Parallel Iterative FEM Solver with Initial Guess for Frequency Domain Electromagnetic Analysis

The finite element method is a key player in computational electromagnetics for designing RF (Radio Frequency) components such as waveguides. The frequency-domain analysis is fundamental to identify the characteristics of the components. For the conventional frequency-domain electromagnetic analysis using FEM (Finite Element Method), the system matrix is complex-numbered as well as indefinite. The iterative solvers can be faster than the direct solver when the solver convergence is guaranteed and done in a few steps. However, such complex-numbered and indefinite systems are hard to exploit the merit of the iterative solver. It is also hard to benefit from matrix factorization techniques due to varying system matrix parts according to frequency. Overall, it is hard to adopt conventional iterative solvers even though the system matrix is sparse. A new parallel iterative FEM solver for frequency domain analysis is implemented for inhomogeneous waveguide structures in this paper. In this implementation, the previous solution of the iterative solver of Matlab (Matrix Laboratory) employing the preconditioner is used for the initial guess for the next step's solution process. The overlapped parallel stage using Matlab's Parallel Computing Toolbox is also proposed to alleviate the cold starting, which ruins the convergence of early steps in each parallel stage. Numerical experiments based on waveguide structures have demonstrated the accuracy and efficiency of the proposed scheme.