Domain Concepts
  • Logical Coordinates:
    The coordinate frame of a reference cell.
  • Domain:
    The computational domain is partitioned into cells called Blocks. Furthermore, each Block must have at most one neighboring Block in each Direction.
  • Block:
    A reference cell embedded into a subset of the computational domain. Blocks are identified by unique integral values.
  • Orientation:
    The information of how the Logical Coordinates between Blocks are related.
  • Block Neighbor:
    The identity and Orientation of a neighbor of a given Block.
  • Direction:
    A logical coordinate axis and a label "Upper" or "Lower" depending on whether the Direction is aligned with or anti-aligned with the logical coordinate axis, respectively.
  • Refinement Level:
    The number of times a Block is split in half in a given dimension.
  • Segment:
    The specific subset of the interval \([-1, 1]\) defined by the Refinement Level and an integer label such that the Segment's interval is \([-1 + 2*(N/D), -1 + 2*(N+1)/D]\) where N is the integer label and D is \(2^{(\textrm{Refinement Level})}\).
  • Segment Identifier:
    The Refinement Level and an integer labeling a Segment.
  • Element:
    A refined subregion of a Block defined by its Segments in each logical coordinate. The properties of the Element are inherited from the block, i.e. it is self-similar to the Block.
  • Element Identifier:
    The Block Identifier containing the Element and a Segment Identifier in each logical coordinate axis.
  • Mesh:
    A regular set of grid points associated with an Element. Represented by the data structure Mesh.
  • External Boundary:
    A face of a Block or Element that has no neighbor.
  • Internal Boundary:
    A boundary that is not an External Boundary.
  • Face Neighbors (Rename C++ Neighbors class to FaceNeighbors):
    The identities and Orientation of the neighbors in a particular direction of a given Element.
  • External Boundary Condition:
    A prescription for updating the solution on an External Boundary. Each External Boundary of Block has exactly one External Boundary Condition associated with it.