Research On Multiscale Electromagnetic Problems Based On Transformation Optics And FDTD Method

In recent years,multi-scale electromagnetic problems have received more and more attention.The multi-scale electromagnetic problem means that the computational domain contains not only the electrically large structure but also the electrically small structure.The finite-difference time-domain(FDTD)method is widely used because it is suited to handle complex and inhomogeneous problems When dealing with multi-scale electromagnetic problems,although it is possible to resolve electrically small targets using small spatial step in all computational domain,it also increase large amounts of unknown.Meanwhile,the maximum time step is limited by the minimum spatial step due to the Courant-Friedrich-Levy(CFL)stability condition,so that the time step must be small enough.These factors will result in inefficient computation.One popular approach overcoming this problem is subgridding FDTD method,fine spatial grids are used to accurately model only the small structures and coarser spatial grids are used elsewhere.The main diff-iculty of subgridding technique is the reduced accuracy and late-time instability due to the temporal and spatial interpolations,especially when the ratio between coarse spatial grids and fine ones is large.Another simple yet useful method is the transformation optics based local mesh refinement method.The region including small targets can be enlarged through the coordinate transformation.Then the whole computational domain can be computed by the FDTD method with uniform coarse spatial grids Compared with the subgridding method,the error caused by the interface of the coarse and fine mesh is avoided,and the late-time instability problem is eliminated However,staircasing errors are introduced by circular transformation boundaries due to they are not aligned with Cartesian mesh,which brings a large relative error to the small targetWe first propose an improved transformation optics FDTD(TO-FDTD)method aiming at above problems.The circular transformation boundaries are replaced with the rectangular transformation boundaries to eliminate staircasing errors caused by the circular transformation boundaries.Besides,the rectangular transformation boundaries are described by a uniform and simple parameterized formulation and easy to implement in code.The stable TO-FDTD formulation for metal and medium in transformation region is derived.Numerical examples of narrow slit diffraction and electromagnetic scattering of small targets verify that the improved TO-FDTD algorithm has higher computational accuracyIn addition,we propose a TO-FDTD method for multi-scale problem of the target with the thin coating and large backing material,which can enlarge only the thin coating of the target,but remain the rest of the target unchanged.The research model extends from coated circular cylindrical targets to coated polygonal cylinder targets with any number of sides.The thin coating is enlarged into a thicker coating after the coordinate transformation,and the stable TO-FDTD formulation for lossy medium in transformation region is derived,so that the uniform coarse grids can be used to compute in the whole computational domain.Through the example of electromagnetic scattering of the targets,the near-field results and the RCS results in the far zone are analyzed and compared.The numerical results show that the method maintains high computation accuracy and greatly improves the computation efficiency.