Iterative solutions of the array equations for rapid design and analysis of large projector arrays. 
A fast computational method for modeling and simulation of large projector arrays is presented.  The method is based on the array equations that account for the acoustic interaction among the projector elements as well as the individual characteristics of each projector.  Unlike the existing solution method in which the acoustic interaction must be known a priori in the form of interaction impedance matrix Z, the present method seeks the solution of modified array equations through iterations without explicitly evaluating the Z matrix.  This significantly speeds up the analysis of complex arrays with surrounding structures, where the evaluation of the Z matrix may require a large number of time-consuming finite element computations.  The method is compared with the traditional Z-matrix method for the case of a cylindrical array of 72 × 8 Tonpilz transducers.  For the same level of accuracy, the iterative method is shown to be up to 2 orders-of-magnitude faster than the Z-matrix method.  The method can be used for rapid design and analysis of active sonar arrays and medical ultrasonic transducers, often made of hundreds and even thousands of elements.