Numerical Integration

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For our interest in the Finite Element Method, the purpose is to describe '''how the element matrices can be integrated numerically'''.
 
For our interest in the Finite Element Method, the purpose is to describe '''how the element matrices can be integrated numerically'''.
  
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== Gauss-Legendre Numerical Integration ==
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To fix the most basic concepts on Numerical Integration, we will focus our description on a one dimensional integration using the Gauss-Legendre quadrature, that is, to solve:
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:<math>I=int_{-1}^{+1} f(\chi) d\chi</math>
  
  
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# '''Carlos A. Felippa''', "'''''A compendium of FEM integration formulas for symbolic work'''''", Engineering Computations, Vol. 21 No. 8, 2004, pp. 867-890, (c) Emerald Group Publishing Limited [http://www.emeraldinsight.com/Insight/viewContentItem.do?contentType=Article&contentId=878215]
 
# '''Carlos A. Felippa''', "'''''A compendium of FEM integration formulas for symbolic work'''''", Engineering Computations, Vol. 21 No. 8, 2004, pp. 867-890, (c) Emerald Group Publishing Limited [http://www.emeraldinsight.com/Insight/viewContentItem.do?contentType=Article&contentId=878215]
 
 
# [http://en.wikipedia.org/wiki/Numerical_integration Numerical Integration]
 
# [http://en.wikipedia.org/wiki/Numerical_integration Numerical Integration]
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# [http://en.wikipedia.org/wiki/Gaussian_quadrature Gaussian Quadrature]
  
 
[[Category:Theory]]
 
[[Category:Theory]]

Revision as of 11:11, 3 November 2009

Numerical integration refers to all the procedures, algorithms and techniques in the numerical analysis to obtain an approximate solution to a definite integral.

That is, how to obtain a numerical value of:

\int_{\lambda_a}^{\lambda_b}\! f(\lambda)\, d\lambda.

where \lambda \, can be a 1D, 2D or 3D domain.


For our interest in the Finite Element Method, the purpose is to describe how the element matrices can be integrated numerically.


Gauss-Legendre Numerical Integration

To fix the most basic concepts on Numerical Integration, we will focus our description on a one dimensional integration using the Gauss-Legendre quadrature, that is, to solve:

I=int_{-1}^{+1} f(\chi) d\chi




References

  1. Carlos A. Felippa, "A compendium of FEM integration formulas for symbolic work", Engineering Computations, Vol. 21 No. 8, 2004, pp. 867-890, (c) Emerald Group Publishing Limited [1]
  2. Numerical Integration
  3. Gaussian Quadrature
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