Large-scale computation and optimization for ultrasound acoustic transducers.

Abstract

This thesis is concerned with efficient numerical techniques for the modeling and design of ultrasonic transducer arrays for therapy. The finite element method provides a rigorous modeling technique for ultrasound transducers. However, the very intensive computation required by ultrasonic frequencies presents a great challenge to numerics. The effectiveness of iterative solution strategies for the large sparse complex linear systems arising from the high frequency response of coupled piezoelectric-elastic-fluid interaction problems is extensively investigated. To remedy the ill-conditioning caused by the fine mesh and vastly different spatial scales of the structures and fluid medium, two preconditioning techniques, SSOR preconditioner and Incomplete LU (ILU) factorization preconditioner, are examined and evaluated through a series numerical experiments. The numerical results show that SSOR preconditioner is the most cost efficient strategy though the ILU factorization is generally more effective in reducing the iteration counts. Also, the simple ILU(0) preconditioner is shown to be more efficient and reliable than recently developed ILUT(<italic>p</italic>,tau) preconditioner. In therapy transducer design, the acoustic power at the operating frequency is a critical figure of merit. A systematic design methodology for enhancing the acoustic power radiated from a fluid-loaded ultrasonic array element at a fixed frequency is developed. A gradient-based optimization algorithm is integrated within the finite element framework to guide the determination of the two design variables, the piezoelectric element thickness and the matching layer thickness, to maximize the acoustic power output. A novel method for avoiding the explicit remeshing in the optimization iterations is presented. Optimized designs are determined numerically and confirmed by the experiments. Cross-talk in therapy arrays decreases the power efficiency and array steering capabilities. To reduce the cross-talk, a density-based design approach is utilized to optimize the topology of kerf fillings in linear phased arrays. Two design schemes, element-by-element design and layer-by-layer design, are developed. The optimized topology of kerf fillings in each design scheme is presented. The radiation of the array is evaluated in both the pressure level and array directivity. Significant improvement of the acoustic field with optimized kerf fillings is demonstrated.