August 2016 - firedrake - imperial.ac.uk

3D SUPG on extruded mesh not working
by Justin Chang 05 Aug '16

05 Aug '16

Hi all, I have the following 3D advection diffusion problem with SUPG formulation: # Mesh meshbase = UnitSquareMesh(seed,seed,quadrilateral=True) mesh = ExtrudedMesh(meshbase,seed) V = FunctionSpace(mesh, 'CG', 1) Q = VectorFunctionSpace(mesh, 'CG', 1) u = TrialFunction(V) v = TestFunction(V) sol = Function(V, name="solution") # Velocity velocity = interpolate(Expression(( ... )),Q) # Dispersion tensor aT = 0.0001 aL = 1 aD = 0.0001 alpha_t = Constant(aT) alpha_L = Constant(aL) alpha_D = Constant(aD) normv = sqrt(dot(velocity,velocity)) Id = Identity(mesh.geometric_dimension()) D = (alpha_D + alpha_t*normv)*Id+(alpha_L-alpha_t)*outer(velocity,velocity)/normv # Forcing function f = Constant(0.0) # Weak form h = CellSize(V.mesh()) Pe = h/(2*normv)*dot(velocity,grad(v)) a_r = Pe*(dot(velocity,grad(u)) - div(D*grad(u)))*dx a = a_r + v*dot(velocity,grad(u))*dx + dot(grad(v),D*grad(u))*dx L = (v + Pe)*f*dx ... But when I try to run this code i get the following error: Traceback (most recent call last): File "3D_advection_diffusion_ex1.py", line 122, in <module> execfile('driver/AD_solver.py') File "driver/AD_solver.py", line 36, in <module> solver_parameters=solver_parameters, options_prefix="linear_") File "/home/justin/Software/firedrake/src/firedrake/firedrake/variational_solver.py", line 261, in __init__ super(LinearVariationalSolver, self).__init__(*args, **kwargs) File "/home/justin/Software/firedrake/src/firedrake/firedrake/variational_solver.py", line 127, in __init__ ctx = solving_utils._SNESContext(problem) File "/home/justin/Software/firedrake/src/firedrake/firedrake/solving_utils.py", line 107, in __init__ for problem in problems) File "/home/justin/Software/firedrake/src/firedrake/firedrake/solving_utils.py", line 107, in <genexpr> for problem in problems) File "/home/justin/Software/firedrake/src/firedrake/firedrake/assemble.py", line 67, in assemble inverse=inverse, nest=nest) File "<decorator-gen-295>", line 2, in _assemble File "/home/justin/Software/firedrake/src/firedrake/firedrake/utils.py", line 62, in wrapper return f(*args, **kwargs) File "/home/justin/Software/firedrake/src/firedrake/firedrake/assemble.py", line 101, in _assemble inverse=inverse) File "/home/justin/Software/firedrake/src/firedrake/firedrake/tsfc_interface.py", line 288, in compile_form number_map).kernels File "/home/justin/Software/firedrake/src/PyOP2/pyop2/caching.py", line 198, in __new__ obj = make_obj() File "/home/justin/Software/firedrake/src/PyOP2/pyop2/caching.py", line 188, in make_obj obj.__init__(*args, **kwargs) File "/home/justin/Software/firedrake/src/firedrake/firedrake/tsfc_interface.py", line 210, in __init__ tree = tsfc_compile_form(form, prefix=name, parameters=parameters) File "/home/justin/Software/firedrake/src/tsfc/tsfc/driver.py", line 54, in compile_form kernels.append(compile_integral(integral_data, fd, prefix, parameters)) File "/home/justin/Software/firedrake/src/tsfc/tsfc/driver.py", line 198, in compile_integral quadrature_degree)) File "/home/justin/Software/firedrake/src/tsfc/tsfc/fiatinterface.py", line 108, in create_quadrature raise RuntimeError("Requested a quadrature rule with %d points" % len(rule.get_points())) RuntimeError: Requested a quadrature rule with 1728 points If I had used a UnitCubeMesh I had no problems. What is going on here and how do I fix/circumvent this issue? Thanks, Justin

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Mixed system
by Anna Kalogirou 05 Aug '16

05 Aug '16

Dear all, I am trying to solve the system found in the attached pdf as a mixed system. I want to solve the same problem as the one found here <https://bitbucket.org/annakalog/buoy2d/src/14334d3c20b9f10ed7c1246cde9e3cb6…>, but with the use of Schur complements and not linear algebra. In a previous discussion about this problem, Lawrence mentioned that the test function for integral(lambda*Theta(x-Lp)dx) needs to be considered as coming from the real space of constant functions. Could you please elaborate on this? Regards, Anna. <https://bitbucket.org/annakalog/buoy2d/src/14334d3c20b9f10ed7c1246cde9e3cb6…> -- Dr Anna Kalogirou Research Fellow School of Mathematics University of Leeds http://www1.maths.leeds.ac.uk/~matak/

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Changing coordinates in one direction only
by Floriane Gidel [RPG] 05 Aug '16

05 Aug '16

Dear all, I use a change of coordinate to solve my equations, and I then save the solutions in the initial domain. The transform is \hat{x} = L(x-R)/(L-R). In 1D, my code to save the data in the initial (not transformed) mesh is: ---------------------------- # mesh on which I solve the equations (\hat{x}) mesh_transformed = mesh.coordinates.vector().get_local() # back to the initial mesh (applying the inverse transform) (x) mesh.coordinates.vector().set_local(mesh_transformed*(L-R)/L + R) # save data on the initial mesh save_h << h save_psi << psi # Back to the transformed mesh to solve the WF (\hat{x}) mesh.coordinates.vector().set_local(mesh_transformed) ---------------------------- This works well in 1D. However, I would like to extend my model in 2D, where the transform is still only in x. Therefore, I would like to apply the previous manipulation to the x coordinate only, and not on the 2D mesh. The previous code changes both x and y. How can I change only x ? Thanks, Floriane

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Re: [firedrake] problems updating and running firedrake
by David Ham 05 Aug '16

05 Aug '16

Hi Francis, Please provide the full output, because the following is based on guesswork because I can't see what is going on. It is true that curl depends on librtmp. If your curl can't find your rtmp, then something is broken on your system. This has nothing to do with Firedrake. I *think* that the only time you use curl is to download the firedrake-install script. If you really can't unbreak curl on your system then you can obtain this script by any of the usual ways (wget, download it with a web browser etc.) Regards, David On Mon, 27 Jun 2016 at 19:35 Francis Poulin <fpoulin(a)uwaterloo.ca> wrote: > Hello David, > > Thanks for finding that. > > I tried a) and that didn't help the update. > > I then tried b) and get an curl error, "error while loading shared > libraries: librtmp.so.0". > > I have done this before but not sure why this is not working now. > > Cheers, Francis > > > > > ------------------ > Francis Poulin > Associate Professor > Department of Applied Mathematics > University of Waterloo > > email: fpoulin(a)uwaterloo.ca > Web: https://uwaterloo.ca/poulin-research-group/ > Telephone: +1 519 888 4567 x32637 > > ------------------------------ > *From:* firedrake-bounces(a)imperial.ac.uk [firedrake-bounces(a)imperial.ac.uk] > on behalf of David Ham [David.Ham(a)imperial.ac.uk] > *Sent:* Monday, June 27, 2016 10:48 AM > *To:* firedrake > *Subject:* Re: [firedrake] problems updating and running firedrake > > Hi Francis, > > It looks like you might have hit the issue they describe here: > http://askubuntu.com/questions/509283/python-no-module-named-datetime > > Basically datetime was apparently rolled into the python binary in a 2.7 > point release. I don't know why this was changed but it makes the python > binary in your virtualenv incompatible with your system python install. > > According to the thread on askubuntu, you have two options. > > a) Apparently you can re-initialise the virtualenv by running: > > virtualenv . > > in your top Firedrake directory. I'm guessing you should do this with the > virtualenv deactivated. > > or > > b) A fresh Firedrake install should work because it will create a fresh > virtualenv based on current Python binary. > > Regards, > > David > > On Mon, 27 Jun 2016 at 15:20 Francis Poulin <fpoulin(a)uwaterloo.ca> wrote: > >> Hello, >> >> I recently updated my ubuntu from 14.04 to 16.04. I tried running >> firedrake and it failed. >> >> I also tried updating firedrake and it failed, see below. >> >> Do I need to install it from scratch or should it be possible to update >> it with a new OS? >> >> Cheers, Francis >> >> >> >> Installing pip dependencies for COFFEE >> /home/fpoulin/software/firedrake/bin/pip install -r >> COFFEE/requirements.txt >> >> Traceback (most recent call last): >> File "/home/fpoulin/software/firedrake/bin/pip", line 7, in <module> >> from pip import main >> File >> "/home/fpoulin/software/firedrake/local/lib/python2.7/site-packages/pip/__init__.py", >> line 14, in <module> >> from pip.utils import get_installed_distributions, get_prog >> File >> "/home/fpoulin/software/firedrake/local/lib/python2.7/site-packages/pip/utils/__init__.py", >> line 27, in <module> >> from pip._vendor import pkg_resources >> File >> "/home/fpoulin/software/firedrake/local/lib/python2.7/site-packages/pip/_vendor/pkg_resources/__init__.py", >> line 36, in <module> >> import plistlib >> File "/usr/lib/python2.7/plistlib.py", line 62, in <module> >> import datetime >> ImportError: No module named datetime >> Traceback (most recent call last): >> File "../bin/firedrake-update", line 974, in <module> >> pip_requirements(p) >> File "../bin/firedrake-update", line 377, in pip_requirements >> run_pip_install(["-r", "%s/requirements.txt" % package]) >> File "../bin/firedrake-update", line 364, in run_pip_install >> check_call(pipinstall + pipargs) >> File "../bin/firedrake-update", line 211, in check_call >> subprocess.check_call(arguments, env=env) >> File "/usr/lib/python2.7/subprocess.py", line 541, in check_call >> raise CalledProcessError(retcode, cmd) >> subprocess.CalledProcessError: Command >> '['/home/fpoulin/software/firedrake/bin/pip', 'install', '-r', >> 'COFFEE/requirements.txt']' returned non-zero exit status 1 >> >> ------------------ >> Francis Poulin >> Associate Professor >> Department of Applied Mathematics >> University of Waterloo >> >> email: fpoulin(a)uwaterloo.ca >> Web: https://uwaterloo.ca/poulin-research-group/ >> Telephone: +1 519 888 4567 x32637 >> >>

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Re: [firedrake] failed update
by David Ham 05 Aug '16

05 Aug '16

Hi Onno, Something (and that something is not firedrake - firedrake has no code to change directory permissions) has set /usr/local to be not writable by your user. If your user cannot write to /usr/local then homebrew will not work, and consequently neither will firedrake-update. You need to change the permissions on /usr/local so that your user can write to it. homebrew has suggested one way that you can do that. If you're not comfortable with that, I suggest you should take your laptop to your tech support and get them to do it. Sorry I can't give you more helpful advice than that but, as noted above, this is not actually a firedrake bug so there is nothing we can directly do about it. Regards, David On Fri, 5 Aug 2016 at 08:08 Onno Bokhove <O.Bokhove(a)leeds.ac.uk> wrote: > brew update > > Error: The /usr/local directory is not writable. > > Even if this directory was writable when you installed Homebrew, other > > software may change permissions on this directory. Some versions of the > > "InstantOn" component of Airfoil are known to do this. > > > You should probably change the ownership and permissions of /usr/local > > back to your user account. > > sudo chown -R $(whoami):admin /usr/local > > > If I then do the sudo one I get a warning that this > > may lead to severe damage. SO I have no yet done that. > > > > > ------------------------------ > *From:* firedrake-bounces(a)imperial.ac.uk <firedrake-bounces(a)imperial.ac.uk> > on behalf of Homolya, Miklós <m.homolya14(a)imperial.ac.uk> > *Sent:* Thursday, August 4, 2016 9:23 PM > *To:* firedrake > *Subject:* Re: [firedrake] failed update > > > Dear Onno, > > > Can you please try these? > > > $ brew update > > $ brew install autoconf > > > What does the following say? > > > $ brew doctor > > > Thanks, > > Miklos > ------------------------------ > *From:* firedrake-bounces(a)imperial.ac.uk <firedrake-bounces(a)imperial.ac.uk> > on behalf of Onno Bokhove <O.Bokhove(a)leeds.ac.uk> > *Sent:* 04 August 2016 21:17:48 > *To:* firedrake > *Subject:* [firedrake] failed update > > > Did: > > firedrake-cleanand/or recovering from the broken installation by > > cd src/firedrake > git pull > ./scripts/firedrake-install --rebuild-script > > then > firedrake-update > > but get error message: > > Error: No such keg: /usr/local/Cellar/autoconf > > Error: Cannot write to /usr/local/Cellar > > Traceback (most recent call last): > > File "/Users/amtob/werk/firedrake/bin/firedrake-update", line 813, in > <module> > > brew_install("autoconf") > > File "/Users/amtob/werk/firedrake/bin/firedrake-update", line 250, in > brew_install > > check_call(["brew", "install"] + arguments) > > File "/Users/amtob/werk/firedrake/bin/firedrake-update", line 228, in > check_call > > subprocess.check_call(arguments, env=env) > > File > "/usr/local/Cellar/python/2.7.10_2/Frameworks/Python.framework/Versions/2.7/lib/python2.7/subprocess.py", > line 540, in check_call > > raise CalledProcessError(retcode, cmd) > > subprocess.CalledProcessError: Command '['brew', 'install', 'autoconf']' > returned non-zero exit status 1 > > > on laptop while firedrake worked few weeks ago. > > >

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failed update
by Onno Bokhove 05 Aug '16

05 Aug '16

Did: firedrake-clean and/or recovering from the broken installation by cd src/firedrake git pull ./scripts/firedrake-install --rebuild-script then firedrake-update but get error message: Error: No such keg: /usr/local/Cellar/autoconf Error: Cannot write to /usr/local/Cellar Traceback (most recent call last): File "/Users/amtob/werk/firedrake/bin/firedrake-update", line 813, in <module> brew_install("autoconf") File "/Users/amtob/werk/firedrake/bin/firedrake-update", line 250, in brew_install check_call(["brew", "install"] + arguments) File "/Users/amtob/werk/firedrake/bin/firedrake-update", line 228, in check_call subprocess.check_call(arguments, env=env) File "/usr/local/Cellar/python/2.7.10_2/Frameworks/Python.framework/Versions/2.7/lib/python2.7/subprocess.py", line 540, in check_call raise CalledProcessError(retcode, cmd) subprocess.CalledProcessError: Command '['brew', 'install', 'autoconf']' returned non-zero exit status 1 on laptop while firedrake worked few weeks ago.

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Re: [firedrake] Mixed system
by David Ham 04 Aug '16

04 Aug '16

There is actually a possibly working R implementation on a branch which you could have a go at. I'll try to update it to current master tonight and get back to you tomorrow on this. Regards, David On Thu, 4 Aug 2016 at 17:29 Kramer, Stephan <s.kramer(a)imperial.ac.uk> wrote: > On 27/07/16 11:01, Anna Kalogirou wrote: > > Dear all, > > > > I am trying to solve the system found in the attached pdf as a mixed > > system. I want to solve the same > > problem as the one found here > > < > https://bitbucket.org/annakalog/buoy2d/src/14334d3c20b9f10ed7c1246cde9e3cb6… > >, > > but with the use of Schur complements and not linear algebra. > > > > In a previous discussion about this problem, Lawrence mentioned that the > > test function for integral(lambda*Theta(x-Lp)dx) needs to be considered > > as coming from the real space of constant functions. Could you please > > elaborate on this? > > My guess at what Lawrence means is (it's how I would probably approach > it), is that you add an additional equation that says > > (1) I = integral(lambda*Theta(x-Lp)dx) > > and then substitute I in your third equation. Equation (1) can > be turned into a finite element weak formulation by considering the > function space of functions that are constant over the entire domain > This function space is just 1-dimensional and therefore equivalent to > the space of reals R and hence we denote this function space of > constants simply as R. Then we can consider I to be a trial function in > R, and with a test function v4 in R, we can write: > > v4*lambda*Theta(x-Lp)*dx == v4*I*dx/area(domain) > > This is a proper finite element equation that you could solve in > conjuction with the other equations. I believe however that this > function space R is not currently implemented in Firedrake. It is > available in fenics, and is on the wishlist. > > Cheers > Stephan > > _______________________________________________ > firedrake mailing list > firedrake(a)imperial.ac.uk > https://mailman.ic.ac.uk/mailman/listinfo/firedrake >

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Re: [firedrake] Boundary IDs on extruded meshes
by David Ham 04 Aug '16

04 Aug '16

Hi Justin, Actually the 3d unstructured case could be done for the case Justin is interested in. See: https://arxiv.org/abs/1512.02137 That said, my Firedrake feature request stack is overflowing, so I'm not volunteering to do that work. If you want to take it on, feel free to ask for advice on how ;) David On Tue, 2 Aug 2016 at 10:05 Andrew McRae <A.T.T.McRae(a)bath.ac.uk> wrote: > On 2 August 2016 at 06:40, Justin Chang <jychang48(a)gmail.com> wrote: > >> So I am working with Hanie on this problem. We're using VMS formulation >> for double porosity Darcy equation, which requires strongly enforced normal >> velocity boundary conditions. We're interested in using hexahedron elements. >> >> How easy is it to add support for single component VectorFunctionSpace to >> ExtrudedMeshes? >> >> Also, what is the other workaround we could go with? >> > > You could use separate components instead of a VFS. If you want to make > your forms a bit nicer then I think you can use as_vector to group the > components: > > wSpace = W*V*V*V > p, u1, u2, u3 = TrialFunctions(wSpace) > u = as_vector(u1, u2, u3) > a = dot(u, ...)*dx + ... > bcs = [DirichletBC(wSpace.sub(1), 0.0, (1, 2)), > DirichletBC(wSpace.sub(2), 0.0, (3, 4)), > DirichletBC(wSpace.sub(3), 0.0, ("bottom", "top"))] > > (haven't run, so may contain typos, bugs, ...) > > >> Make a hexahedral mesh out of GMSH and use the appropriate physical ID's? >> > > No, as Firedrake doesn't support unstructured hexes, only extruded quad > meshes. There are hard orientation issues to think about when the hexes > are fully unstructured. > > >> >> Thanks, >> Justin >> >> On Mon, Aug 1, 2016 at 6:08 PM, Andrew McRae <A.T.T.McRae(a)bath.ac.uk> >> wrote: >> >>> Hi Hanie, >>> >>> An ExtrudedMesh inherits boundary ids from the 'base mesh', plus the >>> extra identifiers "bottom" and "top". So, the sides x==0 through y==1 are >>> id 1-4, because this is what the base mesh has. Then z==0 is "bottom" and >>> z==1 is "top". >>> >>> However, your code is failing because (I believe) you're trying to set >>> one component of a VectorFunctionSpace to 0. Firedrake allows you to do >>> this on normal meshes, but doesn't yet support this on extruded meshes, >>> hence the error message. (You could set all components of the vector to 0 >>> by using just wSpace.sub(0), but presumably this isn't what you want). >>> >>> There are various workarounds you could use for now, such as setting the >>> boundary condition weakly, but they're not completely satisfying. >>> >>> Andrew >>> >>> On 1 August 2016 at 21:15, Hanie Joodat <hanie.joodat88(a)gmail.com> >>> wrote: >>> >>>> Dear all, >>>> >>>> I want to enforce DirichletBCs on an extruded mesh. For a normal unit >>>> cube tetrahedron mesh I could use the following face ID's: >>>> >>>> 1: x ==0 >>>> 2: x==1 >>>> 3: y==0 >>>> 4: y==1 >>>> 5: z==0 >>>> 6: z==1 >>>> >>>> However, when I do the following: >>>> >>>> meshbase = RectangleMesh(Nx, Ny, Lx, Ly, quadrilateral=True) >>>> mesh = ExtrudedMesh(meshbase, Nz, Dz) >>>> >>>> I get this error: >>>> >>>> Traceback (most recent call last): >>>> File "VMS_patch_test_3D_Double_firedrake.py", line 51, in <module> >>>> FrontBackBC1 = DirichletBC(wSpace.sub(0).sub(1),Constant(0.0),(3,4)) >>>> File "/data/Software/firedrake/src/firedrake/firedrake/bcs.py", line >>>> 68, in __init__ >>>> raise NotImplementedError("Indexed VFS bcs not implemented on >>>> extruded meshes") >>>> NotImplementedError: Indexed VFS bcs not implemented on extruded meshes >>>> >>>> What should I do to properly identify my boundary faces? >>>> >>>> Regards, >>>> >>>> Hanie >>>> >>> >>> >>> _______________________________________________ >>> firedrake mailing list >>> firedrake(a)imperial.ac.uk >>> https://mailman.ic.ac.uk/mailman/listinfo/firedrake >>> >>> >>

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out of memory error during assemble
by moritz braun 02 Aug '16

02 Aug '16

Dear Colleagues I have a strange out or memory error when calling assemble on a bilinear form How can that happen in firedrake? Regards Moritz -- Prof M Braun Tel.:27-12-4298006/8027 Physics Department Fax.: 27-12-4293643 University of South Africa (UNISA) moritz.braun(a)gmail.com P.O. Box 392 0003 UNISA South Africa http://moritz-braun.blogspot.com

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Re: [firedrake] Boundary IDs on extruded meshes
by Andrew McRae 02 Aug '16

02 Aug '16

On 2 August 2016 at 06:40, Justin Chang <jychang48(a)gmail.com> wrote: > So I am working with Hanie on this problem. We're using VMS formulation > for double porosity Darcy equation, which requires strongly enforced normal > velocity boundary conditions. We're interested in using hexahedron elements. > > How easy is it to add support for single component VectorFunctionSpace to > ExtrudedMeshes? > > Also, what is the other workaround we could go with? > You could use separate components instead of a VFS. If you want to make your forms a bit nicer then I think you can use as_vector to group the components: wSpace = W*V*V*V p, u1, u2, u3 = TrialFunctions(wSpace) u = as_vector(u1, u2, u3) a = dot(u, ...)*dx + ... bcs = [DirichletBC(wSpace.sub(1), 0.0, (1, 2)), DirichletBC(wSpace.sub(2), 0.0, (3, 4)), DirichletBC(wSpace.sub(3), 0.0, ("bottom", "top"))] (haven't run, so may contain typos, bugs, ...) > Make a hexahedral mesh out of GMSH and use the appropriate physical ID's? > No, as Firedrake doesn't support unstructured hexes, only extruded quad meshes. There are hard orientation issues to think about when the hexes are fully unstructured. > > Thanks, > Justin > > On Mon, Aug 1, 2016 at 6:08 PM, Andrew McRae <A.T.T.McRae(a)bath.ac.uk> > wrote: > >> Hi Hanie, >> >> An ExtrudedMesh inherits boundary ids from the 'base mesh', plus the >> extra identifiers "bottom" and "top". So, the sides x==0 through y==1 are >> id 1-4, because this is what the base mesh has. Then z==0 is "bottom" and >> z==1 is "top". >> >> However, your code is failing because (I believe) you're trying to set >> one component of a VectorFunctionSpace to 0. Firedrake allows you to do >> this on normal meshes, but doesn't yet support this on extruded meshes, >> hence the error message. (You could set all components of the vector to 0 >> by using just wSpace.sub(0), but presumably this isn't what you want). >> >> There are various workarounds you could use for now, such as setting the >> boundary condition weakly, but they're not completely satisfying. >> >> Andrew >> >> On 1 August 2016 at 21:15, Hanie Joodat <hanie.joodat88(a)gmail.com> wrote: >> >>> Dear all, >>> >>> I want to enforce DirichletBCs on an extruded mesh. For a normal unit >>> cube tetrahedron mesh I could use the following face ID's: >>> >>> 1: x ==0 >>> 2: x==1 >>> 3: y==0 >>> 4: y==1 >>> 5: z==0 >>> 6: z==1 >>> >>> However, when I do the following: >>> >>> meshbase = RectangleMesh(Nx, Ny, Lx, Ly, quadrilateral=True) >>> mesh = ExtrudedMesh(meshbase, Nz, Dz) >>> >>> I get this error: >>> >>> Traceback (most recent call last): >>> File "VMS_patch_test_3D_Double_firedrake.py", line 51, in <module> >>> FrontBackBC1 = DirichletBC(wSpace.sub(0).sub(1),Constant(0.0),(3,4)) >>> File "/data/Software/firedrake/src/firedrake/firedrake/bcs.py", line >>> 68, in __init__ >>> raise NotImplementedError("Indexed VFS bcs not implemented on >>> extruded meshes") >>> NotImplementedError: Indexed VFS bcs not implemented on extruded meshes >>> >>> What should I do to properly identify my boundary faces? >>> >>> Regards, >>> >>> Hanie >>> >> >> >> _______________________________________________ >> firedrake mailing list >> firedrake(a)imperial.ac.uk >> https://mailman.ic.ac.uk/mailman/listinfo/firedrake >> >> >

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