[Getdp] ... Formulation question ...

[mkoch at gvtc.com]

Hello Olivier,

so I tried exactly what you suggested below (I think). And I tried it  
with the TimeLoopTheta scheme set to 0.0, 0.5 and 1.0. In all cases,  
GetDP no longer complains about any errors, which is nice. BUT, in  
neither case does it appear as if the second Galerkin term is anything  
but zero. I am certain that Spd[] is not zero, so I suspect Norm[{d  
Phi}] somehow remains zero?

I even tried Sqrt[{d Phi}*{d Phi}] instead of Norm[{d Phi}], but that  
does not work either. How is that possible? In the general heat  
conduction equation posted on the Wiki, there is a radiation term, and  
it uses something equivalent to {Phi}^4, and that seems to work  
(although, it also uses source and boundary terms, which are absent  
from my equations).

How come {Phi}^4 turns into something non-zero after a while, but  
Norm[{d Phi}] seemingly does not? I mean, I even know that Phi is  
initialized to something that does not create a zero Norm[{d Phi}].  
So, from the start, Norm[{d Phi}] should be noon-zero and thus drive  
Dt[Dof{Phi},{Phi}] to something other than zero for the other time  
steps as well!? Instead, I get a solution that is equivalent to  
d/dt(Phi) = 0, rather than the desired d/dt(Phi) + Spd*Norm(Grad(Phi))  
= 0.

Any thoughts?

Regards,

Matt

----- Message from castany at quatramaran.ens.fr ---------
     Date: Sun, 4 Mar 2007 21:37:55 +0100
     From: Olivier Castany <castany at quatramaran.ens.fr>
Reply-To: Olivier Castany <castany at quatramaran.ens.fr>
  Subject: Re: [Getdp] ... Formulation question ...
       To: getdp at geuz.org


> Hello,
>
> now that you give a more precise desciption of your problem, I
> understand that you want to solve a dynamic equation.
>
> I can only be of little help since I do not understand the part b) of
> the algorithm you want to program.
>
> I can just say that it is possible to program the equation :
>
>> a) d/dt(Phi) + Spd*Norm(Grad(Phi)) = 0
>
> the formulation would be :
>
> Galerkin { Dt [ Dof{Phi} , {Phi} ] ; ... }
> Galerkin { [ Spd[] * Norm[{d Phi}]  , {Phi} ] ; ... }
>
> and the resolution with "TimeLoopTheta" will be an explicit Euler
> algorithm.
>
> As I don't really understand your algorithm with b), I can't say if it
> is possible to do it with GetDP. My feeling is that it is not currently
> possible without modifying the program.
>
> Regards,
>
> O.C.
>
> PS : if you manage to do something nice with the level set equations,
> maybe you can post it later or put it on the wiki ?
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>


----- End message from castany at quatramaran.ens.fr -----