Sparse Wavelet Element Method for Piezoelectric Equations in an Unbounded Domain

Abstract

This paper is concerned with devising an efficient numerical method for the piezoelectric equations in an unbounded domain, which plays a fundamental role in design and analysis of microacoustic devices with piezoelectric substrate. We make use of the perfectly matched layer method to transform the underlying problem as a surrogate in a bounded domain, which is further solved by a sparse wavelet element method. The latter method can be viewed as a combination of a wavelet element method and a sparse grid method. The numerical results are performed to show the proposed method is very efficient and outperforms the usual finite element method. It can be naturally extended to two/three dimensional problems in an unbounded domain whose boundary consists of line segments or rectangles parallel to coordinate lines or planes.