[Dune] tranformed geometry across periodic boundaries

Mon May 21 17:12:32 CEST 2012

Hi Matteo,

hopefully I found the problem in the conforming case. If the intersection is 
non-conforming, the cache for the local geometries is still lacking.

Could you test the attached patch?

Best,

Martin

On 05/21/2012 02:49 PM, Martin Nolte wrote:
> Hi Matteo,
>
> you are right: the trick does not work for ALUCubeGrid in 2d. The reason is
> that 2d ALUGrid's local intersection geometries are currently computed from
> the intersection geometry and the outside geometry (except for conforming
> intersections in a trianglular grid). I'll have a further look into this.
>
> Best,
>
> Martin
>
> On 05/21/2012 10:44 AM, Matteo Semplice wrote:
>> Thanks Martin,
>>
>> I take that the trick you meant is obtaining the displacement from the
>> boundary as
>>
>>
>> GlobalCoordinate displacement =
>>
>> outside.geometry().center()
>>
>> - outside.geometry().global(face.geometryInOutside().center());
>>
>> and then computing the outside center as
>>
>> GlobalCoordinate gl_out_cx_trick = face.geometry().center() + displacement;
>>
>> The problem is that is does not work as expected, because also
>> face.geometryInOutside() seems to behave
>> in an inconsistent way across different grid implementations.
>>
>> I attach a test.cc code and two dgf's for periodic sqare/cube grids that I
>> used in my tests. I also
>> attach the output of the program, when compiled and run with different grids
>> (some comments are in there)
>>
>> The code sould be compiled by defining GRIDTYPE and GRIDDIM as in the
>> grid-howto examples.
>> Also note that since I was surprised by the YASP grid failure to create a
>> periodic grid at all,
>> I tried to rule out a mistake in the dgfparser, so can also compile the code
>> with FORCE_YASP defined
>> and it will create a periodic 2d YASP without using the dgfparser (the results
>> are the same, though)
>>
>> Here is a summary of the results
>>
>> yes = works as in the official interface
>>
>> trick = not conformant to official interface, but your trick works
>>
>> no = neither the offical interface method nor the trick works
>>
>> no b.c. = grid does not handle the periodic b.c.
>>
>> crash = won't compile, or crash during execution
>>
>> 2D 3D
>>
>> YASP no b.c. no b.c.
>>
>> SGRID no b.c. no b.c.
>>
>> ALBERTA trick trick
>>
>> ALUCUBE no crash
>>
>> ALUSIMPLEX trick crash
>>
>> Best,
>> Matteo
>>
>> On 16/05/2012 13:36, Martin Nolte wrote:
>>> Hallo Matteo,
>>>
>>> the problem is that discussion about periodic boundary conditions got stuck
>>> around 3 years ago.
>>>
>>> The documentation of dune-grid describes the "official" interface for
>>> implementing perioditicy and is only implemented by YaspGrid.
>>>
>>> AlbertaGrid, ALUGrid and SPGrid support periodic boundary conditions in a
>>> different (unofficial) way (as you already observed): They return the original
>>> element on the other side. Since the intersection reports itselft as boundary,
>>> you can now choose the appropriate boundary condition (e.g., periodic). Notice
>>> that this is interpreted as a special choice of boundary condition and you
>>> have to do something by hand, here.
>>>
>>> To obtain the transformation, AlbertaGrid's intersection implementation has a
>>> method transformation (in case that helps you). Apart from that, you can use
>>> the geometryInOutside and the outside element geometry to obtain the world
>>> coordinates of the intersection on the outside element.
>>>
>>> The big problem is that only 1 developer (me) needed periodicity for a long
>>> time and, hence, the necessary interface discussion is still pending. I hope
>>> this clarifies the current situation, even if it does not really help.
>>>
>>> So, you will have to decide which technique you like better and either use the
>>> existing grids implementing it or implement such a grid yourself.
>>>
>>> Best,
>>>
>>> Martin
>>>
>>> On 05/16/2012 12:09 PM, Matteo Semplice wrote:
>>>> Hi dune,
>>>> I think I need some explanation on the exact meaning of the phrase
>>>> "transformed geometry" in the documentation of Dune::Intersection
>>>> <http://www.dune-project.org/doc/doxygen/dune-grid-html/class_dune_1_1_intersection.html#_details>
>>>>
>>>>
>>>>
>>>>
>>>> (By the way, the Detailed Description mentions a method "outer()" which is
>>>> not
>>>> listed in the interface, so I assume that it means "outside()"...)
>>>>
>>>> Say I have a 2d grid with 9 1x1 cells organized as follows
>>>>
>>>> 7,8,9
>>>> 4,5,6
>>>> 1,2,3
>>>>
>>>> so cell 1 has center at [.5,.5], cell 2 at [1.5,.5] and so on.
>>>> Suppose also that the x direction have periodic boundary conditions, i.e. my
>>>> dgf file has the section
>>>>
>>>> PERIODICFACETRANSFORMATION
>>>> 1 0 , 0 1 + 3 0
>>>> #
>>>>
>>>> From the phrase "outer() cell has a periodically transformed geometry (so
>>>> that one does not see a jump or something like that)" in the section on
>>>> periodic boundaries, I would expect that
>>>>
>>>> if the intersection "face" is the left side of cell 1, and I do
>>>>
>>>> EntityPointer pOut = face.outside();
>>>> Entity out = *pOut;
>>>>
>>>> then mapper(out) points me to data related to cell 3, but that
>>>> out->geometry().center()
>>>> returned [-0.5,0.5], so that effetively I would see the data of cell 3 as if
>>>> they were at the left of cell 1 and a PDE code does not need to know about
>>>> the
>>>> boundary transformation.
>>>>
>>>> As this is not the case (out->geometry().center() returns [2.5,0.5]) ,
>>>> what is
>>>> the meaning of that phrase?
>>>> And, given the current situation, does the grid implementation provide a
>>>> method to transform the [2.5,.5] into [-.5,.5] ?
>>>>
>>>> Best regards,
>>>> Matteo
>>>>
>>
>>
>>
>>
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>

-- 
Dr. Martin Nolte <nolte at mathematik.uni-freiburg.de>

Universität Freiburg                                   phone: +49-761-203-5630
Abteilung für angewandte Mathematik                    fax:   +49-761-203-5632
Hermann-Herder-Straße 10
79104 Freiburg, Germany
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