Speaker: XueMing Shi
A new approach using three-dimensional(3-D) vector/edge finite element (VFE) method combined with divergence corrections based on the magnetic field (H), denoted as VFEH++, has been developed for computing the magnetotelluric (MT) responses of 3-D conductivity structures. The VFEH++ algorithm comprises three steps: First, a conventional vector finite element method based on the use of the magnetic filed, denoted as VFEH, applying the Galerkin method of weighted residuals is derived to solve the system of equations for the magnetic fields governed by the second order differential Maxwell’s equation. The resulting large banded (33 nonzero elements), sparse, symmetrical, non-Hermitian complex system of equations Ax=b can be efficiently solved by using the quasi-minimal residual method (QMR) with a no-fill-in incomplete LU decomposition (ILU) pre-conditioner. Second a finite difference method is used to solve the system of equations for the nodal/scalar potentials governed by the magnetic flux conservative equation. Finally the solutions of the nodal potentials are used to correct the magnetic fields obtained from the vector finite element method, which guarantees the solutions obey the conservation laws and makes the solutions physical. The divergence correction procedures being the complementary of Galerkin formulation are adaptively employed during the iteration process of the vector finite element method, which greatly increase the speed of convergence of solutions of VFEH and improve accuracy especially at low frequencies and large conductivity contrasts. The synthetic results of 3-D models in the COMMEMI project show that our codes have comparable accuracy to those of integral equation method whereas the calculation speed is a little slower than that of staggered-grid finite difference method but faster than those of T- finite element method. The results imply that the vector finite element combined with divergence corrections based on the magnetic fields be another powerful tool for numerical modeling of 3-D inhomogeneous conductivity structures and can be applied to 3-D MT inverse problems of field data.