Good to hear. I'm slightly surprised that snippet works: gmsh documentation says that Circle creates an arc of angle "(strictly) smaller than Pi", which is why the usual snippet breaks it into 4 quarter-circle segments (slightly cleaner than 3, I guess). On 19 March 2017 at 16:31, Francis Poulin <fpoulin@uwaterloo.ca> wrote:

Thank you Andrew.

Adding a Physical Surface was what I was missing.

I found a more compact version and including it here, in case others might benefit from it.

// mesh width associated with points lc = 0.1; ln = 1.0;

// Two antipodal points on the circle, the third point is the circle center Point(1) = {-ln, 0, 0, lc}; Point(2) = { ln, 0, 0, lc}; Point(3) = { 0, 0, 0, lc};

Circle(1) = {1,3,2}; Circle(2) = {2,3,1};

Line Loop(100) = {1,2};

Plane Surface(200) = {100};

Physical Surface(300) = {200};

Also, I now see that it's silly to wan to run gmsh on firedrake. Sorry.

Cheers, Francis

------------------ Francis Poulin Associate Professor Department of Applied Mathematics University of Waterloo

email: fpoulin@uwaterloo.ca Web: https://uwaterloo.ca/poulin-research-group/ Telephone: +1 519 888 4567 x32637 <(519)%20888-4567>

------------------------------ *From:* firedrake-bounces@imperial.ac.uk [firedrake-bounces@imperial.ac.uk] on behalf of Francis Poulin [fpoulin@uwaterloo.ca] *Sent:* Sunday, March 19, 2017 12:04 PM *To:* firedrake@imperial.ac.uk *Subject:* Re: [firedrake] circles in firedrake?

Thank you Andrew for your help. I am a bit sorry to see CircleMesh go away but if it only gave a structured mesh, then I can see the advantage to using gmsh. Also, I should really learn how to use gmsh better, so this will force me to do just that.

I looked around for circle.geo but couldn't find it in the repo.

I found another version of circle.geo that seems to build a circle. It is copied here

L = 10; dx = 1;

Point(1) = { 0, 0, 0, dx}; Point(2) = { L, 0, 0, dx}; Point(3) = {-L, 0, 0, dx}; Point(4) = { 0, L, 0, dx}; Point(5) = { 0,-L, 0, dx};

Circle(1) = {3,1,5}; Circle(2) = {5,1,2}; Circle(3) = {2,1,4}; Circle(4) = {4,1,3};

Line Loop(5) = {1,2,3,4};

Plane Surface(6) = {5};

I am not sure why the origin needs to be included but it does give the correct shape at least.

Unfortunately, when I try importing this in firedrake using

from firedrake import *

#gmsh -2 circle.geo

mesh = Mesh("circle.msh")

I get the error

Traceback (most recent call last): File "test.py", line 7, in <module> mesh = Mesh("circle.msh") File "<decorator-gen-261>", line 2, in Mesh File "/home/fpoulin/software/firedrake/src/PyOP2/pyop2/profiling.py", line 61, in wrapper return f(*args, **kwargs) File "/home/fpoulin/software/firedrake/src/firedrake/firedrake/mesh.py", line 1259, in Mesh topology = MeshTopology(plex, name=name, reorder=reorder, distribute=distribute) File "<decorator-gen-259>", line 2, in __init__ File "/home/fpoulin/software/firedrake/src/PyOP2/pyop2/profiling.py", line 61, in wrapper return f(*args, **kwargs) File "/home/fpoulin/software/firedrake/src/firedrake/firedrake/mesh.py", line 348, in __init__ dmplex.validate_mesh(plex) File "firedrake/dmplex.pyx", line 1009, in firedrake.dmplex.validate_mesh (firedrake/dmplex.c:14063) ValueError: Provided mesh has some entities not reachable by traversing cells (maybe rogue vertices?)

Can you point out what I'm doing wrong? Or where to find the circle.geo?

Also, I tried use gmsh in firedrake as commented above and that didn't work. Should gmsh work in the latest version?

Cheers, Francis

------------------ Francis Poulin Associate Professor Department of Applied Mathematics University of Waterloo

email: fpoulin@uwaterloo.ca Web: https://uwaterloo.ca/poulin-research-group/ Telephone: +1 519 888 4567 x32637 <(519)%20888-4567>

------------------------------ *From:* firedrake-bounces@imperial.ac.uk [firedrake-bounces@imperial.ac.uk] on behalf of Andrew McRae [A.T.T.McRae@bath.ac.uk] *Sent:* Sunday, March 19, 2017 8:07 AM *To:* firedrake@imperial.ac.uk *Subject:* Re: [firedrake] circles in firedrake?

We used to have a CircleMesh in Firedrake, but it was removed in this commit <https://github.com/firedrakeproject/firedrake/commit/54bff6b70e046106ddd4e72c23f48a2999510155>. If I recall correctly, this is because we outsourced the creation of that mesh to gmsh, but the gmsh-from-Python packages are no longer available with newer versions of Ubuntu.

That commit has a small gmsh snippet (.geo). You could manually run this through gmsh to build a mesh (.msh), and load this in to your firedrake script: mesh = Mesh("circle.msh"). Note that this CircleMesh (and, IIRC, FEniCS's equivalent) give a "structured" mesh with radial lines, and correspondingly small cells in the middle. If this is undesirable, you might be better off making a simple unstructured circle mesh in gmsh and loading it in.

Regarding the code you gave in your email, I think this has also worked just fine. However, the built-in Firedrake plotting functionality only seems to support 2D triangle and "unstructured" quadrilateral cells, rather than the "interval x interval" cells created by an extruded mesh. (I suspect this was an accidental omission)

If you instead do File("temp.pvd").write(U) and open the result in Paraview, I'm sure it would look fine. Of course, if you use this to get a circular mesh, it will also have small cells at the centre.

Best, Andrew

On 18 March 2017 at 17:29, Francis Poulin <fpoulin@uwaterloo.ca> wrote:

...

Hello,

I want to define my mesh to be a circle. In Fenics I know there is a command called CircleMesh that makes this very easy.

Q1) Is there a simple way of doing this in Firedrake?

I looked around and see how circlemanifoldmesh can do this with help for ExtrudedMesh. I found some code that can make a ring and I tried running it myself and defining a function on that mesh. Unfortunately, I get an error, see below.

Q2) If one needs to use CircleManifoldMesh is there something else one needs to do to use a circular geometry as your mesh?

Below are the lines that I tried and the error

...

...

...

from firedrake import * m = CircleManifoldMesh(20, radius=2) mesh = ExtrudedMesh(m, 5, extrusion_type='radial') x = SpatialCoordinate(mesh) V = FunctionSpace(mesh,'CG',1) U = Function(V).interpolate(-(pow(x[0]-0.5,2) + pow(x[1]-0.5,2))) plot(U); Traceback (most recent call last): File "<stdin>", line 1, in <module> File "/home/fpoulin/software/firedrake/src/firedrake/firedrake/plot.py", line 308, in plot **kwargs) File "/home/fpoulin/software/firedrake/src/firedrake/firedrake/plot.py", line 502, in two_dimension_plot num_sample_points) File "/home/fpoulin/software/firedrake/src/firedrake/firedrake/plot.py", line 457, in _two_dimension_triangle_func_val raise RuntimeError("Unsupported Functionality") RuntimeError: Unsupported Functionality

------------------ Francis Poulin Associate Professor Department of Applied Mathematics University of Waterloo

email: fpoulin@uwaterloo.ca Web: https://uwaterloo.ca/poulin-research-group/ Telephone: +1 519 888 4567 x32637 <(519)%20888-4567>