Block Triangular Preconditioners for Discretized Complex Surface Acoustic Wave Piezoelectric Equations

When utilizing the finite element method for simulating SAW devices, a large‐scale complex linear system of equations is generated. The efficiency of device simulation primarily depends on the storage requirement and computational speed for solving the linear system. However, the convergence rate of an iterative solver is confined by the ill‐conditioned nature of the coefficient matrix, which is non‐Hermitian and indefinite. In this paper, we propose several approximations for the Schur complement matrix. These approximations can be generated by the finite element method instead of matrix‐matrix multiplication and matrix inversion operations. Based on them, we develop the lower triangular preconditioners for the coefficient matrix and analyze the eigenvalue distribution of the preconditioned matrices as well. Theoretical analysis reveals that the preconditioned matrix is diagonalizable, with its eigenvalues confined to a small rectangular region, thus ensuring rapid convergence of iterative solvers. The theoretical considerations are supported by numerical results.