各向異性介質(zhì)在三維ADI-FDTD中的應(yīng)用
Application of Artificial Anisotropy in 3-D ADI-FDTD Method
-
摘要: 該文研究一種減小三維交替方向隱式時(shí)域有限差分法(ADI-FDTD)數(shù)值色散的新方法。通過(guò)在三維空間中合理添加各向異性介質(zhì)，達(dá)到調(diào)整相速的目的，從而減小數(shù)值色散，使計(jì)算結(jié)果更加精確。首先對(duì)添加各向異性介質(zhì)后的三維ADI-FDTD迭代公式進(jìn)行變形，并得到新的數(shù)值色散關(guān)系，從而求解得到各向異性介質(zhì)的相對(duì)介電常數(shù)。以空心波導(dǎo)和具有介質(zhì)不連續(xù)性的波導(dǎo)作為數(shù)值算例，分析不同的各向異性介質(zhì)和添加方法對(duì)計(jì)算精度的影響，并與傳統(tǒng)ADI-FDTD得到的結(jié)果和計(jì)算資源占用情況進(jìn)行比較。結(jié)果表明通過(guò)正確選擇各向異性介質(zhì)和添加方法，可以有效地減小三維ADI-FDTD數(shù)值色散。Abstract: Attention is focused on a new method to reduce the numerical dispersion of the 3-D Alternating-Direction Implicit Finite-Difference Time-Domain(ADI-FDTD) method through artificial anisotropy. As the wave propagation can be speeded up by introducing proper anisotropy parameters into the 3-D ADI-FDTD method, the numerical dispersion can be reduced and the accuracy can be improved significantly. First, the numerical formulations of the 3-D ADI-FDTD method are modified. Secondly, the new numerical dispersion relation is derived. And consequently the relative permittivity tensor of artificial anisotropy can be obtained. In order to demonstrate the accuracy and efficiency of this new method, a hollow waveguide and a waveguide with discontinuous structure are simulated as examples. In addition the reduction of numerical dispersion is investigated as a function of the relative permittivity tensor of artificial anisotropy. Furthermore, the numerical results and the computational requirements of the proposed method are compared with those of the conventional 3-D ADI-FDTD method. It is found that this new method is accurate and efficient.
-
Namiki T. A new FDTD algorithm based on alternating-direction implicit method[J].IEEE Trans. on Microwave Theory Tech.1999, 47(10):2003-2007[2]Juntunen J S, Tsiboukis T D. Reduction of numerical dispersion in FDTD method through artificial anisotropy[J].IEEE Trans. on Microwave Theory Tech.2000, 48(4):582-588[3]劉波, 任武, 高本慶, 等. 一種有效減少ADI-FDTD數(shù)值色散的方法[J]. 微波學(xué)報(bào), 2003, 19(2): 19-23.[4]Zhao Anping. Improvement on the numerical dispersion of 2-D ADI-FDTD with artificial anisotropy[J].IEEE Microwave and Wireless Components Lett.2004, 14(6):292-294[5]Zheng Fenghua, Chen Zhizhang. Numerical dispersion analysis of the unconditionally stable 3-D ADI-FDTD Method[J].IEEE Trans. on Microwave Theory Tech.2001, 49(5):1006-1009[6]Lin X P, Naishadham K. A simple technique for minimization of ABC-induced error in the FDTD analysis of microstrip discontinuities[J].IEEE Microwave Guided Wave Lett.1994, 4(12):402-404[7]Krupezevic D V, Brankovic V J, Arndt F. The wave-equation FD-TD method for the efficient eigenvalue analysis and S-matrix computation of waveguide structures[J].IEEE Trans. on Microwave Theory Tech.1993, 41(12):2109-2115 -
計(jì)量
- 文章訪問(wèn)數(shù): 2642
- HTML全文瀏覽量: 76
- PDF下載量: 797
- 被引次數(shù): 0
下載:
