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Combined Field Integral Equation

One of the most common integral equation deficiencies is failure to have a unique solution at certain discrete frequencies. At these frequencies, there exist nontrivial solutions of the source-free (homogeneous) form of the integral equation. It has been shown theoretically that neither the H-field equation nor the E-field equation has unique solutions for the current on a conducting body at frequencies corresponding to resonant frequencies of the region enclosed by the conducting surface, but the combined-field equation does have a unique solution [53],[52].

In this section, the scatterer is an arbitrarily shaped perfectly conducting body with a closed surface . denotes the electric surface current induced on by the incident field (). This current satisfies () and (). The question is whether () alone is sufficient to determine , whether () alone is sufficient, or whether both are necessary. The answer is given by Mautz [53]. In [53], Mautz has proven that the solution to () is not unique for values of k (wave number) at which the equations

which are valid when there is no incident field, admit a nontrivial solution. This solution is called a magnetic cavity mode. Applying the duality theory, one concludes that the solution to () is not unique for the same value of k.

The combined field formulation, which is a linear combination of () and (), is given by

The solution of () is unique and satisfies both () and () whenever is a positive real number (see [53]).

Since () is the linear combination of () and () with a relative weight , the method of moments formulation obtained from () is the same linear combination of () and (). Hence,

where all matrices and column vectors have the same meaning as in Section 2.2 and 2.3, and is a constant. From experience, should be between 0.2 and 1.0.



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Sat Dec 3 17:51:03 EST 1994