A parallel and improved goal-oriented adaptive finite-element approach for 3-D direct current resistivity anisotropic forward

Abstract This study presents a parallel and accurate adaptive finite element algorithm for 3-D anisotropic direct current (DC) resistivity forward modeling. It enables the simulation of 3-D complex environments, including undulating topography, intricate subsurface structures, and arbitrary anisotropic distributions. The study improves the goal-oriented posterior error estimation strategy by introducing a volume factor into the dual problem. This improvement not only enhances the numerical accuracy of measurement points located far from the source but also improves the error distribution within the measurement region. Additionally, to solve the linear equation system, we employ an algebraic multigrid preconditioned conjugate gradient solver. Furthermore, to accelerate the solving of large-scale 3-D problems, the domain decomposition technique is incorporated into the solver. The newly developed algorithm’s high accuracy is validated through a two-layer anisotropic model. Compared with published results, the testing results on a 3-D synthetic model with undulating topography demonstrate the algorithm’s efficiency in terms of solving time and memory usage.