Chapter 11
Inside the Library: FieldUtils

In this chapter, we walk the reader through the different components of the FieldUtils Directory. We begin with a discussion of the mathematical fundamentals, for which we use the book by Karniadakis and Sherwin [44] as our principle reference. We then provide the reader with an overview of the primary data structures introduced within the FieldUtils Directory (often done through C++ objects), and then present the major algorithms – expressed as either object methods or functions – employed over these data structures.

  9.2.4 Variables at the Level of Continuous Field Expansions
 9.3 The Fundamental Algorithms within MultiRegions
 9.4 Preconditioners
  9.4.1 Mathematical formulation
  9.4.2 Preconditioners
  9.4.3 Low energy