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.

Accelerating Electromagnetic Field Simulations Based on Memory-Optimized CPML-FDTD with OpenACC

“…The GPUs give exactly the same solution. Finally, we can establish that OpenACC is an excellent tool to accelerate wave propagation simulation codes based on FDTD [36,37].…”

“…In this case, is used a numerical method based on finite differences scheme based on a staggered grid. The characteristics of this method make the algorithm highly parallelizable with OpenACC as previously studied by [36,37]. The execution time used for reading the initial conditions, memory allocation, or variables initialization variables does not cause overhead since they are only executed once during the entire program.…”

Borehole transient electromagnetic response calculation and experimental study in coal mine tunnels

“…In equation (22), J s m = iωµ 0 M s is the magnetic current density of the source. In equation (23), J s e = iωp s is the current density.…”

“…At present, many studies have been conducted on the use of TEM for ground transmission, downhole, or borehole reception, but little research has been conducted on the use of TEM for borehole transmission and borehole reception. Research has mainly focused on numerical simulations of small multi-turn coils based on the whole space TEM theory [20][21][22] and discussion of the transient electromagnetic response characteristics of small coils, as well as inversion interpretation and analysis methods [23,24].…”

A Fast and Efficient Method for 3-D Transient Electromagnetic Modeling Considering IP Effect

“…As a crucial tool, the finite-difference time-domain (FDTD) method have been widely developed to solve electromagnetic scattering issues, such as alternating-direction implicit FDTD [36]- [38], Crank-Nicolson FDTD [39]- [40], Crank-Nicolson direct-splitting FDTD [41], backward Euler direct-splitting FDTD (BEDS-FDTD) [42] and et al In this paper, BEDS-FDTD method is used to discretize the partial differential equations (PDEs) obtained after the SOE approximation of Maxwell's equation with a CCM dispersion. Then the SOE-BEDS and Caputo-BEDS method are implemented to numerically simulate the fractional derivative.…”