Efficient Mixed-order FDTD Using the Laguerre Polynomials on Non-uniform Meshes

Abstract

In this paper, we propose a mixed-order approximating method to improve the computational efficiency of the FDTD using the weighted Laguerre polynomial technique. In it, both low-and high-order spatial approximations are used together with a non-uniform mesh; in the interior of a solution domain, a coarse grid is employed and a high-order spatial finite-difference approximation is applied; in a region close to a boundary, a fine grid is used and a low-order spatial finite-difference approximation is applied; As a result, a minimum number of numerical grid cells is used while the boundary handling difficulty with high-order schemes are avoided at no expense of the accuracy and the unconditional stability of the Laguerre-polynomial based FDTD method. Numerical experiments illustrate the effectiveness of the proposed method in improving computational efficiency.