An accelerated alternating iterative algorithm for data completion problems connected with Helmholtz equation - Berdawood, Karzan Ahmad; Nachaoui, Abdeljalil; Nachaoui, Mourad (Statistics, Optimization & Information Computing, 2023)
This paper deals with an inverse problem governed by the Helmholtz equation. It consists in recovering lacking data on a part of the boundary based on the Cauchy data on the other part. We propose an optimal choice of the relaxation parameter calculated dynamically at each iteration. This choice of relaxation parameter ensures convergence without prior determination of the interval of the relaxation factor required in our previous work. The numerous numerical example shows that the number of iterations is drastically reduced and thus, our new relaxed algorithm guarantees the convergence for all wavenumber k and gives an automatic acceleration without any intervention of the user.