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Many computational methods in electromagnetics, including the method of moments (MoM) and the finite-element method (FEM), require integrating a function over a given domain. In many cases, analytical solutions for the integrals are not available, and some type of numerical integration must be used. One-dimensional numerical-integration techniques are widespread throughout popular mathematical and engineering texts. However, two-dimensional and three-dimensional numerical-integration methods are discussed only in specialized reports and journal articles, and almost never in the electrical engineering literature. This synopsis reviews the available literature on numerical integration over triangular and tetrahedral domains.
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Savage et al. (1996) studied this question.
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