May 2018 - firedrake - imperial.ac.uk

did not get your answer because I get firedrake digest only? (re: mesh coordinates and boundaries questions)
by Ed Bueler 14 May '18

14 May '18

David -- *After* I wrote my latest to the firedrake mailing list I found your answer at the archive: http://mailman.ic.ac.uk/pipermail/firedrake/2018-May/003406.html I did not get it before. (Its not in my spam or trash.) Probably because I get only the digest version of the mailing list? Or is there a need to CC me in addition to sending to the list? Not sure what are best practices to avoid crossing this way. Sorry! Regarding the content of your answer: 1) I still don't know how to use the subdomain id to get anything other than the *measure* for the boundary, e.g. "ds(id)". How do I get an indicator function, for example? This is what I am missing as "idiom". 2) How does interpolate work if I have data only locally on the boundary, and not as an analytical function of x, and the data only lives on the process that holds its part of the boundary? That is, I have "values of w(x)" on the boundary (as stated) but not a formula in x (i.e. the "expression" needed for interpolate). Said a different way, the last sentence at https://www.firedrakeproject.org/interpolation.html#id2 namely "This will also work in parallel, as the interpolation will occur on each process,...", can't possibly be true in the situation where values w(x), for x in some range, are only known to the process which holds that part of the boundary (i.e. for x in that range). I think all-to-all communication is needed to answer my question in general. Said yet another way, in the general setting I think that constructing the "mydata(X)" described in same the firedrake doc would require setting up an entire VecScatter or solve() anyway. I think both of your answers assume I have a formula in terms of x. I don't in the application which drove my questions. Thanks, and sorry for the fumble, Ed -- Ed Bueler Dept of Math and Stat and Geophysical Institute University of Alaska Fairbanks Fairbanks, AK 99775-6660 301C Chapman

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nonlinear diffusion with space-time Robin condition
by Onno Bokhove 13 May '18

13 May '18

Dear Firedrakers, (i) Will & I tried to build a theta-time-step solver including Crank-Nicolson for theta=1/2 but only get it to work for theta=0 (Forward Euler); see the attached code at "HERE2" which matches (32) in the attached pdf. [This is really a test set-up atm for a larger question on dynamic boundary conditions for an elliptic problem, but the system may be amusing by itself as a tentative FD-example.) (ii) The working explicit Forward Euler code for theta=0 is very slow, at least 10x slower than the same algorithm in a FEM matlab code (-). See "HERE1" in the attached code; why is the code so slow? [I have also attached the basic matlab code.] This example may be amusing because of the space-time Robin condition (14) applied to (11), leading to the Firedrake weak form (32) --when time is discretised as well. The question can also be solved, slightly differently wrt the implementation of the Robin boundary condition, using finite differences, which makes for an amusing comparison. I am not even sure whether this space-time bc and nonlinear diffusion eqn is well-posed but the finite difference and FEM numerics seems to be consistent. Thank you and best wishes, Onno

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demo for printing and doing certain all-reduce operations smoothly in parallel?
by Ed Bueler 09 May '18

09 May '18

Dear Firedrake -- So far so good! However, I am not sure of certain best practices in parallel. Consider the following familiar Helmholtz example. I have added some printing fluff before and after: from firedrake import * mesh = UnitSquareMesh(10, 10) V = FunctionSpace(mesh, "CG", 1) u = TrialFunction(V) v = TestFunction(V) f = Function(V) x, y = SpatialCoordinate(mesh) print('setting up problem') f.interpolate((1+8*pi*pi)*cos(x*pi*2)*cos(y*pi*2)) a = (dot(grad(v), grad(u)) + v * u) * dx L = f * v * dx u = Function(V) solve(a == L, u, options_prefix='s', solver_parameters={'ksp_type': 'cg'}) f.interpolate(cos(x*pi*2)*cos(y*pi*2)) L2err = sqrt(assemble(dot(u - f, u - f) * dx)) umax = u.dat.data.max() print('L2 error norm = %g, max(u) = %g' % (L2err,umax)) Suppose we run first in serial and then on two processes: (firedrake) ~$ python3 helmholtz.py -s_ksp_converged_reason setting up problem Linear s_ solve converged due to CONVERGED_RTOL iterations 13 L2 error norm = 0.0625707, max(u) = 1.03139 (firedrake) ~$ mpiexec -n 2 python3 helmholtz.py -s_ksp_converged_reason Linear s_ solve converged due to CONVERGED_RTOL iterations 28 setting up problem L2 error norm = 0.0625707, max(u) = 0.803552 setting up problem L2 error norm = 0.0625707, max(u) = 1.03138 This reveals several issues: 1. Should I use "if COMM_WORLD.rank == 0:" to avoid printing n times? Or should I use a collective print like PetscPrintf()? If so where could I find a demo? (I'm familiar with the C API not petsc4py ...) 2. There is a flush issue if I only print on rank 0; the solver reports CONVERGED before the first print happens. How to flush or avoid the need to flush? 3. It looks like "assemble()" does a MPI_Allreduce() to get the right L2 error. Is that right? How to do this myself, for example for the solution maximum to appear on all ranks? (Probably a petsc4py call?) Is there a demo which shows how the firedrake developers prefer to do these things? Parallel best-practices, more or less. All the demos I can find seem to be serial w.r.t. the above niceties. The page https://www.firedrakeproject.org/parallelism.html addresses less-introductory parallelism issues in my opinion. I am not worried about the math either; I'm aware that the above difference in CG iterations has everything to do with the difference in default preconditioning. Thanks! Ed -- Ed Bueler Dept of Math and Stat and Geophysical Institute University of Alaska Fairbanks Fairbanks, AK 99775-6660 301C Chapman

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Schedule for Firedrake 18
by Lawrence Mitchell 02 May '18

02 May '18

Dear all, the schedule for the Firedrake meeting this summer is now available: https://easychair.org/smart-program/Firedrake'18/ All talks will be 15 minutes + 5 minutes for questions. (For those of you still wavering, it is still possible to register, but that window will close soon). We look forward to seeing you in the summer. Thanks, Lawrence (for the Firedrake team)

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