Stormy Seas Ahead

College has finally started after a long three months of vacation, and I really don’t know where this numerical methods programming is going to head, considering that progress was terrible during the hols. And now with even less free time, I’m not sure about what we’re going to do. But some advantages with being at the hostel are that I can spend longer hours in front of the computer and my friend and I can work together. Another big advantage is that Linux works here (at home, I used the same CPU but a different monitor, and SuSE 10.0 refused to work because just that one change) and both my friend and I can work on the standard GCC compiler.

Okay, I just realised I have this major problem with Suse 10.0 which I figure a lot of others have too, looking at all the forums on the net. I am not able to install softwares from RPMs that are on the hard drive and keep getting the error “Installation sources not refreshed”. I found out that this was because the hard drive was a static source. I could install softwares from online repositories without any problems but that’s not always convenient. I tried out the suggestions to get rid of the problem but they were in vain. I’m seriously considering changing my distro, but I guess I’ll wait. I wanted to start working on Linux more, but then every time I decide to do that, some problem or the other crops up. If it’s only GCC that I may finally want to use, I guess I shouldn’t be in too much of a hurry to change, because that works fine.

Right now work on Laplace’s Equation is coming to a standstill. We haven’t even looked at it ever since college started. I don’t get it. It’s something so simple. Yet we procrastinate so much. I wonder what we’ll do once we get to the next stage. I just thought I’d write down some observations. Hopefully we’ll get back to it soon.

The supposedly more efficient method is taking more time, and I think this is because it has more calculations involved (as in float multiplications and divisions) to determine parameters for different mesh sizes. I also feel that converging from an approximate value to machine precision might take a lot more time than reaching that average value in the first place. But of course, this argument may be wrong as this method is a well known one. And supposedly it’s working alright for my friend. Anyway, we decided it’s best we started working together more rather than do things separately and then analyse each other’s work.

One thing about the run times that took me a log time to realise was that for a doubling of the mesh size, the run time ncreased by approximately 16 times. If we assume that the time taken per grid point per iteration is constant for all mesh sizes (which is a reasonable assumption and one that had been verified from data collected), then a doubling of mesh size should increase the total time by a factorr of four (since number of grid points are quadrupled). But the number of iterations also increase by four times. I didn’t understand why this should happen but I guess I haven’t given it enough thought yet.

There’s also other stuff about what checks we use to determine convergence, improving the efficiency of the Gauss Elimination method to solve the whole system of linear equations obtained from the grid, and to check the error in value between the real solution and that obtained by using numerical methods. I think I’m starting to get frustrated writing about this. I could go on and on. But it only makes me think of how much more I have left to do. I guess I’ll stop here.