“…However, they could not fully model the piezoelectric effects in their models. Some recent progresses were contributed by the FE method [101,102], the boundary element method [21,103,104,105,106], finite difference method [107,108,109] and time-reversal of ultrasonic fields [110,111]. FE method has the advantage in modeling the complicated electrical and mechanical boundary conditions of IDT, and eliminates the need for lengthy analytical solution [112].…”