Mimetic discretization methods
 Responsibility
 José E. Castillo, Guillermo F. Miranda.
 Language
 English.
 Imprint
 Boca Raton : CRC Press, c2013.
 Physical description
 xxiii, 235 p. : ill. ; 24 cm.
Access
Available online
Math & Statistics Library
Stacks
Call number  Status 

QA297 .C35 2013  Unknown 
More options
Creators/Contributors
 Author/Creator
 Castillo, José E.
 Contributor
 Miranda, Guillermo F.
Contents/Summary
 Bibliography
 Includes bibliographical references (p. 217230) and index.
 Contents

 Introduction Continuum Mathematical Models Physically Motivated Mathematical Concepts and Theorems General 3D Use of Flux Vector Densities Illustrative Examples of PDEs A Comment on the Numerical Treatment of the grad Operator Notes on Numerical Analysis Computational Errors Order of Accuracy Norms and Condition Numbers Linear Systems of Equations Solution of Nonlinear Equations Mimetic Differential Operators CastilloGrone Method for 1D Uniform Staggered Grids HigherDimensional CGM 2D Staggerings 3D Staggerings Gradient Compositions Nullity Tests HigherOrder Operators Formulation of Nonlinear and TimeDependent Problems ObjectOriented Programming and C++ From Structured to ObjectOriented Programming Fundamental Concepts in ObjectOriented Programming ObjectOriented Modeling and UML Inheritance and Polymorphism Mimetic Methods Toolkit (MTK) MTK Usage Philosophy Study of a DiffusiveReactive Process Using the MTK Collaborative Development of the MTK: Flavors and Concerns Downloading the MTK Nonuniform Structured Meshes Divergence Operator Gradient Operator Case Studies Porous Media Flow and Reservoir Simulation Modeling Carbon Dioxide Geologic Sequestration Maxwell's Equations Wave Propagation Geophysical Flow Appendix A: Heuristic Deduction of the Extended Form of Gauss' Divergence Theorem Appendix B: Tensor Concept: An Intuitive Approach Appendix C Total Force Due to Pressure Gradients Appendix D: Heuristic Deduction of Stokes' Formula Appendix E: Curl in a Rotating Incompressible Inviscid Liquid Appendix F: Curl in Poiseuille's Flow Appendix G: Green's Identities Appendix H: Fluid Volumetric TimeTate of Change Appendix I: General Formulation of the Flux Concept Appendix J: FourthOrder CastilloGrone Divergence Operators References Index Sample Problems appear at the end of each chapter.
 (source: Nielsen Book Data)
 Publisher's Summary
 To help solve physical and engineering problems, mimetic or compatible algebraic discretization methods employ discrete constructs to mimic the continuous identities and theorems found in vector calculus. Mimetic Discretization Methods focuses on the recent mimetic discretization method codeveloped by the first author. Based on the CastilloGrone operators, this simple mimetic discretization method is invariably valid for spatial dimensions no greater than three. The book also presents a numerical method for obtaining corresponding discrete operators that mimic the continuum differential and fluxintegral operators, enabling the same order of accuracy in the interior as well as the domain boundary. After an overview of various mimetic approaches and applications, the text discusses the use of continuum mathematical models as a way to motivate the natural use of mimetic methods. The authors also offer basic numerical analysis material, making the book suitable for a course on numerical methods for solving PDEs. The authors cover mimetic differential operators in one, two, and three dimensions and provide a thorough introduction to objectoriented programming and C++. In addition, they describe how their mimetic methods toolkit (MTK)available onlinecan be used for the computational implementation of mimetic discretization methods. The text concludes with the application of mimetic methods to structured nonuniform meshes as well as several case studies. Compiling the authors' many concepts and results developed over the years, this book shows how to obtain a robust numerical solution of PDEs using the mimetic discretization approach. It also helps readers compare alternative methods in the literature.
(source: Nielsen Book Data)
Subjects
 Subject
 Numerical analysis.
Bibliographic information
 Publication date
 2013
 Note
 "A Chapman & Hall book."
 ISBN
 9781466513433 (hdbk. : acidfree paper)
 1466513438 (hdbk. : acidfree paper)