A Nonconformal FEM-DDM With Tree–Cotree Splitting and Improved Transmission Condition for Modeling Subsurface Detection Problems

Numerical modeling of electromagnetic subsurface detection is always challenging because the computational domain is large and the frequency is very low. This paper describes a nonconformal finite-element-method-based domain decomposition method (NC-FEM-DDM) for an efficient and accurate modeling of subsurface detecting problems in any frequency band. It first compares several transmission conditions (TCs) employed in DDM and identifies the most appropriate TC for subsurface applications. A tree-cotree splitting (TCS) strategy is then applied to hexahedral-based hierarchical basis functions to eliminate the low-frequency breakdown of NC-FEM-DDM at very low frequencies. Numerical results of a few testing problems show excellent convergence and accuracy obtained with an improved second-order TC in conjunction with the TCS at any frequencies even close to dc. Numerical results of a real-life application further demonstrate the efficiency and capability of this method for subsurface detection applications.