Fdtd

IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 40, NO. 4, APRIL 1992

351

Finite-Difference Time-Domain Modeling of Curved Surfaces
Thomas G. Jurgens, Member, IEEE, Allen Taflove, Fellow, IEEE Korada Umashankar, Senior Member, IEEE, and Thomas G. Moore, Member, IEEE deformed to conform with the surface locus. Slightly modified time stepping expressions for the field components adjacentto the surface are obtained by applying either a modified finite volume technique [2] or the CP technique. 2) Globally distorted grid models, body fitted. These employ available numerical mesh generation schemes to construct non-Cartesian grids which are continuously and globally stretched to conform with smoothly shaped structures. In I. INTRODUCTION effect, the Cartesian grid is mapped to anumerically genersignificant flaw in previous finite-difference time- ated coordinate system wherein the structure surface contour domain (FDTD) models of structures with smooth occupies a locus of constant equivalent "radius. '' Timecurved surfaces has been to use stepped edge (staircase) stepping expressions are adapted either from the Cartesian approximations of the actual structure surface.Although not FDTD case [3] or from a characteristics based method used a serious problem for modeling wave penetration and scatter- in computational fluid dynamics [4]. ing for low-Q metal cavities, recent FDTD studies have 3) Globally distorted grid models, unstructured. These shown that stepped approximations of curved walls and aper- employ available numerical mesh generation schemes to conturesurfaces can shift center frequencies of resonant re- struct non-Cartesian grids comprised of an unstructured array sponses by 1 to 2% for Q factors of 30 to 80, and can of space filling cells. Structure surface features are appropripossibly introduce spurious nulls [11. In the area of scattering ately fit into the unstructured grid, with local grid resolution by complex shapes, the use of steppedsurface approxima- and cell shape selected to provide the desired geometric tions has limited the application of FDTD for the modeling of modeling aspects. An example of this class is the control the important target class where surface roughness, exact region approach discussed in [5]. Research is ongoing for each of these types of conformable curvature, and dielectric or permeable loading isimportant in determining the radar cross section. This paper reports on a surface models. Key questions concerning the usefulness of generalization of the FDTD method, the contour path (CP) each model include the following: method, where grid cells local to structure surfaces are 1) computer resources involved in mesh generation; deformed. Recently, three different types of FDTD conformable sur2)severity of numerical artifacts introduced by grid distortion, which includes numerical instability, dispersion, face models have been proposed and examined for scattering and nonphysical wave reflection, and subtraction noise; problems. 1) Locally distorted grid models. These preserve the 3) limitation of the near-field computational range due to basic Cartesian grid arrangement of field components atall subtraction noise; space cells except those immediately adjacent to the structure 4) comparative computer resources for running realistic surface. Space cells adjacent to the structure surface are scattering models, especially for three-dimensional targets spanning 10 wavelengths or more.
Abstract-In this paper the finite-difference time-domain (FDTD) method is generalized to include theaccurate modeling of curved surfaces. This generalization, the contour path (CP) method, accurately models the illumination of bodies with curved surfaces, yet retains the ability to model corners and edges. CP modeling of two-dimensional electromagnetic wave scattering from objects of various shapes and compositions is presented.

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Manuscript received October 20, 1989; revised September 30,...