Time-domain FEM analysis of quasi-static magnetic fields around nonperfectly conductive shields

A time-domain analysis of quasi-static magnetic fields around nonperfectly conductive shields is performed by a numerical procedure based on the nodal-based finite element method (FEM), Eliminating the shield region from the computational domain, a new boundary is generated where impedance network boundary conditions (INBCs) are imposed to take into account the field discontinuity produced by the shield. The INBCs are boundary conditions of the third kind which couple the electric and magnetic field tangential components on the shield surfaces. The application of the INBCs in time domain leads to the solution of convolution integrals. By using exponential expressions for the INBCs and discretizing the time by central finite differences, an efficient algorithm is proposed to solve recursively the convolution integrals. Finally, the implementation of the INBCs in a time domain FEM procedure is illustrated.