On Tue, May 24, 2011 at 2:11 AM, Ian Hinder ian.hinder@aei.mpg.de wrote:
On 23 May 2011, at 23:49, Bruno Coutinho Mundim wrote:
- Bruno still has troubles with RotatingSymmetry180 when using the
development version of ET for the BBH example (parfile is in subversion)
- will try running without RotatingSymmetry180
Just got the results: no problem without RotatingSymmetry180.
OK good, so we know where the problem is.
- convergence in norms is bad, somewhat better in 1D data for a short
time after simulation startup
A closer look into the initial data revealed that both the l2-norm of the hamiltonian constraint and its value along the x-axis converge to the expected order, 4th order. This convergence is not observed anymore in the very next coarse step when the comparison is done again.
The time prolongation is only 3rd order accurate so I wouldn't expect convergence at 4th order.
Time prolongation is second order accurate.
You can use tapered grids, which avoids all time interpolation except possibly during regridding. If you are careful about regridding you don't need time interpolation for this either. This gives you clean fourth order convergence, except near the outer boundary if you are cheating there (and we all are).
Another issue to consider is how you set up the past timelevels. If you copy the data from the current time level, then you are introducing a first order error. If you use the three-timelevel-initialisation, then you are second order accurate. Again, these past timelevels are used only for time interpolation, but they can reduce the convergence order even further if they are not well initialised.
-erik