Mathematical simulation of adaptive vector finite element method for the analysis of electromagnetic vibration spectrum field response

Abstract

Mathematical simulation plays a vital role in the analysis of electromagnetic vibration spectrum field response. This article realizes a three-dimensional adaptive vector finite meta-acting algorithm of controlled source electromagnetic vibration spectrum (CSEM) field to address 3D meshing for the simulation of terrain fluctuations and complex electrical anomalies. The adaptive methods utilized in this article is employed for one-time field and secondary field separation in order to calculate electromagnetic vibration spectrum field response. This response can effectively solve the source singularity in finite meta-simulation and improves the numerical accuracy of electromagnetic vibration spectrum field near the field source. The two approaches analysed in this article are CSEM one-dimensional positive algorithm and finite meta-method.The adaptive mesh refinement algorithm based on post-test error estimation is used in this paper to guide the mesh refinement to reduce man-made errors caused by designing a grid. The validity of the proposed algorithm is verified through numerical simulation of one-dimensional and three-dimensional models. The outcomes obtained reveals that the finite solution of one-dimensional model coincides well with the analytical solution. The relative error of electromagnetic vibration spectrum field amplitude is about 1 %, and the overall phase difference of less than 1 degree is observed. It is analysed that the three-dimensional model finite solution also fits well with the finite volume solution and the controlled source electromagnetic vibration spectrum response with three-dimensional tilt plate abnormality is simulated. This experimental analysis shows the ability and effectiveness of the algorithm to simulate the electromagnetic vibration spectrum field of complex geoelectrical structure.