2D FDTD modelling of objects with curved boundaries, using embedded boundary orthogonal grids

An FDTD algorithm was developed using an embedded boundary orthogonal grid system. The algorithm is based on the complex Laplace equation to implement conformal mapping that minimises the magnitudes of the mesh gradients and therefore leads to the smoothest coordinate line distribution over the solution domain. In conjunction with the global rectangular meshes, the local non-orthogonal grids provide versatility of geometry. There is no need to perform interpolation on the boundaries between the local and global grids. As a result, computational time and memory requirements are substantially reduced. The field solution to the unbounded Laplace equation in nonorthogonal coordinates is obtained, and is used as the exciting source to expedite the convergence of the FDTD computations. Numerical examples show good agreement with the results presented in previous publications, both guided wave and scattering problems