Active Control of Exterior Wavefields and Applications

Broadly speaking, this dissertation is centered on developing a mathematical understanding of wave phenomena in acoustics and electromagnetism towards the design of numerically stable methods for their active control. More specifically, it is focused on the study of constructive schemes for the active manipulation of fields satisfying the scalar or vector Helmholtz equation, or Maxwell's equations. This includes the theoretical analysis of these equations supported by numerical simulations in various geometrical settings.

We studied the control of Helmholtz fields in three environments, namely, in free space, in a homogeneous ocean and in a two-layered ocean with constant depth. In the first two, we developed a strategy for a near field control with a simultaneous multi-directional far field control. On the other hand, we worked on the control of electromagnetic waves only in a homogeneous environment, but included several dynamic applications and passive control strategies. In each of these areas, we included a detailed theoretical analysis and a multitude of numerical experiments. The theoretical analysis resulted to existence and stability results for the arising inverse problems. To illustrate and numerically validate these results, we used a method of moments employing a Tikhonov regularization routine coupled with the Morozov discrepancy principle.