3D transient electromagnetics forward modeling using BEDS-FDTD and its stability verification

Conventional FDTD algorithm requires the time steps to satisfy the Courant-FriedrichLewy (CFL) stability condition, which leads to too many time iteration steps and makes the 3D TEM forward modeling very time-consuming. In this paper, the Backward Euler (BE) difference method is used to approximate the time derivative in Maxwell' s equations. Then the Direct Splitting (DS) strategy is introduced to decouple the electromagnetic field components and to reduce the order and reconstruct the large sparse matrices into a series of triple diagonal matrices of low order and dominated by the main diagonal, making the solution of the equation more efficient. Moreover, in order to reduce the model size, for the above-mentioned improved new equation, this paper adopts the bilinear transform (BT) method to theoretically deduce the complex frequency shifted perfectly matched layer (CFS-PML) absorption boundary. A new algorithm for transient electromagnetic 3D forward modeling is formed: BEDS-FDTD. First, the stability of the BEDS-FDTD algorithm in a lossy medium under non-uniform time steps is proved using the von Neumann method. Then, to verify the accuracy of the algorithm, the calculation results of BEDS-FDTD are compared with the semi -analytical solution of the layered model, and it is verified that the accuracy of the new algorithm meets the requirements of simulation calculation. After that, the performance of the new algorithm is tested. When using the Tesla A100 designed for high-performance computing,BEDS-FDTD only takes lOs to simulate a model with 50/50 X 50 cells, and even if the number of cells is increased to 200 X 200 X 200, the new algorithm takes less than 4 minutes (224 s). Finally, the BEDS-FDTD algorithm is applied to a complex three-dimensional model.