An Adaptive Explicit High-Order Space-Time FDTD Method in the Fictitious Wave Domain for marine controlled-source EM

Abstract The Fictitious Wave Domain (FWD) method establishes an efficient computational framework for independently characterizing the lossless propagation and energy attenuation of low-frequency marine controlled-source electromagnetic (CSEM) fields, while also providing a novel perspective for interpreting diffusive EM wave propagation. It simplifies traditional diffusive-domain modeling by avoiding complex grid discretization. However, the traditional explicit Finite-Difference Time-Domain (FDTD) method used to compute fictitious electromagnetic wave time series in the FWD is limited by the Courant-Friedrichs-Lewy (CFL) stability condition, which restricts the maximum allowable time step. To overcome this, a high-order spatiotemporal FDTD (HAIT-FDTD) scheme is proposed, incorporating an optimized stability framework based on Taylor polynomial expansions of electromagnetic fields. This method allows time steps up to 6.5 times larger than conventional FDTD while maintaining numerical stability. For further optimization in complex marine environments with heterogeneous conductivity, an adaptive HAIT-FDTD (AHAIT-FDTD) algorithm is proposed. It dynamically selects the optimal time step according to the conductivity range of the model and assigns tailored Taylor polynomial orders to different media, thereby effectively resolving the conflict between large grid sizes permissible in conductive regions and the small time steps required in resistive areas. Moreover, as a versatile computational framework, AHAIT-FDTD seamlessly integrates with existing mesh generation strategies and spatial discretization algorithms, without requiring any modifications to the underlying parallelization scheme, meshing, or difference operators. In models characterized by a sparse distribution of high-resistivity bodies, this framework achieves up to a twofold increase in computational efficiency.