On 03/27/2015 04:48 PM, Robert Cimrman wrote:
On 03/27/2015 05:31 PM, Alex Eftimiades wrote:
On Friday, March 27, 2015 at 10:45:19 AM UTC-4, Robert Cimrman wrote:
Hello Alex,
yes, contributions are welcome!
I am not sure if your code is directly applicable - am I right that it uniformly meshes a rectangle or cube by a regular simplex mesh?
The idea was to uniformly mesh manifolds of arbitrary topology and dimension by breaking it into partitions that can be mapped K-cells, then gluing arbitrary subsets of the cells together.
OK I see (sort of - I know nothing about discrete exterior calculus etc - forgive me my stupid questions :)). Can it be used to triangulate other shapes than K-cells? More examples would be nice, if you have some.
Discrete exterior calculus is not really mainstream--at least in its most general form. It seems to have been reinvented for different purposes a few times. On such example is the Yee scheme commonly used for electromagnetics simulations.
Anyway, about the the triangulation code: The idea was to be able to triangulate just about anything you'd come across in physics or engineering. I attached some pictures of eigenmodes of triangulated structures. The structures triangulated are a torus, a Möbius strip, and a Klein bottle. I've also triangulated circles, spheres and cylinders. I also attached the corresponding meshes (though with less elements so you could see the pattern). In principle, you could triangulate 8 dimensional regions embedded in 12 dimensional spaces if you had the inclination and computational power. The idea was to keep the framework as general as possible.
But anyway, let us try to find something that would be interesting for you and useful for sfepy. Did you manage to install it without problems?
I just ran the unit tests on the version on github, and everything seems to be working, though test_input_navier_stokes2d_iga.py complained about not being able to find "igakit".
Good. Yes, igakit is needed for that one. We should add it as a dependency into setup.py etc.
I'm not exactly sure what direction(s) sfepy is looking to expand in, but I'd love to help in whatever way I can. I've spent a fair amount of time discretizing wave equations (usually electromagnetic and acoustic) if that helps.
Yes, the more of your background I know, the better I could steer you to a suitable topic. Electromagnetic problems are among the things that are missing in sfepy, and would be nice to have. Do you have some experience with the vector elements (e.g. of Nedelec or Raviart-Thomas type)? What is your experience with FEM? Do you know other discretization methods, such as discontinuous Galerkin?
My background has been rewriting an open source implementation of discrete exterior calculus, PyDEC http://www.math.uiuc.edu/%7Ehirani/papers/BeHi2012_TOMS.pdf so that it would work under more general conditions http://arxiv.org/abs/1405.7879, in parallel, and in a generally faster manner. I admittedly lack industry experience with FEM, and I am hoping to gain some more practical experience from collaborating on open source projects.
As you can see from the attached pictures, I have some experience with eigenvalue problems and wave propagation. I am looking to expand my skill set working other problems.
As a start, I suggest you read the tutorial and the primer, so that you get a feel of how the code can be used. Also check the examples.
Will do.
Thanks for your interest! r.