and control theory in real-time with applications in engineering; data assimilation, geometry registration, and parameter estimation with special attention to real-time computing in biomedical engineering and computational physics; real-time visualization of physics-based simulations in computer science; the treatment of high-dimensional problems in state space, physical space, or parameter space; the interactions between different model reduction and dimensionality reduction approaches; the development of general error estimation frameworks which take into account both model and discretization effects. This book is primarily addressed to computational scientists interested in computational reduction techniques for large scale differential problems.

Splitting Methods in Communication Imaging Science and Engineering

Splitting Methods in Communication  Imaging  Science  and Engineering
Author: Roland Glowinski,Stanley J. Osher,Wotao Yin
Publsiher: Springer
Total Pages: 820
Release: 2017-01-05
ISBN: 3319415891
Category: Mathematics
Language: EN, FR, DE, ES & NL

Splitting Methods in Communication Imaging Science and Engineering Book Excerpt:

This book is about computational methods based on operator splitting. It consists of twenty-three chapters written by recognized splitting method contributors and practitioners, and covers a vast spectrum of topics and application areas, including computational mechanics, computational physics, image processing, wireless communication, nonlinear optics, and finance. Therefore, the book presents very versatile aspects of splitting methods and their applications, motivating the cross-fertilization of ideas.

Activities of the Institute for Computer Applications in Science and Engineering

Activities of the Institute for Computer Applications in Science and Engineering
Author: Anonim
Publsiher: Unknown
Total Pages: 64
Release: 1985
ISBN: 1928374650XXX
Category: Electronic Book
Language: EN, FR, DE, ES & NL

Activities of the Institute for Computer Applications in Science and Engineering Book Excerpt: