The Method of Moments in Electromagnetics, 3rd Edition

Chapter 12

Integration

In this book we have considered many integrals, where most were in one or two dimensions. Though some of these can be evaluated analytically, most have no analytic solution and numerical integration (quadrature) must be used instead. When using the Moment Method, the accuracy of the solution depends heavily on the accuracy of the matrix elements, thus a reliable and computationally efficient quadrature scheme is vital. In this chapter we will consider several one-dimensional quadrature schemes, as well as quadratures designed specifically for two-dimensional planar triangles.

12.1 One-Dimensional Integration

For the one-dimensional definite integral given by

$$I={\displaystyle {\int }_a^{b}f\left(x\right)dx,}$$(12.1)

a numerical quadrature generates an approximate ...