A stable subgridding algorithm and its application to eigenvalue problems

Abstract

Abstract-In this paper, a new and stable subgridding algorithm is proposed for three-dimensional problems which provides subgridding in both space and time. The concept of an equivalent-circuit representation and a novel leapfrog time integration scheme is used to ensure that the algorithm is stable and efficient. Practical applications of this algorithm in the characterization of arbitrarily filled dielectric resonators are reported.Index Terms-FDTD methods.

A Novel Nonuniform Subgridding Scheme for FDTD Using an Optimal Interpolation Technique

“…Advantageous features of the uniform subgridding schemes [3][4][5][6][7][8][9][10] are inherited for the development of a new robust subgridding scheme. The nearest neighbor interpolation is used as the consistent coupling method in time [3].…”

“…Thoma and Weiland presented a consistent 3-D subgridding scheme using the finite integration technique in [3]. Krishnaiah and Railton also proposed a similar consistent coupling method by introducing an equivalent passive circuit model in [4]. Both methods used linearly interpolated tangential magnetic field components as boundary conditions of the SG region.…”

“…Subgridding schemes [3][4][5][6] successfully achieved the goal of stability, however, they have poor general applicability associated with material discontinuities at the interfaces or require additional special treatment to obtain it. Chilton and Lee, utilizing the "simple" interpolation method [7], developed a conservative and probably stable subgridding scheme based on the finite element principles in [8].…”

“…The former and the latter adopted different refinement factors of 1 : 2 and 1 : 3, respectively. A reduced CFL number by a factor of two was chosen for a stable result in [3], but it was not reported in [4]. Xiao et al proposed an explicit 3-D subgridding algorithm based on the interpolation of current density distribution in [5].…”

Electromagnetic Field Computation for Power Transmission Lines Using Quasi-Static Sub-Gridding Finite-Difference Time-Domain Approach

“…Many researchers in the past have been prompted to investigate subgridding technique as an analysis approach in the interaction between source and scatterer [6][7][8][9][10][11]. In general, this technique is used to condense the lattice at the point of interest locally and does not require any analytical formula to be taken into account, and hence it is appropriate for objects of any shape.…”