Implicit–Explicit Wave Equation-Based Discontinuous Galerkin Time Domain Method

To address the stability constraints associated with small elements in the traditional explicit wave equation-based discontinuous Galerkin time domain (DGTD) method for multiscale modeling, we introduce an implicit–explicit wave equation-based DGTD approach. Utilizing domain decomposition and interior penalty flux techniques, the model is partitioned into multiple subdomains, each capable of independent meshing. Subdomains are empowered to select either an implicit or explicit time integration scheme, guided by respective mesh sizes. This innovation affords the distinct advantage of isolating small-scale structures within the model for fine meshing, coupled with implicit time integration, thereby significantly mitigating stability constraints posed by small elements. Diverse element types, such as tetrahedrons, bricks, or hexahedrons, can be employed for spatial discretization of each subdomain, coupled with either finite element or spectral element methods. The efficacy of this method is examined through three numerical models, which not only validate its accuracy but also demonstrate its superiority in modeling small structures compared to the explicit DGTD method. The proposed implicit–explicit DGTD method is anticipated to advance the numerical modeling of multiscale problems.