EMFEM: A parallel 3D modeling code for frequency-domain electromagnetic method using goal-oriented adaptive finite element method

ABS TRACT We have developed an open-source parallel 3D forward modeling code called EMFEM for the frequency-domain electromagnetic method (FDEM). This code is based on the adaptive finite element method and uses the total-field approach to solve the time-harmonic Maxwell equations. The use of tetrahedral meshes enables modeling of problems with complex geometry and topography. We utilize an iterative solver and an optimal block-diagonal preconditioner and auxiliary Maxwell solver to accelerate the convergence rate. We also use goal-oriented error estimation to adaptively refine the mesh and improve the accuracy of the solution. In addition, we develop a parallel algorithm based on the mesh partitioning approach. The effectiveness of the adaptive mesh refinement is demonstrated through a 1D layered model for marine controlled-source electromagnetic (CSEM) problems. We further present two 3D models for CSEM and magnetotelluric (MT) problems to study the scalability of the parallel algorithm, and the accuracy of the solutions is cross-validated with other open-source codes. The code is implemented in C++ and follows the modular design principle, making it easy to extend and maintain. The code is capable of modeling large-scale 3D problems and utilizing high-performance computing platforms. Furthermore, as the code is freely available, it can serve as a cross-validation tool for other 3D modeling codes and can also be utilized to implement 3D inversion routines.