An Efficient Laguerre-Based BOR-FDTD Method Using Gauss–Seidel Procedure

In this paper, an efficient Laguerre-based body of revolution finite-difference time-domain (BOR-FDTD) method is proposed. A perturbation term and the Gauss-Seidel method are introduced to get the new algorithm. The splitting error caused by the perturbation term can be reduced to a low level by using the iterative method. To be different from its counterpart in the Cartesian coordinate system, the perturbation term used for the off-axis field is not applicable to the field on the axis in the proposed method. On the axis, it is not necessary to add the perturbation term and no nonphysical intermediate variable is involved. No splitting error compensatory term is used for the field on the axis during the iteration. Another difference is that the perturbation term in the proposed method causes a pronounced splitting error on the field point which is close to the axis. Several local iterations near the axis are needed since the splitting error near the axis is especially large. To validate the proposed method, two numerical examples are given. Numerical results show that it obtains a good convergence. Meanwhile, the comparison of the computational expenditure between the proposed method and several other methods indicates its performance.