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Mimetic Discretization Methods by Castillo
From Mathematics Is A Science
Revision as of 12:43, 30 August 2013 by imported>WikiSysop
Mimetic Discretization Methods by Jose E. Castillo
The book is very short on explanation, just as some others. Hence my desire to build something from scratch: Discrete Calculus. An Introduction.
CONTENTS
- 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