Adaptive Finite Element Method for Magnetotelluric Forward Modeling with Gradient Recovery

Abstract

In the frequency domain electromagnetic method such as magnetotelluric method, finite element method is the main numerical simulation method because it can better simulate the complex physical distribution and complex boundary shape of the geoelectric model. In the finite element method, the quality and quantity of mesh generation will directly affect the accuracy and efficiency of the solution. Theoretically, the accuracy of the finite element solution will gradually approach the real solution with the mesh encryption, but the increase of the mesh number will directly affect the speed of the finite element solution and computer memory. In addition, in the frequency domain electromagnetic method, the decay speed of electromagnetic waves is different at different frequencies, and the use of the same grid at different frequencies will also cause errors. The adaptive finite element method based on a posteriori error estimation can overcome the above shortcomings and improve the calculation accuracy and efficiency of forward modeling. In this paper, starting from the principle of superconvergent patch recovery algorithm, the superconvergent patch recovery algorithm is deduced in detail, the processing of the boundary element in the superconvergent patch recovery algorithm is used as the indicator factor of the adaptive finite element posterior error estimation, and a mesh encryption strategy is proposed, the encryption strategy is simple and reliable. Finally, using the characteristics of the superconvergent patch recovery algorithm, it is used in the calculation of auxiliary field of magnetotelluric method. Through the forward modeling of three geoelectric models. It is verified that the adaptive finite element method based on the a posteriori error of the superconvergent patch recovery algorithm combined with the auxiliary field calculation method of the superconvergent patch recovery algorithm can effectively improve the accuracy and feasibility of the finite element forward modeling of the superconvergent patch recovery algorithm.