Difference between "prolongation" and "refine" ("restriction" and "coarse")

[shine Sun]

Hello everyone,

In multigrid method, we have "prolongation" and "restriction" operations to speed up the solving of equations. I notice that there are "refine" and "coarse" operations on tree grid and they are often set as:  xx.refine=xx.prolongation=some method.  

I want to know whether the refine and coarse operations are equivalent to those on multigrid? However, "refine" and "coarse" are for Tree grid? I hope someone can help me clearify the concepts. Thank you!

[Stephane Popinet]

Hi Shine,

The 'prolongation' and 'restriction' operations are used to interpolate
between coarse to fine and fine to coarse grids respectively, typically
for multigrid solvers and/or when computing boundary conditions at
refinement levels for quad/octree grids.

So, yes, they are defined on both multigrid and tree grids.

The 'refine' and 'coarsen' operations are used when performing adaptive
mesh refinement and are thus defined only on tree grids.

('refine' and 'prolongation') and ('coarsen' and 'restriction') are
often identical, but not always i.e. it is useful to be able to tune one
independently fromy the other, depending in particular on the properties
of the field.

hope this helps,

Stephane

[shine Sun]

Thank you Stephane! That helps!