2nd order method

[Christophe Geuzaine]

Lin Ji wrote:
> 
> Hi, Christophe and Jean-Francois,
>     Sorry to bother you again.
>     I tried the 2nd order interpolation and got some weird result. The
> solution value becomes extremingly large (on the order of 10^7) around the
> source as the wave propogates out. Can you take a look at the two problem
> description files : 'Wave_u.pro' and 'test.pro' to see if I get it right?

Yes, it is correct. The problem comes from an under sampling in the
numerical integration: you have to increase the number of Gauss points
(e.g. GeoElement Triangle; NumberOfPoints 6;) since you integrate 2nd
order functions instead of linear ones.

A _big_ warning about the second resolution scheme: if you plan to use
it, you have to explicitly decouple the constraint (here weakly imposed
on \partial_n u) into space and time parts. The reason is the following.
The system of equations gets only assembled once at the first time step,
with the constraint taken as it is for this time step (in our case, this
means we consider dfdt[] at time t==t0). During the computation, the
only treatment that is applied is the modulation of the constraint by
the function given as the argument of the 'Update[]' command (here:
TimeFct[]). What you really impose is thus 'dfdt[t==t0]*TimeFct[]'. With
your definition (TimeFct[]==dfdt[]), this is obviously not correct
(which causes the huge difference in the values obtained by the first
and second resolution). You should thus express TimeFct[] and dfdt[] in
consequence.

Christophe


NB : the problem on SUN/IBM was the one I suggested in my last e-mail
:-( I will update the version available on the web asap.

-- 
Christophe Geuzaine

Tel: 32 (0) 4 366 37 10    http://geuz.org
Fax: 32 (0) 4 366 29 10    mailto:Christophe.Geuzaine at ulg.ac.be