Create a figure to explain AMR

[ouankou]

It may have 4 subfigures.

A grid covers multiple cells. Different level of grid has different number of cells.

1. State 0: grid 0 has two children grid 1 and 2. Then grid 1 has its children grid 3 and 4.
2. Tree 0: 5 grids in a tree.
3. State 1: At some point, grid 3 is not needed and we can remove it and coarsen that section in grid 1. Meanwhile, a section in grid 2 is getting hot. We add refine it to add a child grid 5 to grid 2.
4. Tree 1: 5 grids in a tree, grid 3 is removed, grid 5 is added.

This procedure is called regridding. After this, a grid is fed into GPU or CPU to calculate the value of its cells.

[ouankou]

Sætra, M.L., Brodtkorb, A.R. & Lie, K. Efficient GPU-Implementation of Adaptive Mesh Refinement for the Shallow-Water Equations. J Sci Comput 63, 23–48 (2015). https://doi.org/10.1007/s10915-014-9883-4

Puneet Narula, "An Adaptive Mesh Refinement (AMR) Library Using Charm++", University of Illinois at Urbana-Champaign, 2002.
http://charm.cs.illinois.edu/newPapers/02-02/paper.pdf

They can be used for explaining AMR.

[ouankou]

Two figures have are added to Overleaf to explain AMR in general.