An Adaptive Preconditioning Strategy Based on Real-time Measurements for Discrete System of Time-harmonic Maxwell Equations

We address the issue that a single preconditioner cannot achieve optimal performance for all test problems in solving the discrete system for time-harmonic Maxwell equations in system-in-package (SiP) applications, and it is always difficult to determine the optimal algorithm for a given test case. We propose an adaptive strategy of preconditioning algorithms based on real-time measurements. Firstly, we propose a combined algorithm (COM) which orderly utilizes the Additive Schwarz method (ASM) and Auxiliary Maxwell method (AMS), expanding the set of feasible algorithms for current systems. Then for the iterative process of solving a test case, the optimal algorithm is selected based on real-time measuring of each algorithm in the feasible algorithm space. Numerical experiments including six typical test cases from three different application problems show that this adaptive strategy can achieve performance mostly close to the optimal algorithm in the existing algorithm space. Compared to any other single algorithm, it has the highest overall computational efficiency, which implies its significant practicality and application potential.