Hybrid meshless-FEM method for 3-D magnetotelluric modelling using non-conformal discretization

We propose a novel method for 3-D magnetotelluric (MT) forward modelling based on hybrid meshless and finite-element (FE) methods. This method divides the earth model into a central computational region and an expansion one. For the central region, we adopt scatter points to discretize the model, which can flexibly and accurately characterize the complex structures without generating unstructured mesh. The meshless method using compact support radial basis function is applied to simulate this area's electromagnetic field. While in the expansion region, to avoid the heavy time consumption and numerical error of the meshless method caused by non-uniform nodes, we adopt a node-based finite-element method with regular hexahedral mesh for stability. Finally, the two discretized systems are coupled at the interface nodes according to the continuity conditions of vector and scalar potentials. Considering that the normal electric field is discontinuous at the interface with resistivity discontinuity, while the shape functions for the meshless method are continuous, we further adopt the visibility criterion in constructing the support region. Numerical experiments on typical models show that using the same degree of freedom, the hybrid meshless-finite element method (FEM) algorithm has higher accuracy than the node-based FEM and meshless method. In addition, the electric field discontinuity at interfaces is well preserved, which proves the effectiveness of the visibility criterion method. In general, compared to the conventional grid-based method, this new approach does not need the complex mesh generation for complex structures and can achieve high accuracy, thus it has the potential to become a powerful 3-D MT forward modelling technique.