April 2018 - firedrake - imperial.ac.uk

Re: [firedrake] Poisson equation; homogeneous vs nonhomogeneous
by Lawrence Mitchell 23 Apr '18

23 Apr '18

[Re-adding firedrake(a)imperial.ac.uk] > On 23 Apr 2018, at 08:39, Eric M <eric.malitz(a)gmail.com> wrote: > > But I have a new question, unfortunately: I have a solution u, and I want to take a derivative for use in a W^{1,\infty} norm for example. It doesn't allow for example u.dx(0).dat.data, or grad(u)[0].dat.data. Aha, there is a confusion here between what is a coefficient in some finite element space, and what is a symbolic expression. You start with u, which is a Function in some finite element space. Now grad(u)[0], or u.dx(0) (these actually produce the same thing) are symbolic expressions. If you want to look at the values, you first need to interpolate (or project) the expression into a suitable finite element space: e.g, if u is in FunctionSpace(mesh, "CG", 2) Then perhaps: VGrad = FunctionSpace(mesh, "DG", 1) gradu = project(grad(u), VGrad) gradu.dat.data[:] ... > Wanted to let you know I figured out the max norm thing (the structures were different sizes and had to play around with the notation a bit). And thanks for your help with the multi-grid. > > On Fri, Apr 20, 2018 at 1:07 PM, Eric M <eric.malitz(a)gmail.com> wrote: > Lawrence, > > For the attempt to take to an L^{\inf} norm, here are the relevant code snippets: > > V = FunctionSpace(mesh, "Lagrange", 2) > Sigma = TensorFunctionSpace(mesh, "Lagrange", 2) > VS = V * Sigma > > sigma00=Function(V) > sigma00.interpolate((1+x**2)*exp((x**2+y**2)/2)) > sigma01=Function(V) > sigma01.interpolate(x*y*exp((x**2+y**2)/2)) > sigma10=Function(V) > sigma10.interpolate(x*y*exp((x**2+y**2)/2)) > sigma11=Function(V) > sigma11.interpolate((1+y**2)*exp((x**2+y**2)/2)) > > sigma_exact=as_tensor([[sigma00,sigma01],[sigma10,sigma11]]) > > (then solve a mixed problem for solution us) > > uk, sigmak = us.split() > diff=assemble(sigma_exact-sigmak) Aha, so you could have done one of two things: Either: sigma_exact = interpolate(sigma_exact, Sigma) diff = assemble(sigma_exact - sigma) Or you could have done: diff = interpolate(sigma_exact - sigmak, V) This does interpolation of expressions at the nodes of V. Whereas the `assemble(sigma_exact - sigmak)` attempts to point wise evaluate the given expression (and only works if all the terms in the expression are Functions in the same function space). Cheers, Lawrence

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Re: [firedrake] Poisson equation; homogeneous vs nonhomogeneous
by Lawrence Mitchell 20 Apr '18

20 Apr '18

[also re-adding firedrake cc] > On 18 Apr 2018, at 19:15, Eric M <eric.malitz(a)gmail.com> wrote: > > I had a more pertinent question: could you tell me if it's possible to interpolate a solution found on one grid, to another grid? For example, I find a solution to a problem on a coarse grid, and wish to use this solution somewhere in a linearized problem on a finer grid, so it needs to be interpolated. I have tried the basic things I can think of, but nothing works yet. If you make a MeshHierarchy object, then you can do prolongation easily: coarse_mesh = ... # This does regular refinement. hierarchy = MeshHierarchy(coarse_mesh, number_of_refinements) Now suppose you have a coarse function: coarse = Function(V) you can do: for finer in hierarchy[1:]: Vfine = FunctionSpace(finer, V.ufl_element()) fine = Function(Vfine) prolong(coarse, fine) coarse = fine Now fine contains the prolongation of the coarse function on the finest mesh in the hierarchy. Alternately, if there is not a nice relationship between the two meshes, you can use the advice here: https://firedrakeproject.org/interpolation.html#interpolation-from-external… Thanks, Lawrence

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Re: [firedrake] Poisson equation; homogeneous vs nonhomogeneous
by Lawrence Mitchell 20 Apr '18

20 Apr '18

[re-adding firedrake to CC] > On 17 Apr 2018, at 20:56, Eric M <eric.malitz(a)gmail.com> wrote: > > Thanks for the tips. For a scalar function I think I wrote diff=u-g; max(abs(diff.dat.data)) for instance. Can this be done for sigmak-sigma? I tried to do it with the components individually and it didn’t work. You should be able to do: diff = assemble(sigmak - sigma) and then diff.dat.data should give you the point wise difference. What doesn't work? >> On Apr 17, 2018, at 8:14 AM, Lawrence Mitchell <lawrence.mitchell(a)imperial.ac.uk> wrote: >> >> Hi Eric, >> >>> On 17/04/18 04:14, Eric M wrote: >>> Sorry, hit send too soon; >>> >>> I am coding a mixed problem where the unknowns are the scalar function >>> u and a Hessian D^2u. >>> >>> Among the things I specify are the function spaces: >>> >>> V = FunctionSpace(mesh, "Lagrange", 2) >>> Sigma = TensorFunctionSpace(mesh, "Lagrange", 2) >>> VS = V * Sigma >>> >>> I specify some exact solutions: >>> >>> u = Expression("exp((x[0]*x[0] + x[1]*x[1])/2)") >>> u = Function(V).interpolate(u) >>> sigma00expr= Expression(' (1+x[0]*x[0])*exp((x[0]*x[0]+x[1]*x[1])/2) >>> ' ,degree=5) >>> sigma01expr= Expression('x[0]*x[1]*exp((x[0]*x[0]+x[1]*x[1])/2) ' >>> ,degree=5) >>> sigma10expr= Expression(' x[0]*x[1]*exp((x[0]*x[0]+x[1]*x[1])/2) ' >>> ,degree=5) >>> sigma11expr= Expression(' (1+x[1]*x[1])*exp((x[0]*x[0]+x[1]*x[1])/2) >>> ' ,degree=5) >> >> So I would write these using UFL expressions, and then glue them >> together into a tensor: >> >> x, y = SpatialCoordinate(mesh) >> >> sigma00 = (1 + x**2)*exp((x**2 + y**2)/2) >> sigma01 = ... >> >> etc... >> >> Then you can write: >> >> sigma = as_tensor([[sigma00, sigma01], >> [sigma10, sigma11]]) >> >> ... >>> >>> And solve it: >>> >>> solve(a == L, us, bcs=bcs, solver_parameters=sp_it) >>> uk, sigmak = us.split() >>> >>> Now I analyze uk in L2, H1, etc. error norms. But I can't figure out >>> how to analyze sigmak, that is, extract the components to put in error >>> norms. >>> but this doesn't work here. >> >> Now you can write: >> >> diff = sigmak - sigma >> >> and then L2norm = norm(diff, norm_type="L2") >> >>> Even then, once I extract, say, sigmak00, how do I do for example: >>> L2 norm of sigmak - sigma >>> and >>> L^infinity norm of sigmak - sigma ? >> >> There's no builtin functionality for computing Linf norms, because >> they are tricky! >> >> Hope this helps. >> >> Lawrence

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Cannot install firedrake
by Mohammad Sarraf Joshaghani 10 Apr '18

10 Apr '18

Hello, I'm trying to install firedrake on ubuntu machine and I get the following error. could you please help me resolve it. Thank you. Sincerely, Mohammad Sarraf Joshaghani Phone: +1-281-781-5331

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Firedrake 2018: extended abstract submission deadline
by Lawrence Mitchell 10 Apr '18

10 Apr '18

Dear all, a reminder that the second Firedrake user & developer meeting is taking place this summer (June 7-8) in London. For those of you, and we know you're out there, who have yet to submit an abstract, the abstract deadline is now: 20th April 2018 Early registration has also been extended until then. For more details see: www.firedrakeproject.org/firedrake_18.html We look forward to seeing you in London in June. Cheers, Lawrence

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SIAM UKIE National Student Chapter Conference 2018
by Owen Pembery 05 Apr '18

05 Apr '18

Dear All, This year's SIAM UKIE National Student Chapter Conference is going to be held at the University of Bath on the 18th and 19th of June. The conference will bring together students working in all areas of applied and industrial mathematics, and related fields, from across the UK and Ireland. We're pleased that we can offer travel funding to all students who present - go to http://go.bath.ac.uk/SNSCC-2018 to find out more information and register/submit abstracts. The deadline for submitting abstracts is the 27th of April. Thanks, Owen

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