A Galerkin procedure for optimization in radiation problems
Abstract
An optimization problem arising in antenna theory is studied: that of finding square integrable currents (boundary data) of norm 1 on an arbitrary surface which optimize the power radiated in a preassigned angular sector. Specifically, a constructive method is developed using complete families of solutions of the exterior Helmholtz equation, which produces approximately optimal boundary data in terms of solutions of a generalized eigenvalue problem Bx = lambda(Gx). Convergence of an appropriate subsequence of approximate currents to the optimal current is established.
- Publication:
-
SIAM Journal of Applied Mathematics
- Pub Date:
- December 1984
- Bibcode:
- 1984SJAM...44.1246A
- Keywords:
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- Antenna Radiation Patterns;
- Boundary Value Problems;
- Eigenvalues;
- Galerkin Method;
- Helmholtz Equations;
- Optimization;
- Antenna Design;
- Computer Aided Design;
- Green'S Functions;
- Communications and Radar