[Gmsh] Periodic Line (Curve) not working for second-order elements

[Christophe Geuzaine]

> On 23 Oct 2018, at 21:37, Koen Hillewaert (Cenaero) <koen.hillewaert at cenaero.be> wrote:
> 
> Hi,
> 
> the issue is that the periodic connection for high order nodes uses the transformation, which is not computed anymore. This computation is not univocal (even your case has infinite possibilities for transforming line 2 into 4).
> 
> The approach used for meshing the non-high order vertices assumes the parametric representation of periodic counterparts is fully compatible and then finds the node counterparts simply by using the same parametric coordinates on the other line/surface. Although this assumption is not generally true, we could also make it for the high order nodes in case no transformation is specified. However only by using the transformation to position periodic vertices we can guarantee watertight meshes, in particular since some high order node optimisations may position high order nodes slightly off the surface/edge. I would even be in favour of also using the transformation to position principal vertices instead of assuming the same parametrisation.
> 
> Christophe, what is your opinion ?

If no transformation is given, I would use the parametrization. This would provide backward compatibility with Gmsh 3, and will work on many simple (but common) cases, e.g. straight lines created with the build-in CAD engine, which are always parametrized in [0,1].

> 
> Best,
> 
> Koen
> 
> 
> On 10/23/18 7:57 PM, Christophe Geuzaine wrote:
>> Dear Martien,
>> 
>> It's indeed one more side effect of the changes for correctly handling periodicity for high-order meshes. As a workaround you should currently specify the transformation explicitly, i.e. specify
>> 
>> Periodic Line {2} = {4} Translate{lx,0,0};
>> 
>> instead of
>> 
>> Periodic Line {2} = {-4};
>> 
>> @Koen - do you see an easy fix?
>> 
>> Christophe
>> 
>> 
>>> On 23 Oct 2018, at 18:19, Hulsen, M.A. <M.A.Hulsen at tue.nl> wrote:
>>> 
>>> Hi,
>>> 
>>> The following geo file does not work correctly for gmsh4.0.4 when running with ‘gmsh -2 -order 2’. It does work for ‘gsmh -2’. Also gmsh3.0.6 is fine.
>>> 
>>> ox =  -1.00000000000000;
>>> oy =  -0.50000000000000;
>>> lx =   2.00000000000000;
>>> ly =   1.00000000000000;
>>> dx_box =   0.10000000000000;
>>> // Create domain vertices
>>> Point(1) = {ox,    oy,    0.0, dx_box};
>>> Point(2) = {ox+lx, oy,    0.0, dx_box};
>>> Point(3) = {ox+lx, oy+ly, 0.0, dx_box};
>>> Point(4) = {ox,    oy+ly, 0.0, dx_box};
>>> For i In {1:4}
>>>  Physical Point(i) = i;
>>> EndFor
>>> // Create domain sides
>>> Line(1) = {1, 2};
>>> Line(2) = {2, 3};
>>> Line(3) = {3, 4};
>>> Line(4) = {4, 1};
>>> For i In {1:4}
>>>  Physical Line(i) = i;
>>> EndFor
>>> // Create outer boundary
>>> lin_loop[0] = newll;
>>> Line Loop(lin_loop[0]) = { 1, 2, 3, 4 };
>>> // Make lines periodic
>>> Periodic Line {2} = {-4};
>>> // Create surface mesh
>>> Plane Surface(1) = {lin_loop[]};
>>> Physical Surface(1) = {1};
>>> 
>>> 
>>> Martien
>>> _______________________________________________
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>>> gmsh at onelab.info
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>> —
>> Prof. Christophe Geuzaine
>> University of Liege, Electrical Engineering and Computer Science
>> http://www.montefiore.ulg.ac.be/~geuzaine
>> 
>> Free software: http://gmsh.info | http://getdp.info | http://onelab.info
>> 
>> 
>> 
> 
> -- 
> Koen Hillewaert
> Fluid Dynamics Technology Leader
> 
> https://www.researchgate.net/profile/Koen_Hillewaert
> 
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— 
Prof. Christophe Geuzaine
University of Liege, Electrical Engineering and Computer Science 
http://www.montefiore.ulg.ac.be/~geuzaine

Free software: http://gmsh.info | http://getdp.info | http://onelab.info