Periodic boundary conditions

[JaroCamphuijsen]

I just realized that we need some (almost) consortium wide discussion about something that may sound trivial: what do we do with the periodic planar geometry?
I'd like to bring this up now, because if we want an arbitrarily fine triangular mesh for the periodic geometry, it would be great if we can test this already now and include it in the stanford bunny project for the special issue of the microtubule modeling workshops (deadline September).

First details about what is there, then the questions

Cortical Sim Bio (2D) has periodic geometry in two ways:
geometry periodic X Y D
which gives a X x Y periodic rectangular domain (topologically, this is a donut), without further subdivision. parameter D is a dummy that just needs to be there for the reading routine, but does nothing

geometry grid X Y D
which gives a periodic X x Y domain as above, but the X direction is subdivided into D equal length pieces and the Y direction is subdivided into a matching number (say E) of pieces that gives "grid cells" with an aspect ratio close to 1

I use this geometry a lot for basic questions where I do not wish to investigate the impact of geometry. Under many conditions, this geometry has very little biasing effect on orientation. I almost always use "grid" rather than "periodic", simply because it is way faster. "periodic" has its uses in verification.

There is no equivalent implemented at the moment in Cortical Sim 3D.
There are a few options:
A: port the "square mesh" based method from Cortical Sim Bio; the mesh will be generated on the fly by just 3 (or 4, if you wish) input numbers.
B: develop a routine that generates a triangular mesh that is similarly controlled by a single input parameter
C: create a mesh externally, and spend some effort in telling the edges on the "edge" of the periodic domain that their neighbours are on the other side. This would need to be redone for every possible mesh refinement.
D: the thing I did not think about yet.

What would have your preference? What would be the consequences for linking things to a PDE via MorphoMechanX?
I can imagine the periodic geometry does not make much sense for a mechanical cell, but if you use the same FEM infrastructure and now look at a different PDE (e.g., a Turing-like system representing ROP proteins), then the periodic surface could be quite useful again. I would certainly be interested in having such an option.

[Eva]