Large-Scale 3D Electromagnetic Modelling Using High-Order Finite-Element Method

Abstract:

The finite element method (FEM) is an efficient tool for modeling electromagnetic (EM) fields in complex 3D media. One of the advantages it offers is the adaptive local mesh refinement also known as h-refinement. In geo-electromagnetic applications one usually wants to obtain an accurate solution at the locations of survey stations. This suggests that a mesh needs to be locally refined only where it affects accuracy at the stations. Recently, automatic schemes were derived to carry out such h-refinement for geo-electromagnetic modeling and we present them in this work. Furthermore, the EM field inside every finite element is described by a polynomial. Therefore, in addition to the h-refinement discussed above one can perform p-refinement, i.e. every element can be constructed using an invidual polynomial degree. As a result, h-refinement can be performed in regions where an EM field exhibits strong variations in order to describe small-scale features properly, whereas in parts of the domain where the field is smooth and diffusive, it sufficies to perform p-refinement without refinning the mesh itself. It has been shown that if done properly, exponential convergence rates are attained with this approach. However, in most geo-electromagnetic codes, which use FEM, the lowest-order finite elements (also known as edge-based) are exploited. In this contribution, we investigate the application of high-order finite elements to EM modelling in 3D. To make this task feasible, we have extendeded the robust and scalable auxiliary space preconditioner for high-order elements on non-conforming hexahedral meshes and studied its efficiency.