Validation of a hybrid boundary and finite element method for the simulation of large membrane-based piezoelectric transducer arrays in immersion

Membrane-based piezoelectric ultrasonic transducers, especially piezoelectric micromachined ultrasonic transducers (PMUTs), are a promising technology for the realization of large transducer arrays for use in integrated imaging, sensing, and actuation where a broadband response is desirable. In this work, a hybrid boundary and finite element method is proposed for the transmit simulation of large PMUT arrays in immersion. Finite element software (COMSOL) readily handles the simulation of single membrane structures, from which static deformation (stiffness) and harmonic displacement data is extracted. A boundary element formulation based on these inputs handles the membrane-to-membrane acoustic cross-coupling through the calculation of a mutual impedance matrix. For arrays consisting of hundreds of membranes or more, the problem of quadratic storage and cubic time complexity for boundary element is avoided by employing a multi-level fast multipole algorithm (Shieh et al., IEEE Trans. UFFC, 63, 1967-1979). We validate this hybrid method for common membrane geometries, including square and circular membranes with varying degrees of electrode coverage.