Parallel FEM simulation of transient piezo-acoustic waves

Abstract

The goal of the dissertation is to model the behavior of an ultrasonic sensor. The mathematical model of the piezoelectric oil level sensor includes the modeling of elasto-electric waves in the piezoelectric element (actuator/sensor), the modeling of acoustic waves in the fluid and the interaction between these two models. Piezoelectricity is modeled by equations of electrostatics and elasticity. The propagation of acoustic waves is modeled by the wave equation. These two tasks can be weakly or strongly coupled. In the case of weak coupling, we solve three independent problems: the piezoelectric actuator problem, the acoustics problem, and the piezoelectric sensor problem. Using the finite element semi-discretization method, we obtain a system of ordinary differential equations that can be subsequently discretized over time using a time-stepping scheme, such as the Newmark method. In the time-stepping implicit Newmark method, we solve a system where the mass matrix dominates. This system can be solved using the conjugate gradient method with diagonal preconditioning. Due to the complexity of 3D discretization, the acoustic problem is solved in parallel. Parallelism was implemented using the domain decomposition method. The main contributions of this doctoral thesis are as follows: - A summary of the theory for the mathematical and numerical modeling of the piezoelectricity, acoustics and multiphysics, which couples both models. - A design of a parallel code for high-frequency piezo-acoustic simulations. - A testing the proposed parallel code on the real geometry of an ultrasonic sensor.