Numerical Time Dependent Partial Differential Equations for Scientists and Engineers

Written By Moysey Brio
Numerical Time Dependent Partial Differential Equations for Scientists and Engineers
  • Publsiher : Academic Press
  • Release : 21 September 2010
  • ISBN : 9780080917047
  • Pages : 312 pages
  • Rating : 4/5 from 21 reviews
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Read or download book entitled Numerical Time Dependent Partial Differential Equations for Scientists and Engineers written by Moysey Brio which was release on 21 September 2010, this book published by Academic Press. Available in PDF, EPUB and Kindle Format. 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 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
  • Publisher : Academic Press
  • Release Date : 2010-09-21
  • Total pages : 312
  • ISBN : 9780080917047
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Summary : 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 ...

Continuum Theory and Modeling of Thermoelectric Elements

Continuum Theory and Modeling of Thermoelectric Elements
  • Author : Christophe Goupil
  • Publisher : John Wiley & Sons
  • Release Date : 2016-02-23
  • Total pages : 360
  • ISBN : 9780080917047
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Summary : 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
  • Publisher : American Mathematical Soc.
  • Release Date : 2007-01-01
  • Total pages : 194
  • ISBN : 9780080917047
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Summary : 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 ...

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
  • Publisher : John Wiley & Sons
  • Release Date : 1982
  • Total pages : 677
  • ISBN : 9780080917047
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Summary : "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 ...

Drying Phenomena

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  • Author : Ibrahim Dincer,Calin Zamfirescu
  • Publisher : John Wiley & Sons
  • Release Date : 2016-01-19
  • Total pages : 512
  • ISBN : 9780080917047
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Summary : 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 ...

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  • Author : Maria do Carmo Coimbra,Alirio Egidio Rodrigues,Jaime Duarte Rodrigues,Rui Jorge Mendes Robalo,Rui Manuel Pires Almeida
  • Publisher : CRC Press
  • Release Date : 2016-11-30
  • Total pages : 248
  • ISBN : 9780080917047
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Summary : 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 ...

Proper Orthogonal Decomposition Methods for Partial Differential Equations

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  • Author : Zhendong Luo,Goong Chen
  • Publisher : Academic Press
  • Release Date : 2018-11-26
  • Total pages : 278
  • ISBN : 9780080917047
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Summary : 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 ...

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Implementing Spectral Methods for Partial Differential Equations
  • Author : David A. Kopriva
  • Publisher : Springer Science & Business Media
  • Release Date : 2009-05-27
  • Total pages : 397
  • ISBN : 9780080917047
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Summary : 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....

Numerical Methods and Methods of Approximation in Science and Engineering

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  • Author : Karan S. Surana
  • Publisher : CRC Press
  • Release Date : 2018-10-31
  • Total pages : 478
  • ISBN : 9780080917047
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Summary : 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 ...

Using R for Numerical Analysis in Science and Engineering

Using R for Numerical Analysis in Science and Engineering
  • Author : Victor A. Bloomfield
  • Publisher : CRC Press
  • Release Date : 2018-09-03
  • Total pages : 359
  • ISBN : 9780080917047
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Summary : 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 ...

Simulation of ODE PDE Models with MATLAB OCTAVE and SCILAB

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  • Author : Alain Vande Wouwer,Philippe Saucez,Carlos Vilas
  • Publisher : Springer
  • Release Date : 2014-06-07
  • Total pages : 406
  • ISBN : 9780080917047
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Summary : 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 ...

Matrix Numerical and Optimization Methods in Science and Engineering

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  • Author : Kevin W. Cassel
  • Publisher : Cambridge University Press
  • Release Date : 2021-01-31
  • Total pages : 600
  • ISBN : 9780080917047
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Summary : 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 ...

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
  • Publisher : John Wiley & Sons
  • Release Date : 2014-04-24
  • Total pages : 192
  • ISBN : 9780080917047
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Summary : 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 ...

Domain Decomposition Methods in Science and Engineering XVI

Domain Decomposition Methods in Science and Engineering XVI
  • Author : Olof B. Widlund,David E. Keyes
  • Publisher : Springer Science & Business Media
  • Release Date : 2007-01-19
  • Total pages : 778
  • ISBN : 9780080917047
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Summary : 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....

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  • Author : Alfio Quarteroni,Gianluigi Rozza
  • Publisher : Springer
  • Release Date : 2014-06-05
  • Total pages : 334
  • ISBN : 9780080917047
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Summary : 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 ...