RESUMEN
In the present paper an iterative time-reversal
algorithm that retrofocuses an acoustic wave field to
its controllable part is established. For a fixed temporal support, i.e.,
transducer excitation time, the algorithm generates an optimal retrofocusing in the least-squares sense. Thus the
iterative time-reversal algorithm reduces the temporal support of the
excitation from the requirement of negligible remaining energy to the
requirement of controllability. The time-reversal retrofocusing
is analyzed from a boundary-control perspective where time reversal is used to
steer the acoustic wave field towards a desired state. The wave field is
controlled by transducers located at subsets of the boundary, i.e., the
controllable part of the boundary. The time-reversal cavity and time-reversal
mirror cases are analyzed. In the cavity case, the transducers generate a
locally plane wave in the fundamental mode through a set of ducts. Numerical
examples are given to illustrate the convergence of the iterative time-reversal
algorithm. In the mirror case, a homogeneous half space is considered. For this
case the analytic expression for the retrofocused
wave field is given for finite temporal support. It is shown that the mirror
case does not have the same degree of steering as the cavity case. It is also
shown that the pressure can be perfectly retrofocused
for infinite temporal support. Two examples are given that indicate that the
influence of the evanescent part of the wave field is small.