Comparison of approaches and the software for 3D finite element modeling of harmonic electromagnetic fields

The paper considers the problem of the finite element 3D-modeling of the time-harmonic electromagnetic fields excited by a wire loop. We compare the computational efficiency of two approaches to the finite element (FE) approximation when solving the induction logging problems. These approaches are based on different mathematical models and mesh generation algorithms. They use different types of finite elements and different solvers of FE systems. The first approach is implemented in the Helmholtz3D software and based on the solution of the vector Helmholtz equation without extracting the 1D background medium field. The second approach is implemented in the LogEM-FD software and based on performing the FE approximation of the mathematical model with extracting the 1D background medium field. The LogEM-FD software implements special algorithms of mesh generation with local refinements and deletion of «unnecessary» nodes and the possibilities to use finite elements with terminal («handing») nodes. The research conducted shows that high accuracy of the numerical solution of the induction logging problem has been achieved when both Helmholtz3D and LogEM-FD software packages are used. However, the computational costs required for the Helmholtz3D are significantly higher than those required for the LogEM-FD to obtain equally accurate solutions.