Cubic lattice-based spherical uniaxial perfectly matched layer for the FDTD method

In order to reduce the finite-difference time-domain (FDTD) computational area efficiently, we established spherical uniaxial perfectly matched layer (S-UPML) with regular Yee's lattices in the Cartesian coordinate system. The boundary performed as a curved profile but is constructed with regular hexahedron cells in three-dimensional (3-D) and with regular quadrilateral cells in two-dimensional (2-D) condition. Although the S-UPML's curvilinear outline is approximated by standard meshes, it still maintains the same performance as the orthodox methods. After it is used for absorbing outgoing wave, the computational FDTD lattices are reduced about a half and a quarter in 3-D and 2-D, respectively, in contrast with the conventional Cartesian boundaries. We introduce the radial components to basic formulations of the S-UPML and facilitate the update coefficients of iterative equations. Its suitable thickness is a key parameter to guarantee the performance and is determined through balancing the efficiency and maximum reflection error level. Several numerical trials are implemented to verify the practicability of the proposed boundary in two dimensions. Results show its suitability and the higher efficiency than conventional cubic boundary.