- firedrake - imperial.ac.uk

Stochastic differential equations
by Angwenyi David 26 Jun '16

26 Jun '16

Dear all, Is it possible to solve pdes driven by some noise using Firedrake? For example, see equation 3.2 in the attachment whose discretisation yields a system 3.3 and 3.4, where dW(t):=sqrt(dt)N(0,Identity). My other related concern is whether It is possible to implement, say, A Kalman filter with equation 3.2 as model equation on Firedrake. Thanks in advance. Angwenyi David

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Re: [firedrake] upwind example remark; extension to CN in time
by Andrew McRae 26 Jun '16

26 Jun '16

D+ and D- refer to the values either side of an interior facet between two cells. On the boundary (exterior facets), there is no such ambiguity, so just D is used. In the steady-state example on the website, this D enters the left-hand-side integral over the outflow part of the boundary, while the prescribed function D0 is used in the integral over the inflow part. "In general", you can write a term that contains both D and D0 and 'picks the right one' depending on the sign of u.n (this is how the interior facet integral works). Note that n always points *outwards* on the exterior boundary facets. On 26 June 2016 at 12:24, Onno Bokhove <O.Bokhove(a)leeds.ac.uk> wrote: > The issue is that D_('+') (or D_('-')) is not defined but I don't > understand why not, or how to fix it? > > > ------------------------------ > *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:* Sunday, June 26, 2016 12:21 PM > > *To:* firedrake > *Subject:* Re: [firedrake] upwind example remark; extension to CN in time > > > Yes that was my point indeed. > > To build any more advanced code upon this one, one > > would need to use an alternate approach entirely > > through the flux. > > That is why it may be useful to extend the > > example with two alternatives: the simple one shown > > and one flux-based only. > > > By the way, in the attached I have L2=0 and thet=0; > > if I uncomment the actual L2 there is a complaint, > > even though they=0. > > Obviously I need this term for the general theta-scheme, > > including thet=0.5 (Crank-Nicolson). > > I am doing the above simple extensions to get used to FD! > Small steps ... > > The example is ties such that value 1 advects into through the > entire domain in the time set. > ------------------------------ > *From:* firedrake-bounces(a)imperial.ac.uk <firedrake-bounces(a)imperial.ac.uk> > on behalf of Colin Cotter <colin.cotter(a)imperial.ac.uk> > *Sent:* Sunday, June 26, 2016 11:26 AM > *To:* firedrake > *Subject:* Re: [firedrake] upwind example remark; extension to CN in time > > Hi Onno, > In answer to your first question. Things are simplified in the advection > demo because we know which edges are upwind, which are downwind, and which > have no flow through them. If you wanted to generalise this, then we would > need a surface integral over the entire external boundary with a switch > that either gave the internal value of the tracer or the inflow boundary > condition, depending on the direction of u.n, just like we did for the > interior facets. > Instead, in this example, on the outflow boundary we just write an > integral involving the interior value, and on the inflow boundary we write > an integral setting the inflow values. > > all the best > -cjc > > On 25 June 2016 at 16:05, Onno Bokhove <O.Bokhove(a)leeds.ac.uk> wrote: > >> Hi FDs, >> >> >> (i) The upwind example is odd in that the real boundaries are treated >> >> in a special way rather than setting the outside value in >> >> the same numerical flux as anywhere else; >> >> my question is how this can be fixed? >> >> So no special terms at the in- and outflow, just specify >> >> the outside velocity used. This is imo the proper DG way not was is done >> >> now. >> >> >> (ii) Attached my attempt to do a time dependent advection >> >> with Crank Nicolson, which works but does not yet >> >> give the right answer, in part due to (i). >> >> >> [I don't understand why I have to make >> >> my theta variable that a constant but other wise it did not work.] >> >> Any suggestions, corrections, also on other silly things done by me? >> >> Next step is to extend to system with 3 equations; >> hence the few extra but unused variables. >> >> Thanks, from midnight Seoul in old style Korean guesthouse. >> >> Onno >> ------------------------------ >> > > > > -- > http://www.imperial.ac.uk/people/colin.cotter > > www.cambridge.org/9781107663916 > > >

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Re: [firedrake] upwind example remark; extension to CN in time
by Colin Cotter 26 Jun '16

26 Jun '16

Hi Onno, In answer to your first question. Things are simplified in the advection demo because we know which edges are upwind, which are downwind, and which have no flow through them. If you wanted to generalise this, then we would need a surface integral over the entire external boundary with a switch that either gave the internal value of the tracer or the inflow boundary condition, depending on the direction of u.n, just like we did for the interior facets. Instead, in this example, on the outflow boundary we just write an integral involving the interior value, and on the inflow boundary we write an integral setting the inflow values. all the best -cjc On 25 June 2016 at 16:05, Onno Bokhove <O.Bokhove(a)leeds.ac.uk> wrote: > Hi FDs, > > > (i) The upwind example is odd in that the real boundaries are treated > > in a special way rather than setting the outside value in > > the same numerical flux as anywhere else; > > my question is how this can be fixed? > > So no special terms at the in- and outflow, just specify > > the outside velocity used. This is imo the proper DG way not was is done > > now. > > > (ii) Attached my attempt to do a time dependent advection > > with Crank Nicolson, which works but does not yet > > give the right answer, in part due to (i). > > > [I don't understand why I have to make > > my theta variable that a constant but other wise it did not work.] > > Any suggestions, corrections, also on other silly things done by me? > > Next step is to extend to system with 3 equations; > hence the few extra but unused variables. > > Thanks, from midnight Seoul in old style Korean guesthouse. > > Onno > ------------------------------ > -- http://www.imperial.ac.uk/people/colin.cotter www.cambridge.org/9781107663916

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Re: [firedrake] upwind example remark; extension to CN in time
by Colin Cotter 26 Jun '16

26 Jun '16

Onno: please can you explain what you don't like about the output? all the best --cjc On 26 June 2016 at 00:35, Onno Bokhove <O.Bokhove(a)leeds.ac.uk> wrote: > Colin: I know as I was comparing different theta's! > > Francis: Oh I see that it does not allow to attach the mesh file to the > email. Odd. > I attach the base file instead. I know it is a rectangle I > assure you it will be changed to a 4-snaked channel. > > ------------------------------ > *From:* firedrake-bounces(a)imperial.ac.uk <firedrake-bounces(a)imperial.ac.uk> > on behalf of Colin Cotter <colin.cotter(a)imperial.ac.uk> > *Sent:* Saturday, June 25, 2016 9:25 PM > *To:* firedrake > *Subject:* Re: [firedrake] upwind example remark; extension to CN in time > > Hi Onno, > Did you see that you set theta to 0.0? If you want CN then it should be > 0.5? > > cheers > --cjc > > On 25 June 2016 at 16:05, Onno Bokhove <O.Bokhove(a)leeds.ac.uk> wrote: > >> Hi FDs, >> >> >> (i) The upwind example is odd in that the real boundaries are treated >> >> in a special way rather than setting the outside value in >> >> the same numerical flux as anywhere else; >> >> my question is how this can be fixed? >> >> So no special terms at the in- and outflow, just specify >> >> the outside velocity used. This is imo the proper DG way not was is done >> >> now. >> >> >> (ii) Attached my attempt to do a time dependent advection >> >> with Crank Nicolson, which works but does not yet >> >> give the right answer, in part due to (i). >> >> >> [I don't understand why I have to make >> >> my theta variable that a constant but other wise it did not work.] >> >> Any suggestions, corrections, also on other silly things done by me? >> >> Next step is to extend to system with 3 equations; >> hence the few extra but unused variables. >> >> Thanks, from midnight Seoul in old style Korean guesthouse. >> >> Onno >> ------------------------------ >> > > > > -- > http://www.imperial.ac.uk/people/colin.cotter > > www.cambridge.org/9781107663916 > > > -- http://www.imperial.ac.uk/people/colin.cotter www.cambridge.org/9781107663916

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Re: [firedrake] upwind example remark; extension to CN in time
by Colin Cotter 25 Jun '16

25 Jun '16

Hi Onno, Did you see that you set theta to 0.0? If you want CN then it should be 0.5? cheers --cjc On 25 June 2016 at 16:05, Onno Bokhove <O.Bokhove(a)leeds.ac.uk> wrote: > Hi FDs, > > > (i) The upwind example is odd in that the real boundaries are treated > > in a special way rather than setting the outside value in > > the same numerical flux as anywhere else; > > my question is how this can be fixed? > > So no special terms at the in- and outflow, just specify > > the outside velocity used. This is imo the proper DG way not was is done > > now. > > > (ii) Attached my attempt to do a time dependent advection > > with Crank Nicolson, which works but does not yet > > give the right answer, in part due to (i). > > > [I don't understand why I have to make > > my theta variable that a constant but other wise it did not work.] > > Any suggestions, corrections, also on other silly things done by me? > > Next step is to extend to system with 3 equations; > hence the few extra but unused variables. > > Thanks, from midnight Seoul in old style Korean guesthouse. > > Onno > ------------------------------ > -- http://www.imperial.ac.uk/people/colin.cotter www.cambridge.org/9781107663916

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Re: [firedrake] upwind example remark; extension to CN in time
by Colin Cotter 25 Jun '16

25 Jun '16

Onno did attach rectmesh.msh... Onno, is there a reason why you didn't use one of the built-in meshes? cheers --cjc On 25 June 2016 at 16:18, Francis Poulin <fpoulin(a)uwaterloo.ca> wrote: > Hello Onno, > > I just tried running your code but see that I can't because I don't have > the rectmesh.msh. Might you be able to send that so we can see exactly > what you see? > > Francis > > P.S. I would also be curious to see the gmsh file that generated the msh > file if possible. > > > > ------------------ > 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 Onno Bokhove [O.Bokhove(a)leeds.ac.uk] > *Sent:* Saturday, June 25, 2016 11:05 AM > *To:* firedrake > *Subject:* [firedrake] upwind example remark; extension to CN in time > > Hi FDs, > > > (i) The upwind example is odd in that the real boundaries are treated > > in a special way rather than setting the outside value in > > the same numerical flux as anywhere else; > > my question is how this can be fixed? > > So no special terms at the in- and outflow, just specify > > the outside velocity used. This is imo the proper DG way not was is done > > now. > > > (ii) Attached my attempt to do a time dependent advection > > with Crank Nicolson, which works but does not yet > > give the right answer, in part due to (i). > > > [I don't understand why I have to make > > my theta variable that a constant but other wise it did not work.] > > Any suggestions, corrections, also on other silly things done by me? > > Next step is to extend to system with 3 equations; > hence the few extra but unused variables. > > Thanks, from midnight Seoul in old style Korean guesthouse. > > Onno > ------------------------------ > -- http://www.imperial.ac.uk/people/colin.cotter www.cambridge.org/9781107663916

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Re: [firedrake] missing 'comm'
by Colin Cotter 25 Jun '16

25 Jun '16

OK, now it is not finding some libraries: In file included from /usr/include/spatialindex/SpatialIndex.h:30:0, from /usr/include/spatialindex/capi/sidx_config.h:56, from /usr/include/spatialindex/capi/sidx_api.h:34, from firedrake/spatialindex.c:245: /usr/include/spatialindex/tools/Tools.h:59:20: fatal error: iostream: No such file or directory #include <iostream> ^ compilation terminated. error: command 'mpicc' failed with exit status 1 all the best --cjc On 25 June 2016 at 15:41, Homolya, Miklós <m.homolya14(a)imperial.ac.uk> wrote: > I have seen such problems already, so it might be systematic, but I'm not > sure what are the exact circumstances that trigger this problem. > > > Try: > > > make clean all > > > in the Firedrake source directory. > ------------------------------ > *From:* firedrake-bounces(a)imperial.ac.uk <firedrake-bounces(a)imperial.ac.uk> > on behalf of Colin Cotter <colin.cotter(a)imperial.ac.uk> > *Sent:* 25 June 2016 14:54:41 > *To:* firedrake > *Subject:* [firedrake] missing 'comm' > > Dear Firedrakers, > Upon calling > > mesh = IcosahedralSphereMesh(1.0,3,2) > > I get an error, > > Traceback (most recent call last): > File "dcmip_3-1_linear_advection_triangle_bdfm1.py", line 31, in <module> > extrusion_type="radial") > File "<decorator-gen-274>", line 2, in ExtrudedMesh > File "/home/cjc1/firedrake-dev/firedrake/src/PyOP2/pyop2/profiling.py", > line 59, in wrapper > return f(*args, **kwargs) > File > "/home/cjc1/firedrake-dev/firedrake/src/firedrake/firedrake/mesh.py", line > 1232, in ExtrudedMesh > mesh.init() > File > "/home/cjc1/firedrake-dev/firedrake/src/firedrake/firedrake/mesh.py", line > 831, in init > self._callback(self) > File > "/home/cjc1/firedrake-dev/firedrake/src/firedrake/firedrake/mesh.py", line > 1165, in callback > self.topology.init() > File "<decorator-gen-272>", line 2, in init > File "/home/cjc1/firedrake-dev/firedrake/src/PyOP2/pyop2/profiling.py", > line 59, in wrapper > return f(*args, **kwargs) > File > "/home/cjc1/firedrake-dev/firedrake/src/firedrake/firedrake/mesh.py", line > 407, in init > self._callback(self) > File > "/home/cjc1/firedrake-dev/firedrake/src/firedrake/firedrake/mesh.py", line > 375, in callback > dmplex.mark_entity_classes(self._plex) > File "firedrake/dmplex.pyx", line 632, in > firedrake.dmplex.mark_entity_classes (firedrake/dmplex.c:9423) > AttributeError: 'module' object has no attribute 'comm' > > Is this another petsc4py issue? > > cheers > --cjc > > -- > http://www.imperial.ac.uk/people/colin.cotter > > www.cambridge.org/9781107663916 > > > -- http://www.imperial.ac.uk/people/colin.cotter www.cambridge.org/9781107663916

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missing 'comm'
by Colin Cotter 25 Jun '16

25 Jun '16

Dear Firedrakers, Upon calling mesh = IcosahedralSphereMesh(1.0,3,2) I get an error, Traceback (most recent call last): File "dcmip_3-1_linear_advection_triangle_bdfm1.py", line 31, in <module> extrusion_type="radial") File "<decorator-gen-274>", line 2, in ExtrudedMesh File "/home/cjc1/firedrake-dev/firedrake/src/PyOP2/pyop2/profiling.py", line 59, in wrapper return f(*args, **kwargs) File "/home/cjc1/firedrake-dev/firedrake/src/firedrake/firedrake/mesh.py", line 1232, in ExtrudedMesh mesh.init() File "/home/cjc1/firedrake-dev/firedrake/src/firedrake/firedrake/mesh.py", line 831, in init self._callback(self) File "/home/cjc1/firedrake-dev/firedrake/src/firedrake/firedrake/mesh.py", line 1165, in callback self.topology.init() File "<decorator-gen-272>", line 2, in init File "/home/cjc1/firedrake-dev/firedrake/src/PyOP2/pyop2/profiling.py", line 59, in wrapper return f(*args, **kwargs) File "/home/cjc1/firedrake-dev/firedrake/src/firedrake/firedrake/mesh.py", line 407, in init self._callback(self) File "/home/cjc1/firedrake-dev/firedrake/src/firedrake/firedrake/mesh.py", line 375, in callback dmplex.mark_entity_classes(self._plex) File "firedrake/dmplex.pyx", line 632, in firedrake.dmplex.mark_entity_classes (firedrake/dmplex.c:9423) AttributeError: 'module' object has no attribute 'comm' Is this another petsc4py issue? cheers --cjc -- http://www.imperial.ac.uk/people/colin.cotter www.cambridge.org/9781107663916

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install script problem when building spatialindex
by Colin Cotter 25 Jun '16

25 Jun '16

Dear FIredrakers, I currently get this message from the install/update script: Cloning libspatialindex Enter passphrase for key '/home/cjc1/.ssh/id_rsa': Successfully cloned libspatialindex branch master. HEAD is now at 34fd22b Merge pull request #82 from miklos1/master glibtoolize or libtoolize not found. Giving up! Traceback (most recent call last): File "firedrake-install", line 903, in <module> build_and_install_libspatialindex() File "firedrake-install", line 617, in build_and_install_libspatialindex check_call(["./autogen.sh"]) File "firedrake-install", line 211, in check_call subprocess.check_call(arguments, env=env) File "/usr/lib/python2.7/subprocess.py", line 540, in check_call raise CalledProcessError(retcode, cmd) subprocess.CalledProcessError: Command '['./autogen.sh']' returned non-zero exit status 1 What can I do to fix this? cheers --cjc -- http://www.imperial.ac.uk/people/colin.cotter www.cambridge.org/9781107663916

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instability of a vortex in firedrakeQG
by Francis Poulin 17 Jun '16

17 Jun '16

Hello, I recently posted a video on youtube that shows the evolution of the perturbation Potential Vorticity for a Gaussian vortex. Initially you see a tripole structure and then a mode 2 structure that is well predicted by the linear theory. This is all done using the QG firedrake code that we've been developing. https://youtu.be/6YLPT7glvlU One thing that is less than ideal is that I am using white noise for the initial perturbations. Someone mentioned that I should probably solve the Poisson problem where white noise is the RHS, and that should clean things up. I will try and do that but it seems that early on, even after the perturbations establish themselves you can still see the grid. In this case I am using a 400x400 rectangular grid. Do people think that an unstructured mesh might make the grid less apparent? Maybe part of the problem is with how it's being plotted in VisIt, I'm not sure but I thought I would ask people's advice. 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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