Hi Lawrence,
I need a way to distinguish the two subdomains, that are 1) the disk, 2) the square with a hole instead of the disk (see black and blue meshes in the attached figure).
Can I make the equivalent to the blue mesh (i.e., a square with a hole) using PeriodicUnitSquareMesh ? And if so, can I make sure that
the nodes at the boundary of my disk mesh (black) match those of the plane mesh (blue) at the hole boundary?
Cheers,
Floriane
De : Lawrence Mitchell <wencel@gmail.com>
Envoyé : mercredi 7 novembre 2018 14:14
À : Floriane Gidel [RPG]
Cc : David Ham; firedrake
Objet : Re: [firedrake] Periodic domain with imported mesh
> On 7 Nov 2018, at 13:16, Floriane Gidel [RPG] <mmfg@leeds.ac.uk> wrote:
>
> Hi David,
>
> It would be again a disk centered in a square domain and I need the square boundaries to be periodic both in x and y. Now I'm solving a simple problem with a solution u_p in the plane and u_d in the disk that are only y-dependent and satisfy:
>
> Delta_y u_p = 0 in the plane
> grad_y u_p . n_y = n_y at the disk/plane interface.
> u_p periodic
>
> Delta_y u_d = 0 in the disk
> grad_y u_d . n_y = n_y at the disk/plane interface.
> int (u_d) dx(disk) = 0
>
> Note that n_y at the disk/plane interface is equal to sin(theta), which will therefore be the source term in the weak formulations.
>
> So the two problems can be solved independently, but the domain must contain both the disk and the surrounding plane in both cases to apply the condition at the interface (or we need to make sure that the interface nodes are at the same location in both meshes).
> At the moment I use triangular mesh with CG1 basis functions, but that is quite flexible.
You can make a topologically periodic square mesh with:
PeriodicUnitSquareMesh(..., direction="both")
I think that's what you want?
Cheers,
Lawrence