[petsc-users] Fluid-Structure interaction with multiple DMPlex

Thibault Bridel-Bertomeu thibault.bridelbertomeu at gmail.com
Sun Jan 9 10:32:57 CST 2022 

Le dim. 9 janv. 2022 à 17:24, Matthew Knepley <knepley at gmail.com> a écrit :

> On Sun, Jan 9, 2022 at 11:16 AM Thibault Bridel-Bertomeu <
> thibault.bridelbertomeu at gmail.com> wrote:
>
>> Le dim. 9 janv. 2022 à 17:08, Matthew Knepley <knepley at gmail.com> a
>> écrit :
>>
>>> On Sun, Jan 9, 2022 at 10:53 AM Thibault Bridel-Bertomeu <
>>> thibault.bridelbertomeu at gmail.com> wrote:
>>>
>>>> Le dim. 9 janv. 2022 à 15:38, Matthew Knepley <knepley at gmail.com> a
>>>> écrit :
>>>>
>>>>> On Sun, Jan 9, 2022 at 7:49 AM Thibault Bridel-Bertomeu <
>>>>> thibault.bridelbertomeu at gmail.com> wrote:
>>>>>
>>>>>> Le dim. 9 janv. 2022 à 13:05, Matthew Knepley <knepley at gmail.com> a
>>>>>> écrit :
>>>>>>
>>>>>>> On Sat, Jan 8, 2022 at 2:13 PM Thibault Bridel-Bertomeu <
>>>>>>> thibault.bridelbertomeu at gmail.com> wrote:
>>>>>>>
>>>>>>>> However if you use IMEX for strong coupling of the two physics
>>>>>>>> solved in each field, then it means you need to write a single set of PDEs
>>>>>>>> that covers everything, don’t you ?
>>>>>>>> If I want to solve Euler equations in one PetscDS and heat equation
>>>>>>>> in the other one, then I need to write a global set of equations to use the
>>>>>>>> IMEX TS , right ?
>>>>>>>>
>>>>>>>
>>>>>>> The way I think about it. You would have explicit terms for Euler,
>>>>>>> and they would also be confined to one part of the domain, but that just
>>>>>>> impacts how you do the residual integral. You do assemble a combined
>>>>>>> residual for all dogs, however, which I think is what you mean.
>>>>>>>
>>>>>>
>>>>>> Hmm I'm not quite sure yet, probably because I haven't really started
>>>>>> implementing it and I am not familiar with finite elements in PETSc.
>>>>>> The way I see it is that a TS expects to be solving dU/dt = F, that's
>>>>>> why I'm imagining that even with two domains with two different physics,
>>>>>> one has to write the problem under the previous form. And when it comes to
>>>>>> a FVM version of Euler + a FEM version of heat eqn, I'm not quite certain
>>>>>> how to write it like that.
>>>>>> Am I making any sense ? ô_o
>>>>>>
>>>>>
>>>>> Oh, if you have boundary communication, then formulating it as one
>>>>> system is difficult because different cells in supposedly the same DS would
>>>>> have different unknowns, yes. IB solves this by defining the other
>>>>> fields over the whole of each subdomain. Schwarz methods make two different
>>>>> problems and then pass values with what I call an "auxiliary field".
>>>>> You are right that you have to do something.
>>>>>
>>>>
>>>> Let's imagine that we read in a Gmsh mesh into a DMPlex.
>>>> That Gmsh mesh has two physical volumes so the DMPlex will a priori
>>>> show two labels and therefore (?) two fields, meaning we can work with two
>>>> SubDMs.
>>>> Each SubDM basically matches a region of the whole mesh in this case.
>>>> Now each SubDM can have its own DS and we can also attribute each DM to
>>>> a TS.
>>>> We can therefore solve the two problems, say one for fluid dynamics the
>>>> other for heat eqn.
>>>>
>>>> The only thing I am not sure about (actually I haven't coded anything
>>>> yet so I'm not sure of anything but ...) is the following.
>>>> The two SubDMs come originally from the same DM right. Say we work in
>>>> 3D, then the two SubDM must share a layer of triangles (and the segments
>>>> and vertices that go along with them). That layer of triangles exist in
>>>> both SubDM and is a boundary in both SubDM.
>>>> How do I tell, for instance, the fluid SubDM that the information it
>>>> needs on that layer of triangles comes from the other SubDM ? And vice
>>>> versa ? Is it possible to create two SubDMs from the same DM that somehow
>>>> still know each other after the creation ?
>>>> Example 23 from SNES does not do that kind of thing right ? The "top"
>>>> and "bottom" pieces are quite independent or am I misunderstanding sth ?
>>>>
>>>
>>> The way I see it working is that you compose the maps from the original
>>> space to each subDM on the boundary. Then, when you get one solution, you
>>> can map it to points on the boundary of the other solution, which you use
>>> as an auxiliary field.
>>>
>>
>> Okay yes, I get what you mean. Is there a method in PETSc to do such
>> things ? Does it have to do with IS ?
>>
>
> Yes, we can do it. It is just IS manipulation.
>

Tagging that layer of triangles as a physical surface in Gmsh can help
later because it will create another label in the DMPlex, right ?
Then one could maybe rely on DMGetLabelIdIS ?

Thank you Matt as usual for your precious help ! ;)
Thibault


>
>   Thanks,
>
>     Matt
>
>
>> Thanks !
>> Thibault
>>
>>
>>>
>>>   Thanks,
>>>
>>>      Matt
>>>
>>>
>>>> Thanks !!
>>>>
>>>> Thibault
>>>>
>>>>
>>>>>   Thanks,
>>>>>
>>>>>      Matt
>>>>>
>>>>>
>>>>>> Thanks,
>>>>>> Thibault
>>>>>>
>>>>>>
>>>>>>>   Thanks,
>>>>>>>
>>>>>>>     Matt
>>>>>>>
>>>>>>>
>>>>>>>> Thanks,
>>>>>>>>
>>>>>>>> Thibault
>>>>>>>>
>>>>>>>> Le sam. 8 janv. 2022 à 20:00, Matthew Knepley <knepley at gmail.com>
>>>>>>>> a écrit :
>>>>>>>>
>>>>>>>>> On Sat, Jan 8, 2022 at 1:30 PM Thibault Bridel-Bertomeu <
>>>>>>>>> thibault.bridelbertomeu at gmail.com> wrote:
>>>>>>>>>
>>>>>>>>>> Yes I was wondering about different time steps as well because
>>>>>>>>>> usually implicit integration moves much faster.
>>>>>>>>>> But if it not implemented, then maybe going the « weak coupling »
>>>>>>>>>> road with a sub-DM is the way.
>>>>>>>>>> Can I ask how you proceed in the rocket engine code you are
>>>>>>>>>> writing ? IMEX ?
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>> Right now it is IMEX, but we are explicitly substepping particles.
>>>>>>>>> Not sure what the final thing will be.
>>>>>>>>>
>>>>>>>>>   Thanks,
>>>>>>>>>
>>>>>>>>>     Matt
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>> Thibault
>>>>>>>>>>
>>>>>>>>>> Le sam. 8 janv. 2022 à 19:22, Matthew Knepley <knepley at gmail.com>
>>>>>>>>>> a écrit :
>>>>>>>>>>
>>>>>>>>>>> I do not know how. Right now, composable TS does not work all
>>>>>>>>>>> the way.
>>>>>>>>>>>
>>>>>>>>>>>   Matt
>>>>>>>>>>>
>>>>>>>>>>> On Sat, Jan 8, 2022 at 1:03 PM Mark Adams <mfadams at lbl.gov>
>>>>>>>>>>> wrote:
>>>>>>>>>>>
>>>>>>>>>>>> Can you subcycle with IMEX?
>>>>>>>>>>>>
>>>>>>>>>>>> On Sat, Jan 8, 2022 at 10:58 AM Matthew Knepley <
>>>>>>>>>>>> knepley at gmail.com> wrote:
>>>>>>>>>>>>
>>>>>>>>>>>>> On Sat, Jan 8, 2022 at 3:05 AM Thibault Bridel-Bertomeu <
>>>>>>>>>>>>> thibault.bridelbertomeu at gmail.com> wrote:
>>>>>>>>>>>>>
>>>>>>>>>>>>>> Le ven. 7 janv. 2022 à 19:45, Thibault Bridel-Bertomeu <
>>>>>>>>>>>>>> thibault.bridelbertomeu at gmail.com> a écrit :
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Le ven. 7 janv. 2022 à 19:23, Matthew Knepley <
>>>>>>>>>>>>>>> knepley at gmail.com> a écrit :
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> On Fri, Jan 7, 2022 at 12:58 PM Thibault Bridel-Bertomeu <
>>>>>>>>>>>>>>>> thibault.bridelbertomeu at gmail.com> wrote:
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Le ven. 7 janv. 2022 à 14:54, Matthew Knepley <
>>>>>>>>>>>>>>>>> knepley at gmail.com> a écrit :
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> On Fri, Jan 7, 2022 at 8:52 AM Thibault Bridel-Bertomeu <
>>>>>>>>>>>>>>>>>> thibault.bridelbertomeu at gmail.com> wrote:
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> Hi Matthew,
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> Le ven. 7 janv. 2022 à 14:44, Matthew Knepley <
>>>>>>>>>>>>>>>>>>> knepley at gmail.com> a écrit :
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> On Fri, Jan 7, 2022 at 5:46 AM Thibault Bridel-Bertomeu
>>>>>>>>>>>>>>>>>>>> <thibault.bridelbertomeu at gmail.com> wrote:
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> Dear all,
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> First of, happy new year everyone !! All the best !
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> Happy New Year!
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> I am starting to draft a new project that will be
>>>>>>>>>>>>>>>>>>>>> about fluid-structure interaction: in particular, the idea is to compute
>>>>>>>>>>>>>>>>>>>>> the Navier-Stokes (or Euler nevermind) flow around an object and _at the
>>>>>>>>>>>>>>>>>>>>> same time_ compute the heat equation inside the object.
>>>>>>>>>>>>>>>>>>>>> So basically, I am thinking a mesh of the fluid and a
>>>>>>>>>>>>>>>>>>>>> mesh of the object, both meshes being linked at the fluid - solid interface.
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> First question: Are these meshes intended to match on
>>>>>>>>>>>>>>>>>>>> the interface? If not, this sounds like overset grids or immersed
>>>>>>>>>>>>>>>>>>>> boundary/interface methods. In this case, more than one mesh makes sense to
>>>>>>>>>>>>>>>>>>>> me. If they are intended to match, then I would advocate a single mesh with
>>>>>>>>>>>>>>>>>>>> multiple problems defined on it. I have experimented with this, for example
>>>>>>>>>>>>>>>>>>>> see SNES ex23 where I have a field in only part of the domain. I have a
>>>>>>>>>>>>>>>>>>>> large project to do exactly this in a rocket engine now.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> Yes the way I see it is more of a single mesh with two
>>>>>>>>>>>>>>>>>>> distinct regions to distinguish between the fluid and the solid. I was
>>>>>>>>>>>>>>>>>>> talking about two meshes to try and explain my vision but it seems like it
>>>>>>>>>>>>>>>>>>> was unclear.
>>>>>>>>>>>>>>>>>>> Imagine if you wish a rectangular box with a sphere
>>>>>>>>>>>>>>>>>>> inclusion: the sphere would be tagged as a solid and the rest of the domain
>>>>>>>>>>>>>>>>>>> as fluid. Using Gmsh volumes for instance.
>>>>>>>>>>>>>>>>>>> Ill check out the SNES example ! Thanks !
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> First (Matthew maybe ?) do you think it is something
>>>>>>>>>>>>>>>>>>>>> that could be done using two DMPlex's that would somehow be spawned from
>>>>>>>>>>>>>>>>>>>>> reading a Gmsh mesh with two volumes ?
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> You can take a mesh and filter out part of it with
>>>>>>>>>>>>>>>>>>>> DMPlexFilter(). That is not used much so I may have to fix it to do what
>>>>>>>>>>>>>>>>>>>> you want, but that should be easy.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> And on one DMPlex we would have finite volume for the
>>>>>>>>>>>>>>>>>>>>> fluid, on the other finite elements for the heat eqn ?
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> I have done this exact thing on a single mesh. It
>>>>>>>>>>>>>>>>>>>> should be no harder on two meshes if you go that route.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> Second, is it something that anyone in the community
>>>>>>>>>>>>>>>>>>>>> has ever imagined doing with PETSc DMPlex's ?
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> Yes, I had a combined FV+FEM simulation of magma
>>>>>>>>>>>>>>>>>>>> dynamics (I should make it an example), and currently we are doing FVM+FEM
>>>>>>>>>>>>>>>>>>>> for simulation of a rocket engine.
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> Wow so it seems like it’s the exact same thing I would
>>>>>>>>>>>>>>>>>>> like to achieve as the rocket engine example.
>>>>>>>>>>>>>>>>>>> So you have a single mesh and two regions tagged
>>>>>>>>>>>>>>>>>>> differently, and you use the DmPlexFilter to solve FVM and FEM separately ?
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> With a single mesh, you do not even need DMPlexFilter.
>>>>>>>>>>>>>>>>>> You just use the labels that Gmsh gives you. I think we should be able to
>>>>>>>>>>>>>>>>>> get it going in a straightforward way.
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Ok then ! Thanks ! I’ll give it a shot and see what
>>>>>>>>>>>>>>>>> happens !
>>>>>>>>>>>>>>>>> Setting up the FVM and FEM discretizations will pass by
>>>>>>>>>>>>>>>>> DMSetField right ? With a single mesh tagged with two different regions, it
>>>>>>>>>>>>>>>>> should show up as two fields, is that correct ?
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> Yes, the idea is as follows. Each field also has a label
>>>>>>>>>>>>>>>> argument that is the support of the field in the domain. Then we create
>>>>>>>>>>>>>>>> PetscDS objects for each
>>>>>>>>>>>>>>>> separate set of overlapping fields. The current algorithm
>>>>>>>>>>>>>>>> is not complete I think, so let me know if this step fails.
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Ok, thanks.
>>>>>>>>>>>>>>> I’ll let you know and share snippets when I have something
>>>>>>>>>>>>>>> started !
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Talk soon ! Thanks !
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Hi Matthew,
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> I thought about a little something else : what about setting
>>>>>>>>>>>>>> two different TS, one for each field of the DM ? Most probably the fluid
>>>>>>>>>>>>>> part would be solved with an explicit time stepping whereas the solid part
>>>>>>>>>>>>>> with the heat equation would benefit from implicit time stepping. TSSetDM
>>>>>>>>>>>>>> does not allow a field specification, is there a way to hack that so that
>>>>>>>>>>>>>> each field has its own TS ?
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> I see at least two options here:
>>>>>>>>>>>>>
>>>>>>>>>>>>> 1. Split the problems:
>>>>>>>>>>>>>
>>>>>>>>>>>>>     You can use DMCreateSubDM() to split off part of a problem
>>>>>>>>>>>>> and use a solver on that. I have done this for problems with weak coupling.
>>>>>>>>>>>>>
>>>>>>>>>>>>> 2. Use IMEX
>>>>>>>>>>>>>
>>>>>>>>>>>>>     For strong coupling, I have used the IMEX TSes in PETSc.
>>>>>>>>>>>>> You put the explicit terms in the RHS, and the implicit in the IFunction.
>>>>>>>>>>>>>
>>>>>>>>>>>>>   Thanks,
>>>>>>>>>>>>>
>>>>>>>>>>>>>      Matt
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>>> Thanks
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> Thibault
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Thibault
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>   Thanks,
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>      Matt
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Thanks,
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> Thibault
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>   Thanks,
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>      Matt
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> Thanks !
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> Thibault
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>   Thanks,
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>      Matt
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> As I said it is very prospective, I just wanted to
>>>>>>>>>>>>>>>>>>>>> have your opinion !!
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> Thanks very much in advance everyone !!
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>> Cheers,
>>>>>>>>>>>>>>>>>>>>> Thibault
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> --
>>>>>>>>>>>>>>>>>>>> What most experimenters take for granted before they
>>>>>>>>>>>>>>>>>>>> begin their experiments is infinitely more interesting than any results to
>>>>>>>>>>>>>>>>>>>> which their experiments lead.
>>>>>>>>>>>>>>>>>>>> -- Norbert Wiener
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>>> https://www.cse.buffalo.edu/~knepley/
>>>>>>>>>>>>>>>>>>>> <http://www.cse.buffalo.edu/~knepley/>
>>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>> --
>>>>>>>>>>>>>>>>>>> Thibault Bridel-Bertomeu
>>>>>>>>>>>>>>>>>>> —
>>>>>>>>>>>>>>>>>>> Eng, MSc, PhD
>>>>>>>>>>>>>>>>>>> Research Engineer
>>>>>>>>>>>>>>>>>>> CEA/CESTA
>>>>>>>>>>>>>>>>>>> 33114 LE BARP
>>>>>>>>>>>>>>>>>>> Tel.: (+33)557046924
>>>>>>>>>>>>>>>>>>> Mob.: (+33)611025322
>>>>>>>>>>>>>>>>>>> Mail: thibault.bridelbertomeu at gmail.com
>>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> --
>>>>>>>>>>>>>>>>>> What most experimenters take for granted before they
>>>>>>>>>>>>>>>>>> begin their experiments is infinitely more interesting than any results to
>>>>>>>>>>>>>>>>>> which their experiments lead.
>>>>>>>>>>>>>>>>>> -- Norbert Wiener
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>>> https://www.cse.buffalo.edu/~knepley/
>>>>>>>>>>>>>>>>>> <http://www.cse.buffalo.edu/~knepley/>
>>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>> --
>>>>>>>>>>>>>>>>> Thibault Bridel-Bertomeu
>>>>>>>>>>>>>>>>> —
>>>>>>>>>>>>>>>>> Eng, MSc, PhD
>>>>>>>>>>>>>>>>> Research Engineer
>>>>>>>>>>>>>>>>> CEA/CESTA
>>>>>>>>>>>>>>>>> 33114 LE BARP
>>>>>>>>>>>>>>>>> Tel.: (+33)557046924
>>>>>>>>>>>>>>>>> Mob.: (+33)611025322
>>>>>>>>>>>>>>>>> Mail: thibault.bridelbertomeu at gmail.com
>>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> --
>>>>>>>>>>>>>>>> What most experimenters take for granted before they begin
>>>>>>>>>>>>>>>> their experiments is infinitely more interesting than any results to which
>>>>>>>>>>>>>>>> their experiments lead.
>>>>>>>>>>>>>>>> -- Norbert Wiener
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>>> https://www.cse.buffalo.edu/~knepley/
>>>>>>>>>>>>>>>> <http://www.cse.buffalo.edu/~knepley/>
>>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> --
>>>>>>>>>>>>>>> Thibault Bridel-Bertomeu
>>>>>>>>>>>>>>> —
>>>>>>>>>>>>>>> Eng, MSc, PhD
>>>>>>>>>>>>>>> Research Engineer
>>>>>>>>>>>>>>> CEA/CESTA
>>>>>>>>>>>>>>> 33114 LE BARP
>>>>>>>>>>>>>>> Tel.: (+33)557046924
>>>>>>>>>>>>>>> Mob.: (+33)611025322
>>>>>>>>>>>>>>> Mail: thibault.bridelbertomeu at gmail.com
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>> --
>>>>>>>>>>>>>> Thibault Bridel-Bertomeu
>>>>>>>>>>>>>> —
>>>>>>>>>>>>>> Eng, MSc, PhD
>>>>>>>>>>>>>> Research Engineer
>>>>>>>>>>>>>> CEA/CESTA
>>>>>>>>>>>>>> 33114 LE BARP
>>>>>>>>>>>>>> Tel.: (+33)557046924
>>>>>>>>>>>>>> Mob.: (+33)611025322
>>>>>>>>>>>>>> Mail: thibault.bridelbertomeu at gmail.com
>>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>> --
>>>>>>>>>>>>> What most experimenters take for granted before they begin
>>>>>>>>>>>>> their experiments is infinitely more interesting than any results to which
>>>>>>>>>>>>> their experiments lead.
>>>>>>>>>>>>> -- Norbert Wiener
>>>>>>>>>>>>>
>>>>>>>>>>>>> https://www.cse.buffalo.edu/~knepley/
>>>>>>>>>>>>> <http://www.cse.buffalo.edu/~knepley/>
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>> --
>>>>>>>>>>> What most experimenters take for granted before they begin their
>>>>>>>>>>> experiments is infinitely more interesting than any results to which their
>>>>>>>>>>> experiments lead.
>>>>>>>>>>> -- Norbert Wiener
>>>>>>>>>>>
>>>>>>>>>>> https://www.cse.buffalo.edu/~knepley/
>>>>>>>>>>> <http://www.cse.buffalo.edu/~knepley/>
>>>>>>>>>>>
>>>>>>>>>> --
>>>>>>>>>> Thibault Bridel-Bertomeu
>>>>>>>>>> —
>>>>>>>>>> Eng, MSc, PhD
>>>>>>>>>> Research Engineer
>>>>>>>>>> CEA/CESTA
>>>>>>>>>> 33114 LE BARP
>>>>>>>>>> Tel.: (+33)557046924
>>>>>>>>>> Mob.: (+33)611025322
>>>>>>>>>> Mail: thibault.bridelbertomeu at gmail.com
>>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>> --
>>>>>>>>> What most experimenters take for granted before they begin their
>>>>>>>>> experiments is infinitely more interesting than any results to which their
>>>>>>>>> experiments lead.
>>>>>>>>> -- Norbert Wiener
>>>>>>>>>
>>>>>>>>> https://www.cse.buffalo.edu/~knepley/
>>>>>>>>> <http://www.cse.buffalo.edu/~knepley/>
>>>>>>>>>
>>>>>>>> --
>>>>>>>> Thibault Bridel-Bertomeu
>>>>>>>> —
>>>>>>>> Eng, MSc, PhD
>>>>>>>> Research Engineer
>>>>>>>> CEA/CESTA
>>>>>>>> 33114 LE BARP
>>>>>>>> Tel.: (+33)557046924
>>>>>>>> Mob.: (+33)611025322
>>>>>>>> Mail: thibault.bridelbertomeu at gmail.com
>>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>> --
>>>>>>> What most experimenters take for granted before they begin their
>>>>>>> experiments is infinitely more interesting than any results to which their
>>>>>>> experiments lead.
>>>>>>> -- Norbert Wiener
>>>>>>>
>>>>>>> https://www.cse.buffalo.edu/~knepley/
>>>>>>> <http://www.cse.buffalo.edu/~knepley/>
>>>>>>>
>>>>>>
>>>>>
>>>>> --
>>>>> What most experimenters take for granted before they begin their
>>>>> experiments is infinitely more interesting than any results to which their
>>>>> experiments lead.
>>>>> -- Norbert Wiener
>>>>>
>>>>> https://www.cse.buffalo.edu/~knepley/
>>>>> <http://www.cse.buffalo.edu/~knepley/>
>>>>>
>>>>
>>>
>>> --
>>> What most experimenters take for granted before they begin their
>>> experiments is infinitely more interesting than any results to which their
>>> experiments lead.
>>> -- Norbert Wiener
>>>
>>> https://www.cse.buffalo.edu/~knepley/
>>> <http://www.cse.buffalo.edu/~knepley/>
>>>
>>
>
> --
> What most experimenters take for granted before they begin their
> experiments is infinitely more interesting than any results to which their
> experiments lead.
> -- Norbert Wiener
>
> https://www.cse.buffalo.edu/~knepley/
> <http://www.cse.buffalo.edu/~knepley/>
>
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