[Gmsh] How can I make this mesh such that it has periodic sides

[Christophe Geuzaine]

> On 6 Apr 2019, at 22:22, Abiti Adili <aadili1 at lsu.edu> wrote:
> 
> Dear Dr. Geuzaine:
> 
> I added the what you have suggested at the end of my geo file ( attached above). I have created,  just for the sake of trial, a coarse mesh and saved the msh file ( attached above).  I understand that my mesh now is periodic and there is the periodicity information at the end right after the element list in my msh file. The problem now is that I could not  understand how to read this information. For example:
> 
> 1) what is affine and the numbers after it mean?

It's the 4x4 matrix (by row) encoding the affine transformation between the entities.

> 2) Are those two columned numbers are the vertices that correspond to periodic nodes on opposite sides? if yes, how do I read these information.?
> 

From the documentation (MSH 4 file format):

```
$Periodic
  numPeriodicLinks(size_t)
  entityDim(int) entityTag(int) entityTagMaster(int)
  numAffine(size_t) value(double) ...
  numCorrespondingNodes(size_t)
    nodeTag(size_t) nodeTagMaster(size_t)
    ...
  ...
$EndPeriodic
```

So the section provides, for each pair of geometrical entities (`entityTag` and `entityMasterTag`) of dimension `entityDim`, the correspondance between `numCorrespondingNodes` mesh nodes also given as pairs: a node tag (in entity `entityTag`) and its corresponding master node (in entity `entityMasterTag`), etc.

Christophe

> I would appreciate if you could explain this a little or direct me to where I can refer to when reading these information so that I can use them when imposing periodicity condition.
> 
> Thank you very much.
> 
> Adil
> 
> 
> ________________________________________
> From: Christophe Geuzaine <cgeuzaine at uliege.be>
> Sent: Friday, April 5, 2019 11:42:19 AM
> To: Abiti Adili
> Cc: gmsh at onelab.info
> Subject: Re: [Gmsh] How can I make  this mesh  such that it has periodic sides
> 
> 
> 
>> On 4 Apr 2019, at 18:03, Abiti Adili <aadili1 at lsu.edu> wrote:
>> 
>> I have  a tetrahedral mesh over a unit box that has  two balls of different sizes inside the box. The geometry is created by geometrycloser.geo, and the physical  entities and such were created by importing geometrycloser.geo into  omnibuscloser.geo.
>> 
>> I have a periodicity condition to impose where I need to say that
>> 1) right side of the box is the same with left side
>> 2) top side is the same with bottom side
>> 3) front side is the same with the back side
>> 
>> When I tried to make the system matrices periodic using a function that has been tested on other examples, it did not work correctly and I  have concluded that either vertices or facets on the sides of the box may not have been aligned.
>> 
>> I am writing to ask if there is anyway that I can modify the geo files I provided so that I can integrate the periodicity condition into the mesh I make?  Thank you very much.
>> 
> 
> You need to explicitly tell Gmsh that the meshes should be periodic. In your example, add
> 
> Periodic Surface{5} = {6} Translate {1,0,0};
> Periodic Surface{2} = {4} Translate {0,1,0};
> Periodic Surface{1} = {3} Translate {0,0,1};
> 
> at the end of the geo file.
> 
> Christophe
> 
>> 
>> Adil<geometrycloser.geo><omnibuscloser.geo>_______________________________________________
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> —
> Prof. Christophe Geuzaine
> University of Liege, Electrical Engineering and Computer Science
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— 
Prof. Christophe Geuzaine
University of Liege, Electrical Engineering and Computer Science 
http://www.montefiore.ulg.ac.be/~geuzaine