[Help-gsl] Adaptive double integration

[Jonathan Taylor]

Hi all,

I fear this must have come up on the list before, but I haven't been able to 
find much in the way of GSL-specific discussion on the question of adaptive 
double integration. I have a 2D surface integral that I would like to integrate 
adaptively (converging to a specified relative/absolute precision). My 
understanding is that the GSL integration functions are limited to one 
dimension. Clearly one possibility is to perform two nested adaptive single 
integrations, but I suspect that is probably not optimal (but I would be 
delighted to hear encouraging words on its effectiveness!).

The integral in question is a surface integral, and the function in question is 
reasonably well behaved. It is based around spherical harmonics so will involve 
sinusoidal type variations with potentially quite rapid oscillations, but no 
singularities etc. I would be grateful for any advice on what the best way of 
approaching this is. It looks like it will be the bottleneck in my problem, so 
I would like to speed it up as much as possible - at least for a reasonable 
amount of effort invested!

Thanks in advance
Jonny