未來工作與展望

本論文中，吾人所開發之數值方法，對求解三維馬克斯威爾方城組以模擬實 際的複雜幾何物理問題，已經得到了良好的驗證，並且證實了我們的模擬結果，

與實際物理上之實驗測量結果數值相當接近，這樣的結果，亦證實了吾人所開發 之 PRK-DRP FDTD 具備一定的實用性以及優秀的準確度，並且在計算複雜幾何 散射物體之物理問題中，可針對在計算空間中，吾人所關注之散射物體或區域，

進行求解其電磁場之全場/散射場 (Total-Field / Scattered-Field) 並進行分離，進一 步將問題複雜化。例如求解天線輻射問題，藉由近場外推遠場，求得感興趣的天 線輻射場型，或藉此技術，以分析天線的輻射效率以及其天線指向性。另外，本 文所探討之頭部比吸收率問題為總場問題，在本研究中，複雜幾何散射體以及金 屬等色散介質材料之數值處理方法，亦已通過整合，已經成熟發展，足以解決深 入之電磁物理現象。由於所有的電器和電子設備，在其工作時，都會產生間歇或 連續性的電壓／電流變化，這將導致在不同頻帶內產生電磁能量，在電子電路產 業中，諸如此類需要特別關注之電磁現象，分為電磁相容性 (EMC) 與電磁干擾 (EMI) 兩樣重點，為了降低電路中所產生之 EMI 效應，與產品所選擇之屏蔽材料 與電路佈局息息相關。因此，透過吾人所開發之數值方法，未來可應用在電子電 路設計。吾人所開發之非交錯網格下之時域有限差分程式較適合執行平行計算於 GPUs 上，藉由於實際測試前先行模擬並優化產品，以期降低研究經費與所需時 間。

參考文獻

[1] Liping Gao, Bo Zhang, and Dong Liang. Splitting finite difference methods on stag-gered grids for the three-dimensional time-dependent Maxwell’s equations. Com-mun. Comput. Phys, 4:405–432, 2008.

[2] Yanyan Huo, Tianqing Jia, Donghai Feng, Shian Zhang, Jukun Liu, Jia Pan, Kan Zhou, and Zhenrong Sun. Formation of high spatial frequency ripples in stainless steel irradiated by femtosecond laser pulses in water. Laser Physics, 23(5):056101, 2013.

[3] TIBTECH Innovations. Properties table of stainless steel, metals and other con-ductive materials. printed from http://www. tibtech. com/conductivity. php on Aug, 19:1, 2011.

[4] iphone 4 RF Exposure Information. https://www.apple.com-/legal/rfexposure/

iphone3,1/en/.

[5] Kane Yee. Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media. IEEE Transactions on Antennas and Prop-agation, 14(3):302–307, 1966.

[6] Gerrit Mur. Absorbing boundary conditions for the finite-difference approximation of the time-domain electromagnetic-field equations. IEEE Transactions on Electro-magnetic Compatibility, (4):377–382, 1981.

[7] Jean-Pierre Berenger. A perfectly matched layer for the absorption of electromag-netic waves. Journal of Computational Physics, 114(2):185–200, 1994.

[8] J-P Berenger. Perfectly matched layer for the FDTD solution of wave-structure inter-action problems. IEEE Transinter-actions on Antennas and Propagation, 44(1):110–117, 1996.

[9] J Alan Roden, Stephen D Gedney, et al. Convolutional PML (CPML): An efficient FDTD implementation of the CFS-PML for arbitrary media. Microwave and Optical Technology Letters, 27(5):334–338, 2000.

[10] Xiaolei Zhang, Jiayuan Fang, Kenneth K Mei, and Yaowu Liu. Calculations of the dispersive characteristics of microstrips by the time-domain finite difference method.

IEEE Transactions on Microwave Theory and Techniques, 36(2):263–267, 1988.

[11] X Zhang and KK Mei. Time-domain finite difference approach for the calculation of microstrip open-circuit end effect. In Microwave Symposium Digest, 1988., IEEE MTT-S International, pages 363–366. IEEE, 1988.

[12] Zhang Xiaolei and Kenneth K Mei. Time-domain finite difference approach to the calculation of the frequency-dependent characteristics of microstrip discontinuities.

IEEE Transactions on Microwave Theory and Techniques, 36(12):1775–1787, 1988.

[13] Dok Hee Choi and Wolfang JR Hoefer. The finite-difference-time-domain method and its application to eigenvalue problems. IEEE Transactions on Microwave Theory and Techniques, 34(12):1464–1470, 1986.

[14] David M Sheen, Sami M Ali, Mohamed D Abouzahra, and Jin Au Kong. Application of the three-dimensional finite-difference time-domain method to the analysis of pla-nar microstrip circuits. IEEE Transactions on Microwave Theory and Techniques, 38(7):849–857, 1990.

[15] James G Maloney, Kurt L Shlager, and Glenn S Smith. A simple FDTD model for transient excitation of antennas by transmission lines. IEEE Transactions on Antennas and Propagation, 42(2):289–292, 1994.

[16] PJ Dimbylow. FDTD calculations of the whole-body averaged SAR in an anatom-ically realistic voxel model of the human body from 1 MHz to 1 GHz. Physics in Medicine & Biology, 42(3):479, 1997.

[17] 吳宗霖, 鄭博仁, 黃竣南, 張孝甄, 林彥輝, et al. 行動電話及基地臺電磁波對人 體健康之影響程度評估及其防範措施. 2001.

[18] Mohammad Tariqul Islam, Mohammad Rashed Iqbal Faruque, and Norbahiah Mis-ran. Design analysis of ferrite sheet attachment for SAR reduction in human head.

Progress In Electromagnetics Research, 98:191–205, 2009.

[19] Tony W. H, Sheu, YC Wang, and JH Li. Development of a 3D staggered FDTD scheme for solving Maxwell’s equations in Drude medium. Computers & Mathe-matics with Applications, 71(6):1198–1226, 2016.

[20] Bernardo Cockburn, Fengyan Li, and Chi-Wang Shu. Locally divergence-free dis-continuous Galerkin methods for the Maxwell equations. Journal of Computational Physics, 194(2):588–610, 2004.

[21] N Anderson and AM Arthurs. Helicity and variational principles for Maxwell’s equations. International Journal of Electronics, 54(6):861–864, 1983.

[22] JS Kole, MT Figge, and Hans De Raedt. Higher-order unconditionally stable al-gorithms to solve the time-dependent Maxwell equations. Physical Review E, 65(6):066705, 2002.

[23] Stephen D Gedney. An anisotropic perfectly matched layer-absorbing medium for the truncation of FDTD lattices. IEEE Transactions on Antennas and Propagation, 44(12):1630–1639, 1996.

[24] Saul Abarbanel, D Gottlieb, and Jan S Hesthaven. Non-linear PML equations for time dependent electromagnetics in three dimensions. Journal of Scientific Comput-ing, 28(2):125–137, 2006.

[25] Mustafa Kuzuoglu and Raj Mittra. Frequency dependence of the constitutive pa-rameters of causal perfectly matched anisotropic absorbers. IEEE Microwave and Guided Wave Letters, 6(12):447–449, 1996.

[26] Raymond Luebbers, Forrest P Hunsberger, Karl S Kunz, Ronald B Standler, and Michael Schneider. A frequency-dependent finite-difference time-domain formula-tion for dispersive materials. IEEE Transacformula-tions on Electromagnetic Compatibility, 32(3):222–227, 1990.

[27] Philip J Morrison. The Maxwell-Vlasov equations as a continuous Hamiltonian sys-tem. Physics Letters A, 80(5-6):383–386, 1980.

[28] Jerrold E Marsden and Alan Weinstein. The Hamiltonian structure of the Maxwell-Vlasov equations. Physica D: Nonlinear Phenomena, 4(3):394–406, 1982.

[29] XW Lu and R Schmid. Symplectic algorithms for Maxwell’s equations. In Pro-ceedings of the International Conference on New Applications of Multisymplectic Field Theories, pages 10–12, 1999.

[30] Zhi-Xiang Huang and Xian-Liang Wu. Symplectic partitioned Runge-Kutta scheme for Maxwell’s equations. International Journal of Quantum Chemistry, 106(4):839–

842, 2006.

[31] Ikuo Saitoh, Yoshio Suzuki, and Norio Takahashi. The symplectic finite difference time domain method. IEEE Transactions on Magnetics, 37(5):3251–3254, 2001.

[32] Tony W. H, Sheu and R. K Lin. An incompressible Navier-Stokes model imple-mented on nonstaggered grids. Numerical Heat Transfer: Part B: Fundamentals, 44(3):277–394, 2003.

[33] P. H Chiu, Tony W. H, Sheu, and R. K Lin. Development of a Dispersion Relation-Preserving Upwinding Scheme for Incompressible Navier-Stokes Equations on Non-Staggered Grids. Numerical Heat Transfer, Part B: Fundamentals, 48(6):543–569, 2005.

[34] Dejan Krstić, Darko Zigar, Dejan Petković, Dušan Sokolović, Boris Đinđić, Nenad Cvetković, Jovica Jovanović, and Nataša Đinđić. Predicting the biological effects of mobile phone radiation absorbed energy linked to the MRI-obtained structure.

Archives of Industrial Hygiene and Toxicology, 64(1):159–168, 2013.

[35] Allen Taflove and Susan C Hagness. Computational electrodynamics: the finite-difference time-domain method. Artech house, 2005.

[36] A Yasin Citkaya and S Selim Seker. FEM modeling of SAR distribution and tem-perature increase in human brain from RF exposure. International Journal of Com-munication Systems, 25(11):1450–1464, 2012.

[37] iPhone4 circuit diagram. http://win.archimedesys.it/Share/forum/4ant.jpg.

[38] Phantom head model of human. http://grabcad.com.

[39] MR Iqbal-Faruque, N Aisyah-Husni, Md Ikbal-Hossain, M Tariqul-Islam, and Nor-bahiah Misran. Effects of mobile phone radiation onto human head with variation of holding cheek and tilt positions. Journal of Applied Research and Technology, 12(5):871–876, 2014.

[40] Akimasa Hirata and Osamu Fujiwara. The correlation between mass-averaged SAR and temperature elevation in the human head model exposed to RF near-fields from 1 to 6 GHz. Physics in Medicine & Biology, 54(23):7227, 2009.

[41] IEEE Standards Coordinating Committee et al. Ieee standard for safety levels with re-spect to human exposure to radio frequency electromagnetic fields, 3kHz to 300GHz.

IEEE C95. 1-1991, 1992.

[42] Radiofrequency Electromagnetic Fields. Evaluating compliance with FCC guide-lines for human exposure to radiofrequency electromagnetic fields. OET Bulletin, 65:10, 1997.

[43] DABT Michael Wyde, PhD. NTP Toxicology and Carcinogenicity Studies of Cell Phone Radiofrequency Radiation. pages 1–32, 2016.

[44] Deshan Yang, Mark C Converse, David M Mahvi, and John G Webster. Expand-ing the bioheat equation to include tissue internal water evaporation durExpand-ing heatExpand-ing.

IEEE Transactions on Biomedical Engineering, 54(8):1382–1388, 2007.