Domain decomposition techniques for the finite element simulation of ultrasonic transducers

We consider efficient numerical methods for the finite element simulation of the interaction of an ultrasonic transducer and inviscid fluid. We apply a domain decomposition method to axisymmetric and time-harmonic problems, while partitioned analysis schemes are applied to three-dimensional time-dependent problems. We introduce also an efficient iterative method for three-dimensional resonance problems. One of the advantages of these approaches is that they separate the structural and fluid equations such that different solution methods can be used in the elastic and acoustic domains. In this way, we are able to utilize efficient techniques designed for special type of equations. Such techniques include fast direct solution methods and algebraic multigrid methods.