Finite Element Methods for the Radiation of Ultrasonic Phased Arrays into an Acoustic Medium

In this paper, the dynamic response of a piezoelectric transducer in contact with an acoustic media is formulated. This serves as a model problem for an ultrasonic phased array in contact with the human body. These arrays may be used for hyperthermia or ablation surgery; the focus of this paper, however, is the eecient numerical formulation for modeling the array problem. A nite element formulation based on Galerkin and Galerkin Least Squares (GLS) methods is presented. The beneets of the GLS method over the standard Galerkin method are demonstrated through numerical experiments of the dynamic response of a multi{element array. The methods under development can be applied to any uid structure interaction problem and point strongly to the advantage of GLS methods for mid{ and high{ frequency applications. The accuracy of approximate versus exact non{reeecting, truncation boundary conditions is discussed.