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.

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