iMechanica - integration; non polynomial; numerical - Comments

Integration of non polynomial functions

Stephane Bordas — Thu, 02 Oct 2008 04:54:02 -0400

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

Hi, this question remember

lohazard — Tue, 10 Jun 2008 15:13:08 -0400

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

Re: Numerical integration of non-polynomial functions

Dan Cojocaru — Fri, 28 Sep 2007 14:39:17 -0400

This might help:

Kythe and Schaferkotter - "Handbook of Computational Methods for Integration", CRC 2004 (Ch3.7)

Numerical Recipes

tlaverne — Thu, 27 Sep 2007 09:49:23 -0400

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,