Modeling of structures using adaptive mesh in DGTD method for EM solver

Generation of a mesh is the first step in the development of electromagnetic (EM) field solver and mesh quality plays vital role in defining the consumption of computational resources like execution time and memory usage. The modeling of regular structures (structures whose interfaces coincide with the mesh cells) using simple mesh grids is easy to achieve but for irregular structures (structures whose interfaces do not coincide with mesh cells) is hard to achieve. Different methods have already been proposed to deal with domain decomposition for the irregular structures, e.g., thin-layer problems. The methods include subgridding and fine-mesh generation in the locality of the thin layers. This high resolution in the domain decomposition leads to the redundancy of number of cells in the computational domain hence demanding for extra computational resources. This paper presents two adaptive mesh generation techniques in 1-D which have successfully integrated the complicated multilayer structure composed of irregular thicknesses. Adaptation in the mesh for the discontinuous Galerkin time domain (DGTD) based EM solver is achieved by using i) nodes displacement, and ii) node insertion methods. The two methods use an optimum number of nonoverlapping elements (K) for the domain decomposition and adapt the locations of the nodes to incorporate the complex structures. Algorithms and associated methodologies for the two techniques are presented and their validation is achieved by comparing the numerical results with the analytical results for an irregular structure composed of multilayer with different values of thickness. High accuracy is achieved by the both methods but tradeoff exists between the complexity of the algorithms and the execution time. The node displacement method has a complex algorithm and consumes lesser execution time while the node insertion method has the simplest algorithm but requires more execution time for solving the same problem.