A GLOBAL WEAK FORM ELEMENT FREE METHOD FOR DIRECT CURRENT RESISTIVITY FORWARD SIMULATION

Abstract

We present a global weak form element free method (EFM) for simulation of direct current resistivity. EFM is a new numerical simulation method developed on the basis of the finite element method (FEM). The key point of this method is the absence of elements and the nodes free from the elemental restraint, which makes it very flexible and simple in pre-processing. It utilizes the nodes of local support domain to construct shape functions to achieve the accurate approximations of the local domain. Approximations of EFM are of high order and boundary conditions are enforced simply, because the radial point interpolation method (RPIM) is used to construct shape function. Therefore, EFM is more suitable to simulate complex models than FEM. First, the boundary value problem and the corresponding variational problem of direct current resistivity forward simulation are derived starting with the partial differential equation of current field. Second, the construction of RPIM shape function is introduced in details. Third, equations of the global weak form EFM for direct current resistivity are derived in details based on RPIM shape function. Then, a Fortran program is written according to the equations. By this program, a homogeneous half-space model was used to verify our element free approach. At the same time, we compared the solutions of EFM and FEM in details which shows that the solutions of EFM are more accurate. Furthermore, the solutions indicate the correctness and effectiveness of the EFM for direct current resistivity forward simulation. Finally, we improve the simulation accuracy successfully by refining nodes arbitrarily, and the solutions of EFM forward simulation for complex geoelectric models show that EFM has a high degree of flexibility.