A Theory of Inverse Operators for Multiple Excitations
Final technical rept. Sep 88-Sep 89,
DAYTON UNIV OH SCHOOL OF ENGINEERING
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In this report we consider the solution to integral equations that arise in the theory of electromagnetic scattering. We develop an interactive solution valid not for just one excitation but multiple excitations. We first consider a matrix equation obtained as a projection of the integral equation to finite dimensional space. After each iteration an orthogonal vector is determined and from it a corresponding component of the inverse operator. Thus, after each iteration a best estimate to the inverse operator is determined. This may be used to obtain the estimated solution to an arbitrary number of excitations. It is shown that the outer product of the vectors needs to be computed to compute the inverse operator. Since this is an expensive operation, an alternative approach is determined whereby solution to multiple excitations is determined without computing the outer products. This theory, developed in N- dimensional space, is then generalized to infinite dimensional space. This leads to a definition and a computational procedure for inverse integral operator. The theory is illustrated by computing the induced currents on a square cylinder for several excitations.
- Theoretical Mathematics
- Radiofrequency Wave Propagation