Efficient 3D vector finite element modeling for TEM based on absorbing boundary condition

The homogeneous boundary condition is commonly used in the 3D FEM forward modeling of TEM. In order to satisfy the approximation of this boundary condition, it is necessary to construct a large-scale model, which reduces the solving speed of the forward problem. Aiming at the problem, in this paper, absorbing boundary condition was used to reduce the size of the model and accelerate the solution speed instead of homogeneous boundary condition. Firstly, the differential equation of magnetic vector potential based on Coulomb's gauge was derived from Maxwell' s equations in time domain, combining the first-order absorbing boundary condition, the corresponding weak form equation was deduced and simplified. Then, by using the first-order tetrahedral vector element to carry out element analysis, Newmark method for time discretization, an efficient TEM 3D modeling method was realized. The proposed algorithm was validated by comparing the analytical solution of homogeneous half space, the CR1Dmod solution of H-type geoelectric section, with their corresponding finite element solution. The further comparison between the modeling results of absorbing boundary condition and homogeneous boundary condition showed that the absorbing boundary condition could improve the accuracy of 3D modeling or reduce the size of the model and accelerate the solution speed.