Volume-conformation method to study scattering by PEC objects with FDTD zyxw S.Gonzalez Garcia T. Materdey Bao-Hung B.Garcia Olmedo R.Gomez Martin zyxwvutsrqpon Indexing terms: Volume conformation,Scattering, Finite-dgerence time-domainmethods, Maxwell’s curl equations zyxwvu Abstract: zyxwvutsrqpo The paper presents a volume- conformation technique to avoid the staircase approximation in the study of scattering by curved objects with the finite-difference time- domain (FDTD) method. This technique is based on a volume form of the Faraday and Ampere laws and it can easily be added to an existing FDTD code. Results for PEC sharply curved (ogive) and smoothly curved (sphere) objects are presented to show the efficiency of the method. 1 introduction The finite-difference time-domain (FDTD) method for the solution of Maxwell’s curl equations [l, 21 is a very powerful numerical tool that has been extensively used to calculate parameters related to the electromagnetic scattering of structures of arbitrary material and shape. A characteristic of this method is that the body profile needs to be discretised in a stair-stepped manner, to be fitted within a rectangular mesh. Several methods have been proposed in the literature to improve the treatment of curved surfaces. One main division of these methods depends on whether the com- putational grid is deformed locally or globally. Exam- ples of globally deformed grids are found in the work of Holland zyxwvutsrqpo [3] and Fusco et al. [4, 51, which use a cov- ariant form of Maxwell’s differential equations to express them in nonorthogonal general curvilinear co- ordinates. In [6], the integral form of Maxwell equa- tions are used to avoid the necessity of a metric for the co-ordinate system. Some locally deformed models are based on subgridding techniques [7] near the curved objects, with connection conditions, or on the applica- tion of the integral form of Maxwell’s equations near the object: e.g. two-dimensional contour-path (CP) method zyxwvutsr [8], three-dimensional contour FDTD (CFDTD) method [9]. The main advantage of the locally deformed models is that they maintain the general structure of the classi- zyxwvu 0 IEE, 1996 IEE Proceedings online no. 19960247 Paper first received 21st February 1995 and in revised form 11th Decem- ber 1995 The authors are with the Electromagnetic Group of Granada, Depto. Fisica Aplicada. Facultad de Ciencias, University of Granada, Fuen- tenueva sin, 18071 Granada, Spain. cal algorithm: absorbing boundary conditions, illumi- nation and near-to-far field transformation. In this paper we propose a volume-conformation algorithm to take into account the curvature of the scatterer, that will hence be referred to as the VCFDTD method. An important advantage of the VCFDTD method lies in the fact that it can easily be implemented within a previous working FDTD code. AY - - z c Y Fig. 1 Yee unit cell 2 Volume-conformation method in three dimensions The objective of this paper is to extend the FDTD method to treat accurately the problem of scattering by curved surfaces. The starting point is the discretisation of the time and space variables in integer and semi- integer multiples of given increments. In space, the components of the E and H fields are placed in the positions shown by the Yee unit cell (Fig. 1) and in time, the E field is placed in integer multiples of At and the H field in semi-integer multiples of At. The replacement of the derivatives in Maxwell’s curl equations by second-order central differences results in a set of difference equations which allows each field component to advance explicitly in time (Yee algo- rithm). Since the electric and magnetic properties also need to be discretised in fixed positions, curved objects are approximated by staircase contours, as stated in Section 1. The reader is assumed to have some famili- arity with the FDTD method and is referred to [l, 21 for further details. 131 IEE Proc-Microw. Antennas Propag., Vol. 143, No. 2, April 1996