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Numerical integration of non-polynomial functions
Thu, 2007-09-27 03:59 - Stephane Bordas
Hello colleagues,
Would anybody know good references on numerical integration of non-polynomial functions? It would be enough for me to obtain one-dimensional rules. Of course, it could have impact for XFEM applications, but for another, improved XFEM method that we are developing.
Note that I am not talking about integrating singularities, but non-polynomial functions. Examples:
sqrt(x)
cos(x)
sin(x)
product of these.
Thanks for any help,
Stephane
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Comments
Numerical Recipes
You can have a look into Numerical Recipes, chapter 4
http://www.nrbook.com/a/bookcpdf.php
It may be a bit classical but I think it fits well to you problem !
Gaussian quadrature is still a good method in case of non-polynomial function, just be careful when sampling your integration nodes.
Best Regards,
Re: Numerical integration of non-polynomial functions
This might help:
Kythe and Schaferkotter - "Handbook of Computational Methods for Integration", CRC 2004 (Ch3.7)
Hi, this question remember
Hi,
this question remember me of some work published in the field of sound & vibration simulation up to medium frequencies. Some work is currently carried on using a PUFEM with plane waves enrichments. Obviously, the integration of matrix term involve integration of non-polynomial functions.
You could have a look a these publications (& references):
P. Bettess, J. Shirron, O. Laghrouche, B. Peseux, R. Sugimoto and J. Trevelyan, A numerical integration scheme for special finite elements for Helmholtz equation, Int. J. Numer. Methods Engrg. 56 (2003), pp. 531–552.
An integration scheme for electromagnetic scattering using plane wave edge elements
Advances in Engineering Software, In Press, Corrected Proof, Available online 16 May 2008
M.E. Honnor, J. Trevelyan, P. Bettess, M. El-hachemi, O. Hassan, K. Morgan, J.J. Shirron
Hope this helps !
Laurent Hazard
Integration of non polynomial functions
Cheers!
Many thanks, and sorry for the delay in responding.
I will look at this and continue the discussion.
All the best from Glasgow,
Stephane
Dr Stephane Bordas
http://people.civil.gla.ac.uk/~bordas