A hybrid spectral element-infinite element approach for 3D controlled-source electromagnetic modeling

In this study, we developed a novel hybrid approach for 3D controlled-source electromagnetic (CSEM) forward modeling. The hybrid approach combines vector spectral element method (SEM) with scalar infinite element method (IFEM) by using infinite element instead of traditional truncated boundary. Based on Maxwell's equations, the curl-curl control equation satisfied by secondary electric field is derived. The boundary value problem in differential form is transformed into integral weak form by using Galerkin weighted residual method. Then the global problem is discretized by element subdivision and high-order orthogonal basis function interpolation. The computational domain is discretized using hexahedral spectral elements and a single layer of infinite elements is added outside the domain. The SEM with high-order Gauss-Lobatto-Legendre (GLL) vector basis functions is used to represent the interior electric field, and the IFEM with high-order Gauss-Lobatto-Legendre (GLL) scalar basis functions is uesd as a boundary condition. Finally, the global numerical solution is obtained by solving largescale linear equations. The layered model verifies the accuracy and correctness of the approach, and the 3D model verifies the efficiency and numerical stability of the approach. Numerical experiments show that the hybrid SEM-IFEM approach developed in this study can reach similar accuracy to the conventional spectral element method, but the computational domain required can be much smaller, and the corresponding CPU time and memory requirement are greatly reduced, namely, the high precision three-dimensional electromagnetic response can be obtained with less computational resource consumption.