Efficient Modeling of Large-Scale Electromagnetic Well-Logging Problems Using an Improved Nonconformal FEM-DDM

The numerical modeling of the advanced electromagnetic well-logging problems is very challenging because it requires tremendous workload of grid meshing and computation. For example, global meshing and simulation have to be done repeatedly for every logging position, because the model includes complex sensor arrays moving continuously along the borehole. In this paper, an efficient nonconformal finite element domain decomposition method is developed to solve these problems efficiently. First, the well-logging model is divided into two nonconformal subdomains so that the sensing arrays inside the borehole are separated from the beds outside. Since the mesh size between different subdomains can be inconsistent, well-logging modeling can significantly reduce the unknowns and computational cost. Second, a second-order transmission condition is implemented successfully in a quasi-symmetrical form via a novel treatment of Gaussian integration on the nonconformal interface. Finally, a hierarchical hexahedral basis function is introduced to further reduce the unknowns and extend the applicability of the method to multiscale problems. Numerical examples show that this method greatly reduces the memory cost and speeds up the computation compared with the traditional finite element method, especially when the response needs to be simulated repeatedly while the logging tools keep moving along the borehole.