Finite difference method

Abstract: A novel conformal finite-difference time-domain (CFDTD) technique for locally distorted contours that accurately model curved metallic objects is presented in this paper. This approach is easy to implement and is numerically stable. Several examples are presented to demonstrate that the new method yields results that are far more accurate than those generated by the conventional staircasing approach. Example geometries include cylindrical and spherical cavities, and a circular microstrip patch antenna. Accuracy of the scheme is demonstrated by comparing the results derived from analytical and Method of Moments (MoM) techniques.

Abstract: In this paper, a finite-difference time-domain method that is free of the constraint of the Courant stability condition is presented for solving electromagnetic problems. In it, the alternating direction implicit (ADI) technique is applied in formulating the finite-difference time-domain (FDTD) algorithm. Although the resulting formulations are computationally more complicated than the conventional FDTD, the proposed FDTD is very appealing since the time step used in the simulation is no longer restricted by stability but by accuracy. As a result, computation speed can be improved. It is found that the number of iterations with the proposed FDTD can be at least three times less than that with the conventional FDTD with the same numerical accuracy.

Abstract: We present two a posteriori error estimators for the mini-element discretization of the Stokes equations. One is based on a suitable evaluation of the residual of the finite element solution. The other one is based on the solution of suitable local Stokes problems involving the residual of the finite element solution. Both estimators are globally upper and locally lower bounds for the error of the finite element discretization. Numerical examples show their efficiency both in estimating the error and in controlling an automatic, self-adaptive mesh-refinement process. The methods presented here can easily be generalized to the Navier-Stokes equations and to other discretization schemes.

Abstract: We describe a new full-vector finite difference discretization, based upon the transverse magnetic field components, for calculating the electromagnetic modes of optical waveguides with transverse, nondiagonal anisotropy. Unlike earlier finite difference approaches, our method allows for the material axes to be arbitrarily oriented, as long as one of the principal axes coincides with the direction of propagation. We demonstrate the capabilities of the method by computing the circularly-polarized modes of a magnetooptical waveguide and the modes of an off-axis poled anisotropic polymer waveguide.