Hybrid Element-Level and Subdomain-Level DGTD Method for Multiscale Electromagnetic Modeling

In this letter, a hybrid element-level and subdomain-level discontinuous Galerkin time-domain (DGTD) method is proposed for efficient modeling of multiscale electromagnetic problems. Based on the second-order wave equation, the computational domain is partitioned into nonoverlapping element-level and subdomain-level regions: electrically large features with coarse meshes are treated at the element-level, whereas electrically small structures with fine meshes are isolated as subdomains. Interior penalty fluxes are utilized to couple adjacent elements and subdomains, and different Newmark–$\beta$schemes are applied to the two levels, i.e., explicit for element-level regions and implicit for subdomain-level regions. This hybrid strategy alleviates the stability constraints imposed by small elements through subdomain-level implicit integration, while maintaining the flexibility of explicit elements to distributed parallel computing architectures. Three numerical examples demonstrate that the proposed method preserves the accuracy of conventional element-level DGTD while achieving a significant improvement in computational efficiency. The approach shows strong potential for multiscale electromagnetic modeling.