Finite Element Tearing and Interconnecting Method for Electro-Acoustic Modeling of Acoustic-Wave Resonators

High-performance filters based on acoustic resonators have been used extensively in modern communication systems because of their capabilities to meet stringent specifications for steep skirts, wide bandwidths, low insertion losses, high out-of-band suppression, and small sizes. For an efficient design of such filters, it is critical to have an accurate and fast numerical modeling that could capture important characteristics such as wave guiding, spurious transversal modes, and acoustic radiation. Unfortunately, such a numerical modeling is very challenging because the electro-acoustic phenomenon involved represents a large and multi-scale computational problem. Although the finite element method (FEM) is well suited to modeling such a multiscale electro-acoustic problem, the simulation can be very time-consuming because a large number of degrees-of-freedom (DOFs) is required to obtain a high accuracy for practical design. An effective technique to tackle this problem is to employ an effective domain decomposition technique such as the finite element tearing and interconnecting (FETI) method. With the FETI method, we first decompose the computational domain of an acoustic-wave resonator to be simulated into many nonoverlapping subdomains that can be handled with an efficient direct sparse solver. We then enforce transmission conditions (TCs) at subdomain interfaces to couple adjacent subdomains to formulate a global interface system. We finally solve this global interface problem using an iterative method to obtain the solution at the subdomain interfaces, from which we can compute the solution in each subdomain. Although FETI has been extensively studied for a variety of electromagnetic and elastic problems, many technical difficulties have been encountered in the electro-acoustic modeling of acoustic-wave resonators. For example, due to the electromechanical coupling and anisotropic properties of piezoelectric materials, the resulting global interface system in FETI is found to be ill-conditioned, and the convergence of iterative solutions even with a robust Krylov subspace method is slow. To alleviate this issue, we developed two approaches based on the construction of a higher-order TC and design of an effective preconditioner to accelerate the rate of convergence. In this presentation, we will discuss some of the technical issues we have encountered and the solutions we have explored and demonstrate the improved performance of the resulting FETI modeling.