Description
Book SynopsisTo 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 boo
Table of Contents
Introduction. Continuum Mathematical Models. Notes on Numerical Analysis. Mimetic Differential Operators. Object-Oriented Programming and C++. Mimetic Methods Toolkit (MTK). Nonuniform Structured Meshes. Case Studies. Appendices. References. Index.
