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 10: 9780080917047
ISBN 13: 0080917046
Language: EN, FR, DE, ES & NL

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

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

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 10: 3527413375
ISBN 13: 9783527413379
Language: EN, FR, DE, ES & NL

Continuum Theory and Modeling of Thermoelectric Elements Book Review:

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.

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: 2006-06-02
ISBN 10: 0387236201
ISBN 13: 9780387236209
Language: EN, FR, DE, ES & NL

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

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.

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 10: 9780821870372
ISBN 13: 0821870378
Language: EN, FR, DE, ES & NL

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

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.

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 10: 9048122619
ISBN 13: 9789048122615
Language: EN, FR, DE, ES & NL

Implementing Spectral Methods for Partial Differential Equations Book Review:

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.

Drying Phenomena

Drying Phenomena
Author: Ibrahim Dincer,Calin Zamfirescu
Publsiher: John Wiley & Sons
Total Pages: 512
Release: 2016-01-19
ISBN 10: 1119975867
ISBN 13: 9781119975861
Language: EN, FR, DE, ES & NL

Drying Phenomena Book Review:

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 10: 1498723896
ISBN 13: 9781498723893
Language: EN, FR, DE, ES & NL

Moving Finite Element Method Book Review:

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 10: 0128167998
ISBN 13: 9780128167991
Language: EN, FR, DE, ES & NL

Proper Orthogonal Decomposition Methods for Partial Differential Equations Book Review:

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

Handbook of Linear Partial Differential Equations for Engineers and Scientists

Handbook of Linear Partial Differential Equations for Engineers and Scientists
Author: Andrei D. Polyanin,Vladimir E. Nazaikinskii
Publsiher: CRC Press
Total Pages: 1643
Release: 2015-12-23
ISBN 10: 1466581492
ISBN 13: 9781466581494
Language: EN, FR, DE, ES & NL

Handbook of Linear Partial Differential Equations for Engineers and Scientists Book Review:

Includes nearly 4,000 linear partial differential equations (PDEs) with solutionsPresents solutions of numerous problems relevant to heat and mass transfer, wave theory, hydrodynamics, aerodynamics, elasticity, acoustics, electrodynamics, diffraction theory, quantum mechanics, chemical engineering sciences, electrical engineering, and other fieldsO

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 10: 1118548523
ISBN 13: 9781118548523
Language: EN, FR, DE, ES & NL

Time Dependent Problems and Difference Methods Book Review:

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.

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 10: 3319067907
ISBN 13: 9783319067902
Language: EN, FR, DE, ES & NL

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

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.

Partial Differential Equations for Scientists and Engineers

Partial Differential Equations for Scientists and Engineers
Author: Stanley J. Farlow
Publsiher: Courier Corporation
Total Pages: 414
Release: 2012-03-08
ISBN 10: 0486134733
ISBN 13: 9780486134734
Language: EN, FR, DE, ES & NL

Partial Differential Equations for Scientists and Engineers Book Review:

Practical text shows how to formulate and solve partial differential equations. Coverage of diffusion-type problems, hyperbolic-type problems, elliptic-type problems, numerical and approximate methods. Solution guide available upon request. 1982 edition.

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 10: 1118838912
ISBN 13: 9781118838914
Language: EN, FR, DE, ES & NL

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

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.

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 10: 0429647867
ISBN 13: 9780429647864
Language: EN, FR, DE, ES & NL

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

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

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 10: 1315360497
ISBN 13: 9781315360492
Language: EN, FR, DE, ES & NL

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

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.

Partial Differential Equations and the Finite Element Method

Partial Differential Equations and the Finite Element Method
Author: Pavel Ŝolín
Publsiher: John Wiley & Sons
Total Pages: 512
Release: 2005-12-16
ISBN 10: 0471764094
ISBN 13: 9780471764090
Language: EN, FR, DE, ES & NL

Partial Differential Equations and the Finite Element Method Book Review:

A systematic introduction to partial differential equations and modern finite element methods for their efficientnumerical solution Partial Differential Equations and the Finite Element Methodprovides a much-needed, clear, and systematic introduction tomodern theory of partial differential equations (PDEs) and finiteelement methods (FEM). Both nodal and hierachic concepts of the FEMare examined. Reflecting the growing complexity and multiscalenature of current engineering and scientific problems, the authoremphasizes higher-order finite element methods such as the spectralor hp-FEM. A solid introduction to the theory of PDEs and FEM contained inChapters 1-4 serves as the core and foundation of the publication.Chapter 5 is devoted to modern higher-order methods for thenumerical solution of ordinary differential equations (ODEs) thatarise in the semidiscretization of time-dependent PDEs by theMethod of Lines (MOL). Chapter 6 discusses fourth-order PDEs rootedin the bending of elastic beams and plates and approximates theirsolution by means of higher-order Hermite and Argyris elements.Finally, Chapter 7 introduces the reader to various PDEs governingcomputational electromagnetics and describes their finite elementapproximation, including modern higher-order edge elements forMaxwell's equations. The understanding of many theoretical and practical aspects of bothPDEs and FEM requires a solid knowledge of linear algebra andelementary functional analysis, such as functions and linearoperators in the Lebesgue, Hilbert, and Sobolev spaces. Thesetopics are discussed with the help of many illustrative examples inAppendix A, which is provided as a service for those readers whoneed to gain the necessary background or require a refreshertutorial. Appendix B presents several finite element computationsrooted in practical engineering problems and demonstrates thebenefits of using higher-order FEM. Numerous finite element algorithms are written out in detailalongside implementation discussions. Exercises, including manythat involve programming the FEM, are designed to assist the readerin solving typical problems in engineering and science. Specifically designed as a coursebook, this student-testedpublication is geared to upper-level undergraduates and graduatestudents in all disciplines of computational engineeringandscience. It is also a practical problem-solving reference forresearchers, engineers, and physicists.

Geometric Partial Differential Equations Part 2

Geometric Partial Differential Equations   Part 2
Author: Andrea Bonito,Ricardo Horacio Nochetto
Publsiher: Elsevier
Total Pages: 570
Release: 2021-01-26
ISBN 10: 0444643060
ISBN 13: 9780444643063
Language: EN, FR, DE, ES & NL

Geometric Partial Differential Equations Part 2 Book Review:

Besides their intrinsic mathematical interest, geometric partial differential equations (PDEs) are ubiquitous in many scientific, engineering and industrial applications. They represent an intellectual challenge and have received a great deal of attention recently. The purpose of this volume is to provide a missing reference consisting of self-contained and comprehensive presentations. It includes basic ideas, analysis and applications of state-of-the-art fundamental algorithms for the approximation of geometric PDEs together with their impacts in a variety of fields within mathematics, science, and engineering. About every aspect of computational geometric PDEs is discussed in this and a companion volume. Topics in this volume include stationary and time-dependent surface PDEs for geometric flows, large deformations of nonlinearly geometric plates and rods, level set and phase field methods and applications, free boundary problems, discrete Riemannian calculus and morphing, fully nonlinear PDEs including Monge-Ampere equations, and PDE constrained optimization Each chapter is a complete essay at the research level but accessible to junior researchers and students. The intent is to provide a comprehensive description of algorithms and their analysis for a specific geometric PDE class, starting from basic concepts and concluding with interesting applications. Each chapter is thus useful as an introduction to a research area as well as a teaching resource, and provides numerous pointers to the literature for further reading The authors of each chapter are world leaders in their field of expertise and skillful writers. This book is thus meant to provide an invaluable, readable and enjoyable account of computational geometric PDEs

Numerical Solution of Time Dependent Advection Diffusion Reaction Equations

Numerical Solution of Time Dependent Advection Diffusion Reaction Equations
Author: Willem Hundsdorfer,Jan G. Verwer
Publsiher: Springer Science & Business Media
Total Pages: 472
Release: 2013-04-17
ISBN 10: 3662090171
ISBN 13: 9783662090176
Language: EN, FR, DE, ES & NL

Numerical Solution of Time Dependent Advection Diffusion Reaction Equations Book Review:

Unique book on Reaction-Advection-Diffusion problems

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 10: 3540344683
ISBN 13: 9783540344681
Language: EN, FR, DE, ES & NL

Domain Decomposition Methods in Science and Engineering XVI Book Review:

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.

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 10: 3319020900
ISBN 13: 9783319020907
Language: EN, FR, DE, ES & NL

Reduced Order Methods for Modeling and Computational Reduction Book Review:

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.