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Mimetic Discretization Methods by Castillo

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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
  • Case Studies
  • 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