A finite-element based implementation of time-reversal and phase-conjugation acoustic source localization techniques in COMSOL multiphysics

Abstract

In this work, we develop a general working procedure for a finite-element (FE) based implementation of time-reversal (TR) and phase-conjugation (PC) acoustic source localization techniques in COMSOL multiphysics commercial package using its in-built acoustics modules. To this end, a detailed step-by-step algorithm of the forward propagation is presented which includes creation of the computational domain and absorbing boundaries, defining acoustic source(s), meshing, solving, i.e., carrying out a time- or frequency-domain simulation followed by extracting data at virtual microphone array (nodes). The same procedure is used for implementing the TR simulations and frequency-domain PC except that source(s) inside the domain are now deactivated, and time-reversed or phase-conjugated data is enforced at the array nodes, followed by computation of the source map. The test-case of an idealized monopole in a 2D free-space is first considered whereby it is shown that both FE-based TR and PC methods deliver identical results which are in an excellent agreement with a finite-difference time-domain (FDTD) solver results, thereby validating the procedure. Next, the problem of localizing an idealized source in the presence of multiple scatterers and reflections which resemble an urban environment is considered. The COMSOL algorithms are shown to produce satisfactory results which demonstrate the efficiency of commercial FE solvers in handling complex geometries which otherwise tend to become tedious using the traditional FDTD solvers.