Mimetic Discretization Methods by Castillo

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