Fast 3D transient electromagnetic forward modeling using BEDS-FDTD algorithm and GPU parallelization

Abstract

The time-step sizes of the conventional finite-difference time-domain (FDTD) method are severely restricted by the Courant-Friedrichs-Lewy stability condition. This may result in excessive iterations, high cost and large runtime, and increasing late-stage cumulative errors in 3D transient electromagnetic (TEM) forward modeling. At present, forward modeling speed is a major obstacle in the development of 3D TEM inversion. To address this issue, a new 3D TEM forward modeling algorithm is presented. In the new algorithm, the backward Euler (BE) scheme is used with a view toward relaxing the stability constraint. However, after using the BE approach, a huge sparse matrix needs to be inverted in each iteration. Directly solving such matrices by Gaussian elimination or an iterative method is still time-consuming and requires large amounts of computer memory. To improve computational efficiency, the direct-splitting (DS) strategy is adopted to transform the large sparse matrices into a series of small diagonally dominant tridiagonal matrices, which are easier to solve. Then, the complex-frequency-shifted perfectly matched layer boundary condition is implemented using the bilinear transform method to reduce the size of the model. To further speed up the calculation process, the codes are then programmed to run on graphics processing unit (GPU) devices. Three models are used for calculations, and the results are compared with other numerical methods to verify the accuracy of our algorithm. After that, to demonstrate the BEDS-FDTD algorithm’s ability to model complex earth structures, a model with a very complex shape is used for the calculation via the conformal mesh technique. In addition, the modeling speed is tested using different GPU devices. We find that an NVIDIA Tesla A100 is able to calculate the 50 × 50 × 50 cell model in only 8 s.