what does it mean “the neighbor is coarser, but still has children which are finer than our current cell” in step 30？

[曾元圆]

hi, I am reading the tutorial of step-30, it talks about anisotropic refinement.

it says: "It might be, that the neighbor is coarser, but still has children which are finer than our current cell. This situation can occur if two equally coarse cells are refined, where one of the cells has two children at the face under consideration and the other one four. The cells in the next graphic are only separated from each other to show the individual refinement cases."

"The left cell marked with # has two finer neighbors marked with +, but the actual neighbor of the left cell is the complete right mother cell, as the two cells marked with + are finer and their direct mother is the one large cell."

what it mean by saying "the actual neighbor of the left cell is the complete right mother cell"?  Can somebody help to explain this in detail? By the way, where can I find a documentation simply explain the data structure and the hierarchy in anisotropic refinement?

[Bruno Turcksin]

Hi,

Basically, what happen is that if you ask for the right neighbor of the cell # you will get the coarse right cell. The reason is that when you ask for the neighbor, you get a cell that has the same level of refinement or that is coarser. Now, when you look at cell # you could think that the neighbor is a coarse cell formed by the two cells + but this is not the case because that potential coarse cell does not exist.  You either have the whole coarse cell or the four refined cells. Does that make sense?

Best,

Bruno

[曾元圆]

Thank you for your reply, Bruno. 

Now I understand what you mean. But I'm still curious about how the cell # can figure out the correct "neighbor" of it. You mentioned that when you ask for the neighbor of cell #, you get a cell that has the same level of refinement or that is coarser. But in anisotropic refinement we don't identify a coarser cell though the "level" it belongs to, which is the case in isotropic refinement.

I suppose we have stored a "neighbor" of cell # correctly before ask for that. But how do we in fact set the link between cell# and it's neighbor, i.e. the right whole mother cell? I just want to know how these cells belonging to different "levels" are connected. I know perhaps it is not easy to explain in a few words, so it's preferable if there are some available thesis or documentation related to this. 

Thank you again anyway.

在 2017年11月16日星期四 UTC+8下午10:07:53，Bruno Turcksin写道：

[Wolfgang Bangerth]

On 11/16/2017 07:55 PM, 曾元圆 wrote:
> Thank you for your reply, Bruno.
> Now I understand what you mean. But I'm still curious about how the cell # can
> figure out the correct "neighbor" of it. You mentioned that when you ask for
> the neighbor of cell #, you get a cell that has the same level of refinement
> or that is coarser. But in anisotropic refinement we don't identify a coarser
> cell though the "level" it belongs to, which is the case in isotropic refinement.
> I suppose we have stored a "neighbor" of cell # correctly before ask for that.
> But how do we in fact set the link between cell# and it's neighbor, i.e. the
> right whole mother cell? I just want to know how these cells belonging to
> different "levels" are connected. I know perhaps it is not easy to explain in
> a few words, so it's preferable if there are some available thesis or
> documentation related to this.

I don't know whether that's documented in great detail anywhere, but it
happens at the end of refining each cell:

https://github.com/dealii/dealii/blob/master/source/grid/tria.cc#L4493

In other words, each cell's neighbors are the children of its parent's neighbors.

We're always interested in improving documentation, and if you think that
there is a good place to add this sort of information, we'd be quite happy to
include whatever you come up with!

Best
W.



--
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Wolfgang Bangerth email: bang...@colostate.edu
www: http://www.math.colostate.edu/~bangerth/