An efficient numerical method for surface acoustic wave equations over unbounded domains
Jianguo Huang, Likun Qiu
TL;DR
This work addresses numerical simulation of surface acoustic wave equations on semi-unbounded domains by combining perfectly matched layer truncation with a FETI domain decomposition approach that exploits periodic structure. A dimensionless scaling is introduced to balance system blocks, and an efficient Sherman–Morrison–Woodbury-based solver for the ill-conditioned Lagrange multiplier system (augmented by a Double-Newton method for a quadratic matrix equation) enables large-scale SAW simulations with millions of DOFs on modest hardware. Numerical results show that the FETI method outperforms conventional quadratic FEM for large N, remains robust under varied electrode voltages, and can solve large-scale problems on a laptop, highlighting significant gains in memory and time efficiency for SAW device design. The technique provides a practical, scalable pipeline for accurate SAW predictions in complex periodic geometries and supports extensions to periodic loading conditions.
Abstract
Surface acoustic wave (SAW) devices are widely used in modern communication equipment and SAW equations describe the critical physical processes of acoustic-electric conversion in SAW devices. It is very challenging to numerically solve such equations, since they are typically three dimensional problems defined on unbounded domains. In this paper, we first use the perfectly matched layer method to truncate the unbounded domain and then propose a finite element tearing and interconnecting algorithm for the truncated equations based on the periodic structure of the truncated domain. We also design an effective solver for the ill-conditioned linear system of the Lagrange multipliers arising from discretization. Several numerical results are performed to demonstrate the efficiency of the proposed algorithm.