Iterative Solution of Some Direct and Inverse Problems in Electromagnetics and Acoustics

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Abstract
International audienceFive radiation and scattering problems in electromagnetics and acoustics are successively investigated to illustrate the interest and drawbacks of iterative solutions with respect to conventional direct ones, if they exist. All these solutions are based upon integral formulations of the fields. The iterative ones are in general developed from two conjugate-gradient algorithms whose main properties are recalled herein from the viewpoint of linear operator equations in Hilbert space. The first two problems concern radiation by rotational thick antennas and by large wire-structures. Methods of moments are applied as usual and the linear systems deduced from are directly or iteratively solved; conditioning is confirmed to be the main reason of either choice. The next two concern scattering by inhomogeneous cylindrical targets: fluid ones illuminated by a compressional plane-wave in acoustics, and lossy dielectric ones illuminated by a wave whose field is parallel with the target cross-section In electromagnetics. Both problems are suitably handled using conjugate-gradient algorithms that are directly derived from the fields integral formulations. However, acoustic fields inside and outside large but weakly-refractive targets are, shown to be faster calculated from Neumann's series provided that the latter converge. The fifth problem concerns the experimental probing of dielectric slabs from the transient fields they reflect. An optimal profile is constructed by means of a conjugate-gradient algorithm that minimizes a particular cost function. At each step, the gradient of this function is calculated from the solutions of one direct and of one adjoint problem obtained by marching-on-in-time. Such a procedure appears to perform fairly well, especially in view of the amount of errors on the data

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