An Arbitrary High Order SETD Method With Local Time-Stepping: Exponential Convergence and Computational Efficiency for Multiscale Electromagnetic Analysis

An arbitrary high order spectral-element time-domain method with local time-stepping (LTS-ADER-SETD) is proposed for transient electromagnetics simulation. An expression for the second-order wave-equation-based LTS-ADER-SETD method is comprehensively derived by replacing the time derivatives with space derivatives. Innovatively, this technology achieves subdomain coupling without temporal synchronization constraints, enabled by a unified treatment of local time-stepping (LTS) scheme. The proposed method achieves exponential error reduction with increasing spatiotemporal discretization order while significantly enhancing computational efficiency in multiscale electromagnetic analysis. Numerical convergence results demonstrate the high accuracy in both the space domain and time domain, even with an extremely large time step ratio. Further validation is provided, indicating the proposed method is computationally efficient for electromagnetic problems with strongly varying element sizes.