Acoustic Black Holes (ABHs) can be realized by embedding cuneate indentations of power-law profile in plates. ABHs have shown promising applications in vibration and noise suppression, in energy harvesting thanks to strong focalization, and in wave manipulation techniques involving lensing and negative refraction and bi-refraction. As regards the latter, it can only be achieved for very high frequencies. Existent works on the topic report rectangular arrays of ABHs, whose behavior are mostly characterized by means of the finite element method (FEM). This results in considerable computational cost. As an alternative, in this paper we suggest the use of two-dimensional Gaussian functions to decompose the vibration field under the framework of the Rayleigh-Ritz method, and combine it with a matrix-replacing strategy to deal with arrays of ABHs of many shapes and sizes. To eliminate the waves reflected from the plate boundaries, a Perfectly Matched Layer (PMLs) is implemented. The method is tested on several distributions of ABHs for lensing applications.