Solve PDE on 2D non-flat surface

1

Hello, I am new to fenics, in fact I have never used it. I read the tutorial-vol1, and am tempted to download and try it but I wonder if it supports the situation that I am interested in before I spend the time to figure this out.

My main question is that whether fenics can solve PDE on two-dimensional non-flat closed surface, embedded in R^3. For example on surface of sphere or torus. The specific case that I have is not a simple surface like these but I have the nodes and the two-dimensional triangular meshes, connecting these nodes.

After reading the tutorial, maybe the more specific questions are:

  1. Can fenics upload a given mesh (what is the format of acceptable mesh)?
  2. If the format of the meshes is not acceptable, how to generate two-dimensional mesh given the nodes of non-flat close surface.
  3. Does V = FunctionSpace(mesh, ’P’, 1) support meshes of non-flat geometry? If it does not, how to do this?
  4. I assume that as soon as V is generated, the variational form can be generated with the same commands as in the flat geometry case. Let me know if this is true.

It will be great if there are examples that I can look at?

John

2

1-2: Yes, you can upload meshes to FEniCS, in an xml or xdmf format. For more details on that subject, see: Transitioning from mesh.xml to mesh.xdmf, from dolfin-convert to meshio for what tools is suggested to use for creating a suitable format.
3-4: Yes, it does, see the example of a PDE on a manifold: https://bitbucket.org/fenics-project/dolfin/src/master/python/demo/undocumented/mixed-poisson-sphere/demo_mixed-poisson-sphere.py , where there are some notes on some things that only has to be done for manifolds.

3

Thanks for your respond. In that case, let me try to set it up and use the demo code in there as a starting point. I guess this means I have to also install dolfin in addition to fenics.

4

Dolfin is the computational backend of FEniCS, unless you are installing from source you would not have to worry about it. What OS are you using?

5

I used Mac OSX. I just read the fenics tutorial again and now I see that Dolfin is simply part of fenics. I will just try to install fenics first following the direction in Section 1.4.1 of the tutorial.