Galerkin
 

Hi!

I am using Galerkin method for heat transfer in a channel. Till now my sets of functions were sin() or cos().

I would like to use the Chebyshev polinomials, but I have a problem to determine coefficients.

Does anybody know where to find a detail discription of calculation proceduce with the Chebyshev polinomials.

Eq. which I am solving is:

(1-z^2)dT/dx=d2T/dz2

Thanks, Andrej

Re: Galerkin - Chebyshev Spectral Method
 

Hi Andrej,

There is a whole litterature on the Chebyshev Spectral Methods, whether Galerkin, Tau, Collocation, etc...

As a good start check this book:

Canuto, Hussaini, Quarteroni and Zang, 1988, Spectral Methods in Fluid Dynamics, New York, Springer Verlag.

I am sure you can find that book at UCLA in the library of Applied Mathematics or something similar.

THe chebyshev polynomial are actually given by:

Tn(y)=cos(n arcos(y))

so that chosing y_j=cos(pi*j/N),

where j=0,1,..N; gives you an easy way to get the coefficient at the points y_j, by using a cosine transform (FFT).

Good luck,

Patrick Godon

Re: Galerkin
 

The book that you will want to get is called "Chebyshev and Fourier Spectral Methods" by John P. Boyd. The second edition will be published by Dover Publications in August 2001. As someone very new to the CFD field, I have found the first edition (out of print) invaluable and easily readable.