An Efficient and Scalable Finite Element Method for 3-D Transient Electromagnetic Forward Modeling Using a Robust Iterative Solver

The transient electromagnetic method (TEM) is a widely used technique for metallic mineral, geothermal, and other natural resource exploration. With the continuous development of exploration technologies, the demand for accurate subsurface models and broader application environments presents significant challenges for the forward modeling of TEM, necessitating higher precision forward modeling strategies and faster computation methods. This paper proposes a subspace iterative solution method based on flexible generalized minimal residual(FGMRES) method, utilizing domain decomposition method for parallel acceleration. Specifically, we optimized the grid for long-period transient electromagnetic response calculations, selecting a set of highly adaptable modeling parameters that reduce grid degrees of freedom without compromising accuracy. Furthermore, we replaced the commonly used second-order schemes with a third-order backward Euler difference scheme and conducted forward modeling tests with different time steps, resulting in a more reasonable time step length that improves computational efficiency. The effectiveness of the algorithm was validated by comparing the layered model with semi-analytical solutions and the three-dimensional model with previous results. The comparison results with other open-source codes and numerical experiments on large-scale models indicate that our method achieves high accuracy and efficiency for both simple and complex models, while requiring relatively less memory.