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.

  6.2.1 Variables at the Level of Geometry
  6.2.2 Variables at the Level of Geometry$D for various Dimensions
  6.2.3 Variables at the Level of Shape-Specific Geometry Information
  6.2.4 Reference to World-Space Mapping
  6.2.5 MeshGraph
 6.3 The Fundamental Algorithms within SpatialDomains