- firedrake - imperial.ac.uk

Re: [firedrake] Laplace equation on subdomain
by David Ham 20 Apr '16

20 Apr '16

Hi Tomasz, I have just put in a pull request fixing your problem. In essence, you were only applying half of the indicator function fix. In order to correctly use indicator functions to solve problems over a subdomain, it is necessary to *both* use the custom boundary condition to force the solution in the rest of the domain to zero *and* multiply the integrands in your forms by the indicator function. You were only doing the former and not the latter. Making this fix causes the error to drop to 10^-5. I haven't done a convergence test to check that the error converges at the right rate, but you should really do so. Regards, David On Tue, 19 Apr 2016 at 11:52 Tomasz Salwa [RPG] <mmtjs(a)leeds.ac.uk> wrote: > Hi David, > > > Here's the code: > > https://bitbucket.org/mmtjs/laplace_extended_domain > > > It's roughly the same as before, just with a gmsh-generated mesh. > > > Regards, > > Tomasz > > > ------------------------------ > *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:* 19 April 2016 09:54 > *To:* firedrake > > *Subject:* Re: [firedrake] Laplace equation on subdomain > Hi Tomasz, > > Can you please post the code you are using for this (preferably by > pointing us to a git repo we can clone). I can't diagnose what is going > wrong just by looking at the visualisation, I'm afraid. > > Regards, > > David > > On Mon, 18 Apr 2016 at 12:12 Tomasz Salwa [RPG] <mmtjs(a)leeds.ac.uk> wrote: > >> Hi, >> >> I plotted the difference between analytical and numerical solutions (see >> attached). It doesn't converge to the right solution with mesh refinement. >> Is it possible that the Neumann BC is not applied at the interface during >> the computation, although the extended Dirichlet BCs enforce resulting zero >> solution beyond the fluid subdomain? >> >> Cheers, >> Tomasz >> >> ________________________________________ >> From: firedrake-bounces(a)imperial.ac.uk <firedrake-bounces(a)imperial.ac.uk> >> on behalf of Lawrence Mitchell <lawrence.mitchell(a)imperial.ac.uk> >> Sent: 15 April 2016 16:00 >> To: firedrake(a)imperial.ac.uk >> Subject: Re: [firedrake] Laplace equation on subdomain >> >> > On 15 Apr 2016, at 15:54, Tomasz Salwa [RPG] <mmtjs(a)leeds.ac.uk> wrote: >> > >> > Hi David, >> > >> > It works partially, i.e. the nodes beyond the fluid subdomain are >> "turned off" now, but it looks like the interface is "smeared". I suspect >> that the assembled matrix's entries involve also integration over elements >> one layer beyond the subdomain boundary. Is it possible to exclude them? >> >> If you have neumann conditions on your subdomain boundary you've only >> constrained the gradient of the solution. Therefore on the boundary nodes >> you may have non-zero solution values. >> >> Because the domain you visualise in paraview extends outside the >> subdomain you'll have (in 1D) something like: >> >> >> ........ >> \............ >> ^ boundary node >> >> Note how the cell at the boundary has a non-zero coefficient value are >> one end, but a zero value at the other (assuming piecewise liners). >> Paraview will linearly interpolate this basis function when visualising, >> which may be the artefact you're seeing. >> >> Can you construct an analytic solution and determine that you converge at >> the correct rate as you refine the mesh? This is a safer test than >> eyeballing the solution. >> >> Lawrence >> >

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Re: [firedrake] Reconstructing a symmetric solution form the part for visualisation purposes
by Andrew McRae 20 Apr '16

20 Apr '16

This sounds like something that should be done by your visualisation software, not by Firedrake. This is a not-dissimilar question I found: http://www.cfd-online.com/Forums/openfoam-paraview/96442-paraview-programma… On 20 April 2016 at 13:07, George Ovchinnikov <lives9(a)gmail.com> wrote: > Dear all, > > I have a partial differential equation on a square and because of the > symmetry of the problem, instead I'm solving equation on the triangle > with appropriately changed boundary conditions. > For visualisation purposes I want to re-create full square composed from > 8 triangles. > > What is the simplest way to achieve it? I can always go with an image > editor, but this is not the route I'd wish to take (and also, this way > it would be hard to automate). > > Sincerely, > George > > > _______________________________________________ > firedrake mailing list > firedrake(a)imperial.ac.uk > https://mailman.ic.ac.uk/mailman/listinfo/firedrake >

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Reconstructing a symmetric solution form the part for visualisation purposes
by George Ovchinnikov 20 Apr '16

20 Apr '16

Dear all, I have a partial differential equation on a square and because of the symmetry of the problem, instead I'm solving equation on the triangle with appropriately changed boundary conditions. For visualisation purposes I want to re-create full square composed from 8 triangles. What is the simplest way to achieve it? I can always go with an image editor, but this is not the route I'd wish to take (and also, this way it would be hard to automate). Sincerely, George

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Re: [firedrake] Issue installing Firedrake
by David Ham 19 Apr '16

19 Apr '16

I have just confirmed this using a clean 15.10 VM. Thanks for finding this, Chris. The bug is now at: https://github.com/firedrakeproject/firedrake/issues/755 On Tue, 19 Apr 2016 at 13:12 Chris Eldred <chris.eldred(a)gmail.com> wrote: > Hey Miklos, > > My bad, that should be Ubuntu 15.10! I will try adding zlib1g-dev and > see if that fixes the issue. > > Regards, > Chris > > On Tue, Apr 19, 2016 at 8:00 AM, Miklós Homolya > <m.homolya14(a)imperial.ac.uk> wrote: > > Hello, > > > >> I am trying to get Firedrake installed on a new Ubuntu 15.04 machine, > > If it is new installation of Ubuntu, why did you choose a version that > has reached its end of life? > > > >> configure: error: Can't find or link to the z library. > > Maybe try installing the zlib1g-dev package and try again? > > > > Regards, > > Miklos > > > >> On 19 Apr 2016, at 06:42, Chris Eldred <chris.eldred(a)gmail.com> wrote: > >> > >> Hey All, > >> > >> I am trying to get Firedrake installed on a new Ubuntu 15.04 machine, > >> and I am having some issues. I have attached the complete output from > >> the install script, the relevant error line seems to be: > >> > >> configure: error: Can't find or link to the z library. Turn off > >> netCDF-4 and opendap with --disable-netcdf-4 --disable-dap, or see > >> config.log for errors. > >> > >> in the PETSc configuration, so I tried: > >> > >> export PETSC_CONFIGURE_OPTIONS="--download-ctetgen --download-triangle > >> --download-chaco --download-metis --download-parmetis > >> --download-scalapack --download-hypre --download-mumps --download-hdf5 > >> --download-exodusii --disable-netcdf-4 --disable-dap" > >> > >> but that still gave the error (in fact, it seems that the install > >> script was still trying to install netcdf-4). This is a totally clean > >> machine, just wiped it and installed Ubuntu 15.04 so I'm not sure what > >> is going on. > >> > >> Any ideas? Is there a hidden dependency for netcdf-4 or dap in the > >> PETSc options I selected? > >> > >> Regards > >> -Chris Eldred > >> -- > >> Chris Eldred > >> Postdoctoral Fellow, LAGA, University of Paris 13 > >> PhD, Atmospheric Science, Colorado State University, 2015 > >> DOE Computational Science Graduate Fellow (Alumni) > >> B.S. Applied Computational Physics, Carnegie Mellon University, 2009 > >> chris.eldred(a)gmail.com > >> <firedrake.log>_______________________________________________ > >> firedrake mailing list > >> firedrake(a)imperial.ac.uk > >> https://mailman.ic.ac.uk/mailman/listinfo/firedrake > > > > > > _______________________________________________ > > firedrake mailing list > > firedrake(a)imperial.ac.uk > > https://mailman.ic.ac.uk/mailman/listinfo/firedrake > > > > -- > Chris Eldred > Postdoctoral Fellow, LAGA, University of Paris 13 > PhD, Atmospheric Science, Colorado State University, 2015 > DOE Computational Science Graduate Fellow (Alumni) > B.S. Applied Computational Physics, Carnegie Mellon University, 2009 > chris.eldred(a)gmail.com > > _______________________________________________ > firedrake mailing list > firedrake(a)imperial.ac.uk > https://mailman.ic.ac.uk/mailman/listinfo/firedrake >

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Issue installing Firedrake
by Chris Eldred 19 Apr '16

19 Apr '16

Hey All, I am trying to get Firedrake installed on a new Ubuntu 15.04 machine, and I am having some issues. I have attached the complete output from the install script, the relevant error line seems to be: configure: error: Can't find or link to the z library. Turn off netCDF-4 and opendap with --disable-netcdf-4 --disable-dap, or see config.log for errors. in the PETSc configuration, so I tried: export PETSC_CONFIGURE_OPTIONS="--download-ctetgen --download-triangle --download-chaco --download-metis --download-parmetis --download-scalapack --download-hypre --download-mumps --download-hdf5 --download-exodusii --disable-netcdf-4 --disable-dap" but that still gave the error (in fact, it seems that the install script was still trying to install netcdf-4). This is a totally clean machine, just wiped it and installed Ubuntu 15.04 so I'm not sure what is going on. Any ideas? Is there a hidden dependency for netcdf-4 or dap in the PETSc options I selected? Regards -Chris Eldred -- Chris Eldred Postdoctoral Fellow, LAGA, University of Paris 13 PhD, Atmospheric Science, Colorado State University, 2015 DOE Computational Science Graduate Fellow (Alumni) B.S. Applied Computational Physics, Carnegie Mellon University, 2009 chris.eldred(a)gmail.com

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Re: [firedrake] Laplace equation on subdomain
by David Ham 19 Apr '16

19 Apr '16

Hi Tomasz, Can you please post the code you are using for this (preferably by pointing us to a git repo we can clone). I can't diagnose what is going wrong just by looking at the visualisation, I'm afraid. Regards, David On Mon, 18 Apr 2016 at 12:12 Tomasz Salwa [RPG] <mmtjs(a)leeds.ac.uk> wrote: > Hi, > > I plotted the difference between analytical and numerical solutions (see > attached). It doesn't converge to the right solution with mesh refinement. > Is it possible that the Neumann BC is not applied at the interface during > the computation, although the extended Dirichlet BCs enforce resulting zero > solution beyond the fluid subdomain? > > Cheers, > Tomasz > > ________________________________________ > From: firedrake-bounces(a)imperial.ac.uk <firedrake-bounces(a)imperial.ac.uk> > on behalf of Lawrence Mitchell <lawrence.mitchell(a)imperial.ac.uk> > Sent: 15 April 2016 16:00 > To: firedrake(a)imperial.ac.uk > Subject: Re: [firedrake] Laplace equation on subdomain > > > On 15 Apr 2016, at 15:54, Tomasz Salwa [RPG] <mmtjs(a)leeds.ac.uk> wrote: > > > > Hi David, > > > > It works partially, i.e. the nodes beyond the fluid subdomain are > "turned off" now, but it looks like the interface is "smeared". I suspect > that the assembled matrix's entries involve also integration over elements > one layer beyond the subdomain boundary. Is it possible to exclude them? > > If you have neumann conditions on your subdomain boundary you've only > constrained the gradient of the solution. Therefore on the boundary nodes > you may have non-zero solution values. > > Because the domain you visualise in paraview extends outside the subdomain > you'll have (in 1D) something like: > > > ........ > \............ > ^ boundary node > > Note how the cell at the boundary has a non-zero coefficient value are one > end, but a zero value at the other (assuming piecewise liners). Paraview > will linearly interpolate this basis function when visualising, which may > be the artefact you're seeing. > > Can you construct an analytic solution and determine that you converge at > the correct rate as you refine the mesh? This is a safer test than > eyeballing the solution. > > Lawrence >

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Re: [firedrake] Laplace equation on subdomain
by David Ham 18 Apr '16

18 Apr '16

Hi Thomasz, You can get the matching CG1 indicator function (to use in the custom BC) using: I_cg = Function(V) par_loop('for (int i=0; i<A.dofs; i++) A[i][0] = fmax(A[i][0], B[0][0]);', dx, {'A' : (I_cg, RW), 'B': (I_f, READ)}) This sets nodes of l_cg to 1 if they touch any cell for which the indicator function is 1. Regards, David On Fri, 15 Apr 2016 at 13:43 Tomasz Salwa [RPG] <mmtjs(a)leeds.ac.uk> wrote: > Ok, I extended the BCs. I'm getting indices out of bounds error. I suppose > this is because I enforce the BCs in DG0, and then solve in CG space. How > can I map it from one to another? > > Thanks, > Tomasz > > > > > Code: > > from firedrake import * > import numpy as np > > nx = 8; ny = 4; Lx = 2.; Ly = 1. > > mesh = RectangleMesh( nx, ny, Lx, Ly ) > V = FunctionSpace( mesh, "CG", 1 ) > V_DG0 = FunctionSpace( mesh, "DG", 0 ) > > def Heaviside( zero_on_left=True, Lp=0. ): > sign = 1. > if zero_on_left == False: > sign = -1. > Hx = Function( V_DG0 ) > Hx_expr = Expression( "0.5*(1.0 + copysign( 1.0, sign*(x[0]-Lp) ))", > sign=sign, Lp=Lp) > Hx.interpolate(Hx_expr) > return Hx; > > I_f = Heaviside( zero_on_left=False, Lp=1. ) > > phi = Function( V ) > trial = TrialFunction( V ) > v = TestFunction( V ) > > a = dot( grad(trial), grad(v) ) * dx > L = Constant(0.) * v * dx > > bc = DirichletBC( V, Expression( "sin(pi*x[1]/Ly)", Ly=Ly ), 1 ) > > class MyBC(DirichletBC): > def __init__(self, V, value, markers): > # Call superclass init > # We provide a dummy subdomain id. > super(MyBC, self).__init__(V, value, 0) > # Override the "nodes" property which says where the boundary > # condition is to be applied. > self.nodes = np.unique(np.where(markers.dat.data_ro_with_halos == > 0)[0]) > > # Now I can use MyBC to create a "boundary condition" to zero out all > # the nodes that are *not* in the fluid domain: > BC_exclude_beyond_fluid = MyBC( V, 0, I_f ) > > solve( a==L, phi, bcs=[bc, BC_exclude_beyond_fluid] ) > > > > Error listing: > > Traceback (most recent call last): > File "laplace_extended_domain.py", line 51, in <module> > solve( a==L, phi, bcs=[bc, BC_exclude_beyond_fluid] ) > File > "/home/tommy/programs/firedrake/local/lib/python2.7/site-packages/firedrake/solving.py", > line 120, in solve > _solve_varproblem(*args, **kwargs) > File > "/home/tommy/programs/firedrake/local/lib/python2.7/site-packages/firedrake/solving.py", > line 147, in _solve_varproblem > solver.solve() > File "<decorator-gen-295>", line 2, in solve > File > "/home/tommy/programs/firedrake/local/lib/python2.7/site-packages/pyop2/profiling.py", > line 203, in wrapper > return f(*args, **kwargs) > File > "/home/tommy/programs/firedrake/local/lib/python2.7/site-packages/firedrake/variational_solver.py", > line 181, in solve > bc.apply(self._problem.u) > File "<decorator-gen-297>", line 2, in apply > File > "/home/tommy/programs/firedrake/local/lib/python2.7/site-packages/pyop2/profiling.py", > line 203, in wrapper > return f(*args, **kwargs) > File > "/home/tommy/programs/firedrake/local/lib/python2.7/site-packages/firedrake/bcs.py", > line 233, in apply > r.assign(self.function_arg, subset=self.node_set) > File > "/home/tommy/programs/firedrake/local/lib/python2.7/site-packages/pyop2/utils.py", > line 64, in __get__ > obj.__dict__[self.__name__] = result = self.fget(obj) > File > "/home/tommy/programs/firedrake/local/lib/python2.7/site-packages/firedrake/bcs.py", > line 162, in node_set > return op2.Subset(self._function_space.node_set, self.nodes) > File > "/home/tommy/programs/firedrake/local/lib/python2.7/site-packages/pyop2/backends.py", > line 118, in __call__ > return t(*args, **kwargs) > File "<decorator-gen-7>", line 2, in __init__ > File > "/home/tommy/programs/firedrake/local/lib/python2.7/site-packages/pyop2/utils.py", > line 130, in wrapper > return f(*args, **kwargs) > File > "/home/tommy/programs/firedrake/local/lib/python2.7/site-packages/pyop2/base.py", > line 840, in __init__ > (self._indices[0], self._indices[-1], self._superset.total_size)) > pyop2.exceptions.SubsetIndexOutOfBounds: Out of bounds indices in Subset > construction: [20, 63) not [0, 45) > > > > > ________________________________________ > From: firedrake-bounces(a)imperial.ac.uk <firedrake-bounces(a)imperial.ac.uk> > on behalf of Lawrence Mitchell <lawrence.mitchell(a)imperial.ac.uk> > Sent: 15 April 2016 11:22 > To: firedrake(a)imperial.ac.uk > Subject: Re: [firedrake] Laplace equation on subdomain > > > On 15 Apr 2016, at 11:08, Tomasz Salwa [RPG] <mmtjs(a)leeds.ac.uk> wrote: > > > > Dear Firedrakers, > > > > As an intermediate part of fluid-structure interaction problem, I would > like to solve Laplace equation (with zero Neumann boundary conditions) on a > subdomain of the full domain. For that reason I define the step function > that is 1 in the subdomain of interest and 0 elsewhere. Multiplying LHS of > the weak form (with trial function) by the step function causes a solver > error. How can I correct it? Code and error listing are below. > > > The problem is that you've knocked out a part of your operator so that > it's: > > laplace 0 > 0 0 > > Particularly, it's zero on the diagonal outside the subdomain. > > To correct this, you'll need to define your own custom boundary condition > class that inherits from DirichletBC that identifies the nodes that are > outside the subdomain and impose strong conditions there. I think we > discussed this when you visited imperial a while ago. > > That way you'll end up with: > > laplace 0 > 0 I > > with the identity on the diagonal outside the subdomain instead. > > As to your comment (how to write 0*v*dx more succinctly) use: > > L = Constant(0)*v*dx > > Thanks, > > Lawrence > > _______________________________________________ > firedrake mailing list > firedrake(a)imperial.ac.uk > https://mailman.ic.ac.uk/mailman/listinfo/firedrake >

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making an rst for a demo
by Francis Poulin 15 Apr '16

15 Apr '16

Hello, I want to put together a demo for firedrake. I know that I need to use sphinx to make an rst file but I wondered whether there was a sample tex file that I could look at to copy the same format. 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

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Laplace equation on subdomain
by Tomasz Salwa [RPG] 15 Apr '16

15 Apr '16

Dear Firedrakers, As an intermediate part of fluid-structure interaction problem, I would like to solve Laplace equation (with zero Neumann boundary conditions) on a subdomain of the full domain. For that reason I define the step function that is 1 in the subdomain of interest and 0 elsewhere. Multiplying LHS of the weak form (with trial function) by the step function causes a solver error. How can I correct it? Code and error listing are below. Thank you, Tomasz from firedrake import * nx = 17; ny = 8; Lx = 2.; Ly = 1. mesh = RectangleMesh( nx, ny, Lx, Ly ) V = FunctionSpace( mesh, "CG", 1 ) V_DG0 = FunctionSpace( mesh, "DG", 0 ) def Heaviside( zero_on_left=True, Lp=0. ): sign = 1. if zero_on_left == False: sign = -1. Hx = Function( V_DG0 ) Hx_expr = Expression( "0.5*(1.0 + copysign( 1.0, sign*(x[0]-Lp) ))", sign=sign, Lp=Lp ) Hx.interpolate(Hx_expr) return Hx; I_f = Heaviside( zero_on_left=False, Lp=1. ) phi = Function( V ) trial = TrialFunction( V ) v = TestFunction( V ) a = dot( grad(trial), grad(v) ) * I_f * dx # step function causes error here !!! L = Function(V) * v * dx # BTW can I put zero here in a simpler manner? bc = DirichletBC( V, Expression( "sin(pi*x[1]/Ly)", Ly=Ly ), 1 ) solve( a==L, phi, bcs=bc ) Error listing: ... Traceback (most recent call last): File "laplace_extended_domain.py", line 36, in <module> solve( a==L, phi, bcs=bc ) File "/home/tommy/programs/firedrake/local/lib/python2.7/site-packages/firedrake/solving.py", line 120, in solve _solve_varproblem(*args, **kwargs) File "/home/tommy/programs/firedrake/local/lib/python2.7/site-packages/firedrake/solving.py", line 147, in _solve_varproblem solver.solve() File "<decorator-gen-295>", line 2, in solve File "/home/tommy/programs/firedrake/local/lib/python2.7/site-packages/pyop2/profiling.py", line 203, in wrapper return f(*args, **kwargs) File "/home/tommy/programs/firedrake/local/lib/python2.7/site-packages/firedrake/variational_solver.py", line 190, in solve solving_utils.check_snes_convergence(self.snes) File "/home/tommy/programs/firedrake/local/lib/python2.7/site-packages/firedrake/solving_utils.py", line 62, in check_snes_convergence %s""" % (snes.getIterationNumber(), msg)) RuntimeError: Nonlinear solve failed to converge after 0 nonlinear iterations. Reason: Inner linear solve failed to converge after 0 iterations with reason: unknown reason (petsc4py enum incomplete?)

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Re: [firedrake] volume integration splitting
by David Ham 15 Apr '16

15 Apr '16

Hi both, Can we see the full context for that integral, as there might be somwthing we can hack up quickly. On Thu, 14 Apr 2016 at 19:31, Cotter, Colin J <colin.cotter(a)imperial.ac.uk> wrote: > Hi Onno, > Not really, I expect you are thinking of something related to water > waves? I was hoping that many issues relating to free surface might be > helped by defining function spaces that are constant throughout the column, > to facilitate coupling between free surface and the bulk. We discussed this > a while back, but nothing was implemented. > > all the best > --cjc > > On 14 April 2016 at 15:36, Onno Bokhove <O.Bokhove(a)leeds.ac.uk> wrote: > >> Hi (-), >> >> >> Can one in Firedrake split a volume integration in 3D, >> >> in a horizontal part (dx dy) and a vertical part (dz), >> >> as follows: >> >> \int_x\int_y f(x,y,t) [ \int_z g(x,y,z,) dz ] dy dx >> >> >> instead of >> >> >> \iiint f(x,y,t) g(x,y,z,t) dx dy dz >> >> ? >> >> >> Best wishes, >> >> >> Onno >> >> >> > > > -- > http://www.imperial.ac.uk/people/colin.cotter > > www.cambridge.org/9781107663916 > > >

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