[Getdp] ... Formulation question ...

[Olivier Castany]

> the first Galerkin term, and then we use it without Dof in the 
> second Galerkin term. I guess, as you say, that makes Phi 
> explicit, so let's hope this scheme is stable. I assume this 
> also means that in the second Galerkin term, the Phi from the 
> previous time step is used? 

Unfortunately, I don't know exactly how it goes in GetDP. My ideas 
are the following :

the equation "dp/dt = f(p)" is discretized by the "TimeLoopTheta" in :
(pn+1 - pn) / dt = (1-theta) f(pn) + theta f(pn+1)

(explicit Euler scheme : theta = 0, implicit Euler : theta = 1)
(pn = value of p at step n)

In the general case when IterativeLoop is used, pn+1 will be 
solved iteratively in the following way :

pn+1(0) = pn
pn+1(k+1) = pn + dt * ((1-theta) f(pn) + theta f(pn+1(k)))

when sufficent convergence is obtained, pn+1(k+1) is taken as a 
value for pn+1.

Maybe Christophe Geuzaine could confirm (or deny).

Rq : If theta = 0 (explicit Euler), there is no need to
use an IterativeLoop inside the TimeLoopTheta.

> I'll start playing with this again 
> sometime early this week. Also, I think my second equation can 
> now be solved in a very similar way, presuming I can come up 
> with the signum function, 

I see no sign function in the GetDP manual. Maybe (not tested) :
Sign[] = $1>0 ? 1 : -1 ;   (does it work ?)

> and presuming I can embed a 
> TimeLoopTheta in a TimeLoopTheta, perhaps like so:

Maybe you can first try without the imbricated IterativeLoop (in 
order to limit the number of possible problems)

Maybe you could also first try a simple level set equation 
(without the reinitialisation).

> Any thoughts on this construct? 

It looks nice.

> I am not sure how the transfer of 
> solutions can be done, though. 

I've never used the DestinationSystem and TransferSolution 
commands, but I am sure some people have.

O.C.