IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES,VOL. 54, NO. 3, MARCH 2006 1269 Cell-Centered Finite-Volume-Based Perfectly Matched Layer for Time-Domain Maxwell System Krishnaswamy Sankaran, Student Member, IEEE, Christophe Fumeaux, Member, IEEE, and Rüdiger Vahldieck, Fellow, IEEE Abstract—The perfectly matched layer (PML) technique is extended for a cell-centered finite-volume time-domain (FVTD) method. A step-by-step procedure for the performance character- ization of the FVTD PML is presented for both structured and unstructured finite-volume meshes. The FVTD PML is compared with the standard first-order Silver–Müller absorbing boundary condition (SM ABC) for practical applications. It is found that the FVTD PML for an unstructured grid achieves a reflection coefficient lower than 40 dB for incident angles up to 45 and outperforms the SM ABC by 15–20 dB. Index Terms—Absorbing boundary condition (ABC), computational electromagnetics (CEM), finite volume time domain (FVTD), Maxwell’s equations, perfectly matched layer (PML). I. INTRODUCTION A CELL-CENTERED finite-volume time-domain (FVTD)- based perfectly matched layer (PML) is modeled and characterized in this paper. Ever since its introduction by Bérenger [1], the PML technique has matured and has been applied to a variety of simulation problems mainly in conjunc- tion with the finite-difference time-domain (FDTD) technique [2]–[5]. More recently work is being reported where the PML is also used for other numerical techniques such as the fi- nite-element time-domain (FETD) formulation [6], [7]. In [8], a vertex-centered FVTD model (variational approach) of the PML was reported for scattering problems, but the performance of the PML was not characterized based on its control param- eters. This paper extends the PML concept to the cell-centered FVTD approach and systematically characterizes its perfor- mance using both structured and unstructured finite-volume meshes. Furthermore, based on reflection-coefficient computa- tion, the suitability of the FVTD PML for practical problems is addressed. The performance of FVTD PML is compared with the standard first-order Silver–Müller absorbing boundary con- dition (SM ABC). Finally, as a practical example, the reflection coefficient is computed for the truncation of a parallel-plate waveguide using an FVTD PML and is compared with that of the SM ABC. Manuscript received October 31, 2005. This work was supported by the Swiss Federal Institute of Technology under ETH Research Grant TH-38/04-1. The authors are with the Laboratory for Electromagnetic Field Theory and Microwave Electronics, Swiss Federal Institute of Technology-ETH Zürich, Zürich CH-8092, Switzerland (e-mail: krishna@ifh.ee.ethz.ch). Digital Object Identifier 10.1109/TMTT.2006.869704 II. DOMAIN DISCRETIZATION A discrete solution to continuum physics requires sampling spatial and temporal quantities into finite space–time cells. Complex curved geometries and the availability of simple, but accurate boundary conditions (BCs) are basic motivations for the development of a co-located finite-volume space–time approach. Each finite-space cell (control volume) stores field quantities at the same point in space and time. Solutions at various time stamps are obtained by introducing the flux-conservation prin- ciple of the field flow, which forms the basis of the FVTD approach. Particular interest is vested on unstructured control volumes, which correspond, for example, to triangular and tetra- hedral meshes in two-dimensional (2-D) and three-dimensional (3-D) models, respectively. For completeness, a brief description of the FVTD method is presented in the following. Readers are referred to [9]–[12] for a detailed explanation on the method. A. Finite Volume: Definitions The computational domain is considered as a union of a finite number of nonoverlapping conformal tessellations called cells and are represented as ; i.e., . We are basically interested in a co-located cell-centered formulation where spatial–temporal variations of field quantities ( and ) are stored at each cell center. Strictly speaking, these values are an approximation of the mean field values over the entire cell . The field values at different space–time stamps are the solutions to Maxwell’s two curl equations written as (1) (2) In (1), the electric-current source term inside is set to zero. Although the method is applicable to inhomogeneous and anisotropic computational domains, (without loss of gen- erality), a homogeneous and isotropic medium is assumed in this paper. In other words, permeability and permittivity are constant inside . Equation (1) and (2) are cast in conservative form with the help of the divergence theorem and integrated over each cell with an appropriate spatial and temporal discretization as (3) (4) 0018-9480/$20.00 © 2006 IEEE