Introduction

In Afivo so-called quadtree (2D) or octree (3D) grids are used, as well as their 1D equivalent.

Quadtree grids

A quadtree grid in Afvio consists of boxes (i.e., blocks) of \(N \times N\) cells, with \(N\) an even number. An example of a quadtree grid with boxes of \(4 \times 4\) cells is shown below.

A box in a quadtree grid can be refined by covering it with four refined boxes ('children'). These children contain the same number of cells as their parent, but half the grid spacing. Each of the children can again be refined, as illustrated above. In Afivo so-called proper nesting or 2:1 balance is ensured, which means that neighboring boxes differ by at most one refinement level.

Octree and 1D grids

Octrees are the 3D equivalent of quadtrees. When a box is refined, it is covered by eight children instead of four in 2D. The 1D equivalent of such trees is also supported in Afivo. Properties of such trees are summarized in the table below.