Integral Equation Method
Each field problem done by the integral equation method has the following steps.
Using Green’s theorem or the Helmholtz theorem (see Section 2.5), develop a suitable expression for the field to be computed as an integral over certain sources. These sources can be real or equivalent currents or charges, or fields or scalar potentials.
Express these sources, in turn, in terms of the field to be computed. This leads to an integral equation either in terms of the field or in terms of the sources.
Develop a partition of the volume or surface over which the integral is taken. That is, divide this volume or surface suitably into a number of subdivisions.
Using this partition and the integral equation, derive a system of equations to be solved for the sources or the field over the volume or surface of integration. If the medium is linear, this is a linear system of equations. If the medium is nonlinear, this is a nonlinear system of equations. In any event, compute the sources over the volume or surface of integration.
Using these sources or fields, the partition, and the integral expression developed in step 1, compute the field at any desired point in space.
KeywordsIntegral Equation Collocation Method Integral Equation Method Field Point Field Problem
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