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Numerical integration of non-polynomial functions

Submitted by Stephane Bordas on
research
integration; non polynomial; numerical

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

http://people.civil.gla.ac.uk/~bordas 

lohazard

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

Tue, 06/10/2008 - 19:13 Permalink