TLM Method with Non-Orthogonal Hexahedral Meshing with Unconditional Stability

This paper presents an unconditionally stable TLM algorithm with non-orthogonal hexahedral meshing. This type of meshing can be very useful when dealing with curved boundaries (e.g., for dosimetry applications). Such non-orthogonal mesh can drastically reduce the staircase error produced by normal orthogonal meshes. Moreover, the staircase approximation in lossy media produces artificial corners and edges. These corners and edges are considered as singularity points/regions in which the electromagnetic fields can keep increasing as we continue to refine the mesh. Therefore, classical convergence tests will fail to tell us if the simulation results are correct or not. However, in this study, we try to minimize such effects by adopting non-orthogonal meshing. Note that non-orthogonal cells can be used only in some regions (e.g., the surface of the human body), while the rest of the computational domain can use traditional orthogonal TLM cells. Moreover, such cells are 6-faced cells as conventional SCN-TLM cells, hence, they fit perfectly inside the computational domain without any modifications to the algorithm at the interface between the non-orthogonal and orthogonal cells. Note that, the use of conventional non-orthogonal cells can result in small timestep reduction, however, their advantages exceed the use of finemeshing. Moreover, in this study we present the mode decomposition scheme to eliminate unstable modes when exceeding the CFL limit, resulting in an unconditionally stable scheme.