Chapter 7
Inside the Library: LocalRegions

In this chapter, we walk the reader through the different components of the LocalRegions Directory. We begin with a discussion of the mathematical fundamentals, for which we use the book by Karniadakis and Sherwin [46] as our principle reference. We then provide the reader with an overview of the primary data structures introduced within the LocalRegions Directory (often done through C++ objects), and then present the major algorithms – expressed as either object methods or functions – employed over these data structures.

 7.1 The Fundamentals Behind LocalRegions
 7.2 The Fundamental Data Structures within LocalRegions
  7.2.1 Variables at the Level of Expansion
  7.2.2 Variables at the Level of Expansion$D for various Dimensions
  7.2.3 Variables at the Level of Shape-Specific Expansions
 7.3 The Fundamental Algorithms within LocalRegions