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Book Chapter

Isoparametric Elements and Gaussian Quadrature

Published:
January 01, 2001

Abstract

The BEM involves a large amount of integration because it divides boundaries into many elements, each of which is integrated over. During the computation of the integrals, it is very troublesome if the variables of integration are denoted by global coordinates (i.e., all the elements are based on coordinates of identical origin). Rather, it benefits the computations to use local coordinates within the elements to denote these variables.

The isoparametric element (Rao, 1982) is a powerful tool that uses local coordinates to perform the integration over the element. The integrals expressed by isoparametric elements usually cannot be calculated through analytical methods because they are rather complicated. Thus, numerical methods must be used. This chapter introduces the isoparametric element, followed by the Gaussian quadrature method of numerical integration (Rao, 1982).

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Society of Exploration Geophysicists Geophysical Monograph Series

The Boundary Element Method in Geophysics

Shi-zhe Xu
Shi-zhe Xu
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Society of Exploration Geophysicists
Volume
9
ISBN electronic:
9781560802112
Publication date:
January 01, 2001

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