conductivity and a non-zero density, which for this problem are those of the shell and its interior.
The sinusoidal steady-state was reached after 1990 time-steps. A three-dimensional plot of the SAR values on the head’s surface is shown in Fig. F.5, where it can be seen that the results are in agreement with what is qualitatively expected from a problem having this configuration.
Figure F.5: Three-dimensional SAR plot for the CENELEC 50361 SAM phantom head.
Finally, a comparison between the three-dimensional radiation patterns of the cell phone at 900 MHz, with and without the SAM phantom head, are presented in Fig. F.6. As can be seen, the presence of the head significantly changes the radiation characteristics of the cellular phone.
Figure F.6: Illustration of the SAM phantom head’s effect on the radiation pattern (directivity) of the cellular phone at 900 MHz.(a) Radiation pattern with SAM; (b) Radiation pattern without SAM.
Bibliography
[1] E. K. Miller, “A Selective Survey of Computational Electromagnetics,”IEEE Transactions on Antennas and Propagation, vol. 36, no. 9, pp. 1281–1305, September 1988.
[2] K. S. Yee, “Numerical Solution of Initial Boundary Value Problems Involving Maxwell’s Equations in Isotropic Media,”IEEE Trans. Antennas Propagat., vol. AP-14, pp. 302–307, May 1966.
[3] Meep. [Online]. Available: http://ab-initio.mit.edu/wiki/index.php/Meep
[4] Sun Microsystems. (2004) JavaTM 2 Platform Standard Edition 5.0 API Specification. [Online].
Available: http://java.sun.com/j2se/1.5.0/docs/api/
[5] (2007) Java 3D API Documentation. [Online]. Available: https://java3d.dev.java.net/#Documentation [6] Sun Microsystem’s Java 3D engineering team. (1999) Java 3D Tutorial. [Online]. Available:
http://java.sun.com/developer/onlineTraining/java3d/index.html
[7] W. L. Stutzman and G. A. Thiele,Antenna Theory and Design, 2nd ed. John Wiley & Sons, 1998.
[8] Wavefront Technologies. (1996) Wavefront OBJ Specification. [Online]. Available:
http://netghost.narod.ru/gff/graphics/summary/waveobj.htm
[9] A. Taflove and S. C. Hagness, Computational Electrodynamics: The Finite-Difference Time-Domain Method, 2nd ed. Artech House, 2000.
[10] K. S. Kunz and R. J. Luebbers,The Finite Difference Time Domain Method for Electromagnetics. CRC Press, 1993.
[11] T. Namiki, “A new FDTD Algorithm Based on Alternating-Direction Implicit Method,” IEEE Trans.
MTT, vol. 47, no. 10, pp. 2003–2007, October 1999.
[12] S. Staker, C. Holloway, A. Bhobe, and M. Piket-May, “Alternating-direction implicit (ADI) formulation of the finite-difference time-domain (FDTD) method: algorithm and material dispersion implementation,”
IEEE Transactions on Electromagnetic Compatibility, vol. 45, no. 2, pp. 156–166, May 2003.
[13] G. Carat, R. Gillard, J. Citerne, and J. Wiart, “An efficient analysis of planar microwave circuits using a DWT-based Haar MRTD scheme,”IEEE Trans. MTT, vol. 48, no. 12, pp. 2261–2269, December 2000.
[14] W. Yu and R. Mittra, “A Technique for Improving the Accuracy of the Nonuniform Finite-Difference Time-Domain Algorithm,” IEEE Trans. MTT, vol. 47, no. 3, pp. 353–356, March 1999.
[15] P. Monk and E. S¨uli, “Error Estimates for Yee’s Method on Non-uniform Grids,” IEEE Transactions on Magnetics, vol. 30, no. 5, pp. 3200–3203, September 1994.
[16] W. Yu and R. Mittra, “Electromagnetic scattering of underground object using nonuniform mesh FDTD and PML,”Microwave and Optical Technology Letters, vol. 21, no. 2, pp. 151–156, April 1999.
[17] W. Heinrich, P. M. Klaus Beilenhoff, and L. Roselli, “Optimum Mesh Grading for Finite-Difference Method,”IEEE Trans. MTT, vol. 44, no. 9, pp. 1569–1574, September 1996.
[18] G. Mur, “Absorbing Boundary conditions for the Finite-Difference Approximation of the Time-Domain Electromagnetic-Field Equations,” IEEE Transactions on Electromagnetic Compatibility, vol. 23, no. 4, pp. 377–382, November 1981.
[19] ——, “Total-Field Absorbing Boundary Conditions for the Time-Domain Electromagnetic Field Equa- tions,”IEEE Transactions on Electromagnetic Compatibility, vol. 40, no. 2, pp. 100–102, May 1998.
[20] J.-P. Berenger, “A Perfectly Matched Layer for the Absorption of Electromagnetic Waves,” Journal of Computational Physics, vol. 114, pp. 185–200, 1994.
[21] S. D. Gedney, “An Anisotropic Perfectly Matched Layer-Absorbing Medium for the Truncation of FDTD Lattices,” IEEE Transactions on Antennas and Propagation, vol. 44, no. 12, pp. 1630–1639, December 1996.
[22] J.-P. Berenger, “The PML Absorbing Boundary Condition,” inEuropean School of Antennas: European Course on Time Domain Techniques for Antenna Analysis, Polytech’Nice Sophia, Universit´e de Nice- Sophia Antipolis, 20-24 November 2006.
[23] ——, “Three-Dimensional Perfectly Matched Layer for the Absorption of Electromagnetic Waves,”Jour- nal of Computational Physics, vol. 127, pp. 363–379, 1996.
[24] P. K. Datta and D. Bhattacharya, “Optimization of Uniaxial Perfectly Matched Layer Parameters for Finite Difference Time Domain Simulation and Application to Coupled Microstrip Lines with Multiple Bend Discontinuities,”International Journal of RF and Microwave Computer-Aided Engineering, vol. 12, no. 6, pp. 508–519, October 2002.
[25] S. D. Gedney, “Comment on “On the Matching Conditions of Different PML Schemes Applied to Multi- layer Isotropic Dielectric Media“,”Microwave and Optical Technology Letters, vol. 30, no. 4, pp. 289–291, August 2001.
[26] D. M. Pozar, Microwave Engineering, 2nd ed. John Wiley & Sons, 1998.
[27] K. R. Umashankar, A. Taflove, and B. Beker, “Calculation and Experimental Validation of Induced Cur- rents on Coupled Wires in an Arbitrary Shaped Cavity,”IEEE Transactions on Antennas and Propagation, vol. 35, no. 11, pp. 1248–1257, November 1987.
[28] G. Marrocco, M. Sabbadini, and F. Bardati, “FDTD Improvement by Dielectric Subgrid Resolution,”
IEEE Transactions on Microwave Theory and Techniques, vol. 46, no. 12, pp. 2166–2169, December 1998.
[29] J. G. Maloney, K. L. Shlager, and G. S. Smith, “A Simple FDTD Model for Transient Excitation of Antennas by Transmission Lines,” IEEE Transactions on Antennas and Propagation, vol. 42, no. 2, pp.
289–292, February 1994.
[30] I. J. Craddock, D. L. Paul, C. J. Railton, P. N. Fletcher, and M. Dean, “Applications of singlemode extraction from finite difference time domain data,” IEE Proc.-Microw. Antennas Propag., vol. 146, no. 2, pp. 160–162, April 1999.
[31] M. A. Schamberger, S. Kosanovich, and R. Mittra, “Parameter Extraction and Correction for Transmis- sion Lines and Discontinuities Using the Finite-Difference Time-Domain Method,”IEEE Transactions on Microwave Theory and Techniques, vol. 44, no. 6, pp. 919–925, June 1996.
[32] C. A. Balanis,Advanced Engineering Electromagnetics. John Wiley & Sons, 1989.
[33] O. M. Ramahi, “Near- and Far-Field Calculations in FDTD Simulations Using Kirchhoff Surface Integral Representation,” IEEE Transactions on Antennas and Propagation, vol. 45, no. 5, pp. 753–759, May 1997.
[34] J. Nocedal and S. J. Wright,Numerical Optimization, 1st ed. Springer, 1999.
[35] Y. Kanai and K. Sato, “Automatic Mesh Generation for 3D Electromagnetic Field Analysis by FD-TD Method,”IEEE Transactions on Magnetics, vol. 34, no. 5, pp. 3383–3386, September 1998.
[36] Y. Srisukh, J. Nehrbass, F. L. Teixeira, J.-F. Lee, and R. Lee, “An Approach for Automatic Grid Generation in Three-Dimensional FDTD Simulations of Complex Geometries,” IEEE Antenna’s and Propagation Magazine, vol. 44, no. 4, pp. 75–80, August 2002.
[37] R. P. Pican¸co, “DESENVOLVIMENTO DE UMA INTERFACE INTEGRADA PARA O PROJETO E AN´ALISE DE ANTENAS UTILIZANDO O M´ETODO DAS DIFERENC¸ AS FINITAS NO DOM´INIO DO TEMPO (FDTD) ,” Masters Thesis, Universidade de Bras´ılia, Faculdade de Tecnologia, March 2006.
[38] J. Hill, “Efficient Implementation of Mesh Generation and FDTD Simulation of Electromagnetic Fields,”
Masters Thesis, Worcester Polytechnic Institute, August 1996.
[39] R. J. Luebbers and K. Kunz, “Finite Difference Time Domain Calculations of Antenna Mutual Coupling,”
IEEE Transactions on Electromagnetic Compatibility, vol. 34, no. 3, pp. 357–359, August 1992.
[40] (2007) Computer Simulation Technology (CST). [Online]. Available: http://www.cst.com/
[41] T. Weiland, “Time Domain Electromagnetic Field Computation with Finite Difference Methods,” Inter- national Journal of Numerical Modelling: Electronic Networks, Devices and Fields, vol. 9, pp. 295–319, 1996.
[42] R. Luebbers, L. Chen, T. Uno, and S. Adachi, “FDTD Calculation of Radiation Patterns, Impedance, and Gain for a Monopole Antenna on a Conducting Box,”IEEE Transactions on Antennas and Propagation, vol. 40, no. 12, pp. 1577–1583, December 1992.
[43] D. M. Sheen, S. M. Ali, M. D. Abouzahra, and J. A. Kong, “Application of the Three-Dimensional Finite- Difference Time-Domain Method to the Analysis of Planar Microstrip Circuits,” IEEE Transactions on Microwave Theory and Techniques, vol. 38, no. 7, pp. 849–857, July 1990.
[44] P. A. Makal, “UWB ANTENNAS FOR WIRELESS APPLICATIONS,” Final Report, IST Lisbon, July 2007.
[45] P. A. Tirkas and C. A. Balanis, “Finite-Difference Time-Domain Method for Antenna Radiation,” IEEE Transactions on Antennas and Propagation, vol. 40, no. 3, pp. 334–340, March 1992.
[46] S. Dey and R. Mittra, “A Locally Conformal Finite-Difference Time-Domain (FDTD) Algorithm for Modeling Three-Dimensional Perfectly Conducting Objects,”IEEE Microwave and Guided Wave Letters, vol. 7, no. 9, pp. 273–275, September 1997.