Theoretical analysis of geo-electromagnetic modeling on Coulomb gauged potentials by adaptive finite element method
Coulomb 规范下地电磁场的自适应有限元模拟的理论分析

There are several serious problems in geo-electromagnetic modeling by using direct solving method at present.The first problem is that it often gives a psedo-solution that does not adequately describe the existing geo-electromagnetic field.The second problem is that the discontinuity of the electromagnetic field at the conductivity interface limits the application of the node-based finite element method.In this paper we propose a new,fast and accurate method of forward modeling using the Coulomb gauged magnetic vector potential and electric scalar potential concept and the newly developed adaptive finite element method.Based on the typical electromagnetic boundary value problem,we introduce a formulation system for magnetic vector potential and electric scalar potential under Coulomb gauged potential,and have analyzed the continuity properties of the vector and scalar potentials.Adopted the Galerkin weighted residual technique,we have formulated the weak integral form of magnetic vector and scalar potentials,and then developed the finite-element linear equations based on the unstructured Hierarchal tetrahedron finite element concept.By using the super-convergence recovery techniques,we are able to estimate the element and global errors on current mesh.We have also done some analyses on this adaptive finite-element method and found that we could achieve a more accurate numerical solution with an optimal computing cost.This new technique presented in this paper can be used as a theoretical guide in a wide range of geophysical electromagnetic explorations.