We have developed a novel methodology, called the inverse Helmholtz solver (iHS) methodology, to computationally recover the spatial distribution of the unknown broadband acoustic impedance at an open boundary of an arbitrarily shaped computational domain (such as one representing an duct or a cavity) in response to acoustic wave propagation in the domain. Once known, such an impedance can then be modeled as time-domain impedance boundary condition representing the aforementioned computational domain in larger simulations, leading to significant reduction in overall computational costs. The iHS is currently being applied to problems in hypersonics, thermoacoustics, and noise control.