[Getdp] ... Formulation question ...
Olivier Castany
castany at quatramaran.ens.fr
Mon Mar 5 22:25:58 CET 2007
> 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.