Mimetic discretization methods
- José E. Castillo, Guillermo F. Miranda.
- Boca Raton : CRC Press, c2013.
- Physical description
- xxiii, 235 p. : ill. ; 24 cm.
Math & Statistics Library
|QA297 .C35 2013||Unknown|
- Includes bibliographical references (p. 217-230) and index.
- Introduction Continuum Mathematical Models Physically Motivated Mathematical Concepts and Theorems General 3-D 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 Castillo-Grone Method for 1-D Uniform Staggered Grids Higher-Dimensional CGM 2-D Staggerings 3-D Staggerings Gradient Compositions Nullity Tests Higher-Order Operators Formulation of Nonlinear and Time-Dependent Problems Object-Oriented Programming and C++ From Structured to Object-Oriented Programming Fundamental Concepts in Object-Oriented Programming Object-Oriented Modeling and UML Inheritance and Polymorphism Mimetic Methods Toolkit (MTK) MTK Usage Philosophy Study of a Diffusive-Reactive 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 Time-Tate of Change Appendix I: General Formulation of the Flux Concept Appendix J: Fourth-Order Castillo-Grone 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 co-developed by the first author. Based on the Castillo-Grone 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 flux-integral 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 object-oriented programming and C++. In addition, they describe how their mimetic methods toolkit (MTK)-available online-can 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)
- Numerical analysis.
- Publication date
- "A Chapman & Hall book."
- 9781466513433 (hdbk. : acid-free paper)
- 1466513438 (hdbk. : acid-free paper)
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