Spatial resolution for creating FEM?

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Eric
Posts: 19
Joined: Mon Jun 10, 2002 2:06 pm

Spatial resolution for creating FEM?

Post by Eric » Tue May 22, 2007 4:08 pm

Hello,
I am creating a 2D domain that is several meters wide and several meters high. Within the domain I have a few very thin layers (geotextile layers that are ~4 mm thick). There are 3 of these layers on top of each other, with soil over and below the stack of geotextile. I am trying to describe the location of these layers in the domain by using internal lines to delineate the top and bottom of each layer. Ideally, I would like to use several internal lines that are parallel (in the horizontal direction) and stacked above each other with a spacing of approximately .3 mm between the layers in the vertical direction. I know that I may be asking a lot of the model, especially given that the total domain size is on the order of meters, but I would like to create the best representation of the physical system that I can, within reason.

My question regards what the spatial resolution in the preprocessor is when discretizing the domain. For example, if I take one of my internal lines and translate/copy it to create a new line that is .2 mm above the original line, the new line does not appear. (Or perhaps it is placed on top of the original line?) If I shift the duplicate line by .8 mm, the new line does does appear on the screen, suggesting that the resolution is somewhere between .2 and .8 mm. In the latter case I get an error message saying that the new line intersects another line above it, though visual inspection of the entire length of both lines does not reveal any points at which they intersect. I assume that the two "overlapping" lines are within some specified distance of each other that the computer programs believes to be the same location (i.e., they are closer than the resolution used within the program). I have tried adjusting the grid spacing to values as small as 0.1 mm but it did not appear to have an effect on this issue. Does the allowed resolution depend on the grid spacing, or is it dependent on some hardwired value in the program? If my expectations for discretizing the model to such small spatial values are unrealistic, any hints about how to represent the thin geotextile layers would be appreciated.

Thanks,

Eric

Mirek
Posts: 406
Joined: Sat Mar 16, 2002 4:00 pm
Location: Czech Republic
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Post by Mirek » Wed May 23, 2007 6:11 pm

Hi Eric,

The problem indeed is in the epsilon defining the model resolution/precision. This epsilon is defined as Eps = R/10000 where R is a "domain radius", i.e. radius of the circle/sphere circumscribing the domain. This epsilon is used for example to compare positions of two points and if their distance is less than Eps than the two points are replaced by a single point (which is correct because "overlapping points" are not allowed). Perhaps I should explain reasons why we define the Eps in this way and not for example as Eps = R/100000:

1/ I can imagine that too small Eps could cause many problems with incorrect definitions of the model. Point coordinates X,Y are usually displayed with 3-4 decimal places in dialogs and other GUI => it would be easy to make a mistake and create overlapping points, etc.

2/ If your model contains details smaller than 1/10000 of the domain radius then I think that your FE-mesh will be huge. A regular (not-refined) mesh would have 10000 x 10000 = 100 000 000 elements which is quite unrealistic for PCs. I know that you can use mesh refinements and perhaps you will be able to create a mesh with an acceptable number of elements but I'm not sure if such mesh would be good for the numerical solver - this is a question for Jirka.

The Summary: I think that the default value for the Epsilon is defined correctly as it is now. However, I understand that you need a solution. The solution could be that we will allow users to specify their own epsilon (specific for a project). With a smaller epsilon you will be able to define those thin geotextile layers but using of this Eps will be "at your risk", i.e. we can not guarantee that all functions (for example manipulations, auto-detection, etc.) will work correctly. This change will be done in the next version (probably in 1-2 weeks).

We will also check the source code to make sure that this epsilon is used correctly in all functions that make geometrical calculations.

Regards
Mirek

Eric
Posts: 19
Joined: Mon Jun 10, 2002 2:06 pm

Post by Eric » Wed May 23, 2007 6:18 pm

Hi Mirek,
Thanks for the detailed answer. The approach you have taken to defining the epsilon is logical and reasonable. Of course, it will be nice if you have a chance to incorporate the added flexibility with epsilon into the next update and I can use it to solve my problem. Or, perhaps the additional option will just provide me with a way to get myself into deeper trouble with HYDRUS. [:D]

Thanks again,

Eric

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