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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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