- firedrake - imperial.ac.uk

Re: [firedrake] Concatenation of function spaces?
by Andrew McRae 30 Jul '15

30 Jul '15

1) Yes, this can be done in Firedrake. However, we consider the local element to be enriched, not the function space: V1 = VectorFunctionSpace... Q_elt = FiniteElement("CG", interval, 1) P_elt = FiniteElement("DG", interval, 0) elt = Q_elt + P_elt V2 = FunctionSpace(mesh, elt) W = V1 * V2 2) Is P1disc the same as P1DG? "All polynomials of degree 1 with no continuity between cells"? If so, none of us have implemented the P1disc elements on quadrilaterals yet in FIAT. We have full support for the third column of http://femtable.org/, which has all the "tensor product construction" elements, but not the fourth. If you want to try implementing P1disc yourself, we can hopefully provide support. On 22 July 2015 at 05:55, Justin Chang <jychang48(a)gmail.com> wrote: > Hi everyone, > > Apologies for sending out so many e-mails in such a short amount of time. > I guess I have a two part question: > > 1) Is it possible to concatenation two or more function spaces? In > FEniCS I was able to do something like this: > > V = VectorFunctionSpace(mesh, "CG", 2) > Q = FunctionSpace(mesh, "CG", 1) > P = FunctionSpace(mesh, "DG", 0) > W = V * (Q + P) > > But the above does not work with Firedrake. Is there a way to do that, > or is there something better? This kind of leads me to the second question: > > 2) I would like to try Q2-P1disc elements for Darcy problem (I see that > this element combination is commonly used for stokes equations, but I don't > know if it will work for Darcy). Is this possible to do? > > If the answer to the above two is no, is there another "locally > conservative" mixed formulation that's currently doable other than the > classical forms like RT0? And preferably with a higher order rate of > convergence? > > Thanks, > Justin > > >

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Re: [firedrake] .dx without operand
by Andrew McRae 27 Jul '15

27 Jul '15

I don't *think* so (I might be wrong -- Martin?), but what about .dx(0).dx(0)? On 29 June 2015 at 19:54, Jacobs, Christian T <c.jacobs10(a)imperial.ac.uk> wrote: > I'm trying to express the following in UFL: > http://amcg.ese.ic.ac.uk/~ctj10/images/k.png where A and B are matrices > and u is a vector of solution variables. > > For the case of k=1 I can write e.g. > > -1*([1*u[0].dx(0) + 2*u[1].dx(0) + 5*u[0].dx(1) + 6*u[1].dx(1), > 3*u[0].dx(0) + 4*u[1].dx(0) + 7*u[0].dx(1) + 8*u[0].dx(0)]) > > But how can I write this for k>1? Having e.g. (1*u[0].dx(0) + 2*u[0].dx(1) > + ...)**2 will result in terms that represent (du/dx)**2 not > (d**2)u/(dx**2). Is there a way of expressing .dx() (of arbitrary order) > without an operand in UFL, so we can just have d^k/dx^k ? >

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Re: [firedrake] More questions
by Fabio Luporini 24 Jul '15

24 Jul '15

Hi, As Lawrence says (point 2), you can ignore that FFC line since local assembly optimisation is entirely handled by COFFEE. Thanks, -- Fabio 2015-07-24 11:29 GMT+01:00 Mitchell, Lawrence < lawrence.mitchell(a)imperial.ac.uk>: > > > On 24 Jul 2015, at 11:06, Justin Chang <jychang48(a)gmail.com> wrote: > > > > Hi everyone, > > > > I have some (what I think are) pretty simple questions that I would like > answered: > > > > 1) How do you print out the global size of the matrix? > > So PyOP2 (and hence firedrake) don't expose global sizes of objects. > However, you can ask PETSc: > > A = assemble(a) > > print A.M.handle.getSizes() > > This returns the same as MatGetSizes. > > You can get the /local/ sizes with: > > A.M.nrows, A.M.ncols > > We should probably just expose the global sizes as well. > > > > 2) When FFC/pyop2 is compiling the forms, it says "Skipping > optimizations, add -O to optimize", how can I tell my program to add this > optimization? > > I believe that many of these optimisations conflict with those that the > COFFEE kernel compiler subsequently applies, so I /think/ that you can't > add this optimisation right now. Maybe Fabio can comment more clearly on > this point. > > > > 3) Is there a way to simply output the number of KSP iterations? I am > guessing it involves getIterationNumber() but I am still kind of new to > petsc4py, so how would I invoke this call in the context of firedrake? > > > Do you want to access this number programmatically, or print to a screen? > > If the latter, you can run with 'ksp_converged_reason': True in your > solver_parameters dict and PETSc will print the converged reason (along > with the number of iterations). > > If programmatically: > > solver = XXXVariationalSolver(...) > > solver.solve() > > print solver.snes.ksp.getIterationNumber() > > If you're using preassembled operators and a LinearSolver: > > solver = LinearSolver(...) > > solver.solve(...) > > print solver.ksp.getIterationNumber() > > Again, we should expose this programmatically in the public interface. > > Lawrence >

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More questions
by Justin Chang 24 Jul '15

24 Jul '15

Hi everyone, I have some (what I think are) pretty simple questions that I would like answered: 1) How do you print out the global size of the matrix? 2) When FFC/pyop2 is compiling the forms, it says "Skipping optimizations, add -O to optimize", how can I tell my program to add this optimization? 3) Is there a way to simply output the number of KSP iterations? I am guessing it involves getIterationNumber() but I am still kind of new to petsc4py, so how would I invoke this call in the context of firedrake? Thanks! Justin

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Re: [firedrake] Second derivatives
by David Ham 22 Jul '15

22 Jul '15

Hi Justin, I'm clearly not understanding your new paper, but why does the new second derivative you create in 4.13 not go away by multiplying by a test funcion and integrating by parts? In addition, I don't understand why it makes sense to take a second derivative of a Q1 element. Q1 does not span P2 so you have a very big part of your space which is linear (and therefore has the same issue as P1). In addition, as Andrew already stated, C0 elements don't have enough continuity to take that derivative, so I don't understand why the second derivative in this case makes sense. Having said all that, as far as I know, it should be possible to just put the second derivative into UFL and let FFC deal with it. Does that produce an error? Cheers, David On Tue, 21 Jul 2015 at 20:17 Justin Chang <jychang48(a)gmail.com> wrote: > I am looking at equal order mixed formulations. Two discretizations in > particular: > > 1) Our group recently released a paper on enforcing local mass balance and > discrete maximum principles through the least-squares finite element > method. The paper can found here: > > http://arxiv.org/pdf/1506.06099v1.pdf > > Equation 4.13 is what I want to solve using firedrake. Everything in that > paper was written in MATLAB because the authors could not get FEniCS to do > what they want. I am guessing it's because there were no Q1 elements > available within FEniCS (double derivative of P1 elements makes no sense). > > 2) The other discretization, based on the variational multi-scale > formulation, for Darcy-Brinkmann equations is described in this paper: > > http://onlinelibrary.wiley.com/doi/10.1002/fld.2544/abstract > > Though I am currently looking at the steady-state version of this. > Appendix A1 describes how they discretize the \delta v and \delta w terms. > > I could perhaps figure these out through trial and error, but I got my > hands full with other things ATM :) > > Thanks, > Justin > > On Tue, Jul 21, 2015 at 4:33 AM, David Ham <David.Ham(a)imperial.ac.uk> > wrote: > >> Hi Justin, >> >> Can you provide a little more information about the sort of >> discretisation you're talking about: if we can see what you're talking >> about then we'd be in a better position to tell you whether Firedrake can >> do that. >> >> Cheers, >> >> David >> >> On Fri, 17 Jul 2015 at 07:39 McRae, Andrew <a.mcrae12(a)imperial.ac.uk> >> wrote: >> >>> It's possible to represent second derivatives in a form, such as >>> assemble(div(grad(f))*dx). I assume this is true in FEniCS as well as >>> Firedrake, because this is just UFL/FFC/FIAT functionality. This would >>> produce the sum (over cells) of the Laplacian of f on each cell. >>> >>> However, like FEniCS, none of our function spaces have more than C^0 >>> continuity. That is, the functions are at most continuous, but won't have >>> continuous derivatives. It's likely that you won't want to use second >>> derivatives of C^0 functions in a practical discretisation (though I'm sure >>> there are methods that *do* do this). >>> >>> Andrew >>> >>> On 17 July 2015 at 01:50, Justin Chang <jychang48(a)gmail.com> wrote: >>> >>>> Hi everyone, >>>> >>>> Is it possible to do second derivatives? What I mean by that is >>>> things like div[grad[u]] and grad[grad[u]]. I haven't tried this out yet, >>>> but we use these discretizations a lot for our research, and FEniC's >>>> inability to do this made us sad (although our more major qualms had to do >>>> with its inability to support quads). >>>> >>>> Thanks, >>>> Justin >>>> >>>> >>> >> _______________________________________________ >> firedrake mailing list >> firedrake(a)imperial.ac.uk >> https://mailman.ic.ac.uk/mailman/listinfo/firedrake >> >> >

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Concatenation of function spaces?
by Justin Chang 22 Jul '15

22 Jul '15

Hi everyone, Apologies for sending out so many e-mails in such a short amount of time. I guess I have a two part question: 1) Is it possible to concatenation two or more function spaces? In FEniCS I was able to do something like this: V = VectorFunctionSpace(mesh, "CG", 2) Q = FunctionSpace(mesh, "CG", 1) P = FunctionSpace(mesh, "DG", 0) W = V * (Q + P) But the above does not work with Firedrake. Is there a way to do that, or is there something better? This kind of leads me to the second question: 2) I would like to try Q2-P1disc elements for Darcy problem (I see that this element combination is commonly used for stokes equations, but I don't know if it will work for Darcy). Is this possible to do? If the answer to the above two is no, is there another "locally conservative" mixed formulation that's currently doable other than the classical forms like RT0? And preferably with a higher order rate of convergence? Thanks, Justin

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Re: [firedrake] Second derivatives
by David Ham 21 Jul '15

21 Jul '15

Hi Justin, Can you provide a little more information about the sort of discretisation you're talking about: if we can see what you're talking about then we'd be in a better position to tell you whether Firedrake can do that. Cheers, David On Fri, 17 Jul 2015 at 07:39 McRae, Andrew <a.mcrae12(a)imperial.ac.uk> wrote: > It's possible to represent second derivatives in a form, such as > assemble(div(grad(f))*dx). I assume this is true in FEniCS as well as > Firedrake, because this is just UFL/FFC/FIAT functionality. This would > produce the sum (over cells) of the Laplacian of f on each cell. > > However, like FEniCS, none of our function spaces have more than C^0 > continuity. That is, the functions are at most continuous, but won't have > continuous derivatives. It's likely that you won't want to use second > derivatives of C^0 functions in a practical discretisation (though I'm sure > there are methods that *do* do this). > > Andrew > > On 17 July 2015 at 01:50, Justin Chang <jychang48(a)gmail.com> wrote: > >> Hi everyone, >> >> Is it possible to do second derivatives? What I mean by that is things >> like div[grad[u]] and grad[grad[u]]. I haven't tried this out yet, but we >> use these discretizations a lot for our research, and FEniC's inability to >> do this made us sad (although our more major qualms had to do with its >> inability to support quads). >> >> Thanks, >> Justin >> >> >

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Re: [firedrake] Second derivatives
by Andrew McRae 17 Jul '15

17 Jul '15

It's possible to represent second derivatives in a form, such as assemble(div(grad(f))*dx). I assume this is true in FEniCS as well as Firedrake, because this is just UFL/FFC/FIAT functionality. This would produce the sum (over cells) of the Laplacian of f on each cell. However, like FEniCS, none of our function spaces have more than C^0 continuity. That is, the functions are at most continuous, but won't have continuous derivatives. It's likely that you won't want to use second derivatives of C^0 functions in a practical discretisation (though I'm sure there are methods that *do* do this). Andrew On 17 July 2015 at 01:50, Justin Chang <jychang48(a)gmail.com> wrote: > Hi everyone, > > Is it possible to do second derivatives? What I mean by that is things > like div[grad[u]] and grad[grad[u]]. I haven't tried this out yet, but we > use these discretizations a lot for our research, and FEniC's inability to > do this made us sad (although our more major qualms had to do with its > inability to support quads). > > Thanks, > Justin > >

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Second derivatives
by Justin Chang 17 Jul '15

17 Jul '15

Hi everyone, Is it possible to do second derivatives? What I mean by that is things like div[grad[u]] and grad[grad[u]]. I haven't tried this out yet, but we use these discretizations a lot for our research, and FEniC's inability to do this made us sad (although our more major qualms had to do with its inability to support quads). Thanks, Justin

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Hardware counters for Firedrake
by Justin Chang 16 Jul '15

16 Jul '15

Hi everyone, I am very new to Firedrake, i recently switched over from FEniCS, so pardon me if this is a newbie question. If I wanted to run hardware performance counters from PAPI to diagnose my firedrake application how would I go about doing this? In FEniCS, my application was written in C++ and I included the PAPI directives and libraries in the CMakefile. With this I was able to specify where in the source code I wanted to start and stop the counters. Is there a way to somehow replicate this if my code is written using Firedrake? Thanks, Justin

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