At last ...

OK, I started working on this at the end of November, but I haven't had the concentration actually to get the program working until now.

Behold: the fourth vibrational mode of the unit disc ...

Yes, there's lots left to be done (and 150,000 triangles per second is far from fast), but at least I'm computing and displaying something which seems to be roughly right.

Next steps:

• Choose which mode to display without recompiling the whole program!
• Better convergence monitoring in the eigenvalue iteration
• Use a sparse solver rather than the LU step, so I can use many more triangles (maybe I can solve on N triangles and use the solution as a start for iteration on 2N - I think the fancy term for this is multi-grid methods)
• Use triangle strips rather than giving each triangle individually; this should get quite a speed-up, particularly on fancier graphics hardware than my laptop has
• Get the vertex normals averaged, so that the triangles don't appear so spiky
• Add ability to do face-on 'contour plot' rather than just the 3D visualisation

Give it another six months ...

I'd be intrigued to hear if the program, here (yes, it's a 1.5MB Windows executable, but I'll vouch for its probity) actually works on anyone's computer but my own (WinXP, Pentium 4, DirectX 9 are the likely-relevant configuration parts; I've no idea what other assumptions I'm making about configuration. If it gives error messages, please tell me; also tell me if it works, so I can break out the Tesco's apple juice and rejoice with great joy.