Conformal Method to Eliminate the ADI-FDTD Staircasing Errors

In this paper, we present an enlarged cell technique (ECT) to avoid the time step reduction encountered in the conformal finite-difference time-domain (CFDTD) method due to small irregular cells truncated by metallic boundaries. We focus our efforts on the discussion of the accuracy and stability of the ECT and its comparison with other conformal methods, especially the one called the uniformly stable conformal (USC) method. We also provide a simplified ECT, which is much easier to implement. In the ECT, a stability criterion is first constructed to identify instable irregular cells, i.e., those having so small an area to cause instability. Those instable cells are then enlarged into their adjacent cells to obtain a large, stable area. Careful treatment is performed on the communication between the intruding and intruded cells in terms of electromotive force by keeping the total electromotive force conservative. This technique is verified by several 3-D numerical experiments. Results show that the ECT is second-order accurate and numerically stable at the regular Courant time step limit.Index Terms-Conformal finite-difference time-domain (CFDTD) method, enlarged cell technique (ECT), finite-difference time-domain (FDTD) method, metallic boundary, staircasing error.

Section: The Enlarged Cell Techniquementioning

confidence: 99%

A 3-D Enlarged Cell Technique (ECT) for the Conformal FDTD Method

Xiao

Liu

2008

“…4. Hence, the equivalent conductance is obtained by evaluating the distributed series connection along of two parallel conductances per unit length that depend on , that is (8) where and are the cross-sectional areas of and regions, respectively, determined by (9) where are cross-sectional areas over the left side and right side (similarly for ), respectively, as indicated in Fig. 4, and the parameters and are given by (10) Effective conductivities and are obtained from (1) and (8) as (11) Last, to obtain and in Fig.…”

Section: (A) Casementioning

confidence: 99%

Locally-Conformal FDTD for Anisotropic Conductive Interfaces

Lee

Teixeira

2010

Locally-conformal discretizations have been developed for the finite-difference time-domain (FDTD) method to mitigate staircasing errors that arise in the modeling of arbitrary (e.g., curved, slanted) interfaces by regular orthogonal grids. In particular, locally-conformal algorithms based on the computation of effective material parameters in partially-filled FDTD cells are attractive because they are simple to implement and maintain the basic conditional stability of FDTD, with only minor changes on the Courant limit. In this paper, we propose a new locally-conformal implementation for FDTD tailored for anisotropic conductive interfaces. Instead of employing arithmetic or geometrical averages, we invoke the quasi-static relationship between the current density and the electric field to derive the effective conductivities of partially-filled FDTD cells.

“…The technique allows optimization of the approximation over the frequency band of interest. The surface-impedance function is approximated by (10) where is the number of terms and and are the poles and coefficients of the approximation, respectively. The approximation is obtained with the vector-fitting technique [21], however, with the derivate term removed to obtain an approximation of the form (10).…”

Section: Sibc Formulation Using Rational Approximationmentioning

confidence: 99%

“…Also locally conformal grids [6]- [9] may result in very small cells near the surface therefore reducing the time step. Conformal PEC schemes directly extend to the ADI-FDTD method [10]. Manuscript The surface-impedance concept [11] is used to simplify electromagnetic field simulations, e.g., by avoiding calculation of fields inside conductors.…”

Section: Introductionmentioning

confidence: 99%

Incorporation of Conductor Loss in the Unconditionally Stable ADI-FDTD Method

Makinen

Kivikoski

2008

A surface-impedance boundary condition (SIBC) is presented for an unconditionally stable alternating-direction implicit (ADI) finite-difference time-domain (FDTD) method. The conformal SIBC formulation based on locally conformal grids is capable of modeling the conductor loss of arbitrarily-shaped lossy metal structures. The work is described in the framework of the finite-integration technique (FIT) formulation of the ADI-FDTD. The paper focuses on the proposed ADI-FDTD SIBC formulation and its extensive validation. For this purpose, cylindrical and spherical cavity resonators are used for numerical tests. The quality factor is directly proportional to wall loss and is particularly sensitive to the accuracy of loss calculation. The resonator structure consists only of a vacuum-filled metal cavity and is thus free of additional sources of error that are caused by other extensions to the basic ADI-FDTD algorithm. The formulation is validated by comparison with analytic results and numerical data calculated using CST Microwave Studio (MWS). The convergence rate of the results is of second order, i.e., the error reduces to one quarter as the mesh resolution is doubled.