2676 IEEE TRANSACTIONS ON MICROWAVE THEORY AND TECHNIQUES,VOL. 48, NO. 12, DECEMBER2000 A Study of Uncertainties in Modeling Antenna Performance and Power Absorption in the Head of a Cellular Phone User Konstantina S. Nikita, Senior Member, IEEE, Marta Cavagnaro, Paolo Bernardi, Fellow, IEEE, Nikolaos K. Uzunoglu, Senior Member, IEEE, Stefano Pisa, Member, IEEE, Emanuele Piuzzi, John N. Sahalos, Senior Member, IEEE, George I. Krikelas, John A. Vaul, Peter S. Excell, Senior Member, IEEE, Graziano Cerri, Simona Chiarandini, Roberto De Leo, and Paola Russo, Member, IEEE Abstract—A set of finite-difference time-domain (FDTD) numerical experiments modeling canonical representations of the human head/cellular phone interaction has been performed in order to investigate the effect of specific simulation details (e.g., antenna numerical representation and absorbing boundary conditions) on computed results. Furthermore, hybrid techniques based on the dyadic Green’s function and the method of auxiliary sources, and on a hybrid method-of-moments–FDTD technique have been used to compute parameters of interest for comparison with the FDTD evaluated parameters. It was found that small, but potentially significant, differences in computed results could occur, even between groups that were nominally using a very similar method. However, these differences could be made to become very small when precise details of the simulation were harmonized, particularly in the regions close to the source point. Index Terms—Biological effects of electromagnetic radiation, dosimetry, error analysis, FDTD methods, hybrid numerical techniques, land mobile radio cellular systems. I. INTRODUCTION I N RECENT years, there has been a growing demand for accurate dosimetric calculations inside lossy bodies exposed to the near field of handheld transceivers to evaluate possible health hazards or to perform compliance testing. In particular, cellular phone compliance tests consist in checking that the power absorption due to mobile telecommunication equipment is below the limits recommended by international safety guidelines [1]–[4]. This analysis can be performed both experimentally and numerically. While in experimental studies error evaluation is usually per- formed so that the power absorbed is always reported together Manuscript received March 1, 2000; revised August 25, 2000. This work was supported under the European Commission Standards Measurements and Testing Programme, Cellular Phone Standard Project. K. S. Nikita and N. K. Uzunoglu are with the Department of Electrical and Computer Engineering, National Technical University of Athens, 157 80 Athens, Greece. M. Cavagnaro, P. Bernardi, S. Pisa, and E. Piuzzi are with the Department of Electronic Engineering, University of Rome “La Sapienza,” 00184 Rome, Italy. J. N. Sahalos and G. I. Krikelas are with the Department of Physics, Aristotle University of Thessaloniki, GR-54006 Thessaloniki, Greece. J. A. Vaul and P. S. Excell are with the Telecommunications Research Centre, University of Bradford, Bradford BD7 1DP, U.K. G. Cerri, S. Chiarandini, R. De Leo, and P. Russo are with the Department of Electronics, University of Ancona, 60131 Ancona, Italy. Publisher Item Identifier S 0018-9480(00)10746-X. with the corresponding uncertainty value, in numerical studies, considerations relating to numerical error have only appeared sporadically. In numerical dosimetry studies for mobile communications, as well as for mobile phone design, the use of the finite-dif- ference time-domain (FDTD) method has dominated over the other numerical methods in recent years, due to its simplicity and its ability to treat highly nonhomogeneous structures. How- ever, even if intensive research work with the FDTD method has led to high confidence in the obtained results, the exact error es- timation of FDTD simulations still remains a difficult task. In particular, since the field interaction is highly dependent on the shape of the scatterer, which usually does not conform to the FDTD orthogonal lattice, unless some locally conformal grid is used, this can lead to substantial error in the calcula- tions [5]. Thus, factors such as the details for building the head or the handset in the Yee grid, and the source numerical repre- sentation, may be responsible for uncertainties in the evaluated parameters. Moreover, even if several approaches for accurate absorbing boundary conditions (ABCs) at the boundary of the computational domain have been proposed [6], improving the approximation of free-space environment with a minimum of air space around the scatterer, the type of ABCs used and the distance between the scatterers and absorbing boundaries can be another source of substantial error in the FDTD results. The aim of this paper is to examine the main uncertainty components of the FDTD method in evaluating the exposure of human head models to mobile communication devices. To this end, numerical results obtained for 12 canonical cases, mod- eling the exposure of well-defined head models to simple an- tennas similar to those of mobile transceivers, have been com- pared in detail. Special emphasis is given to the estimation of un- certainties related to the antenna numerical representation and the ABCs, by performing a set of appropriate numerical experi- ments for a test canonical case. In order to also assess “inter-al- gorithm” variabilities, numerical results obtained by three inde- pendent implementations of the FDTD method at the University of Rome “La Sapienza,” Rome, Italy, at the Aristotle University of Thessaloniki, Thessaloniki, Greece, and at the University of Bradford, Bradford, U.K., are compared in detail. A semianalyt- ical method based on the dyadic Green’s function theory in con- junction with the method of auxiliary sources (Green/MAS), de- veloped at the National Technical University of Athens, Athens, 0018–9480/00$10.00 © 2000 IEEE