基于非零散度關(guān)系的交替方向隱式減縮FDTD算法
An Algorithm of ADI-FDTD and R-FDTD Based on Non-zero Divergence Relationship
-
摘要: 該文證明了即使在無源區(qū)域，交替方向隱式時域有限差分法(ADI-FDTD)所給出的電磁場量不滿足零散度關(guān)系，同時推導(dǎo)出了該散度關(guān)系的具體表達(dá)式。基于該非零散度關(guān)系，將不受Courant穩(wěn)定條件限制的ADI-FDTD法和能節(jié)約最多達(dá)1/3內(nèi)存的減縮時域有限差分(R-FDTD)法結(jié)合，提出了一種新的交替方向隱式減縮FDTD算法。該算法保留了ADI-FDTD能增大時間步長，縮短計(jì)算時間的優(yōu)點(diǎn)，同時與ADI-FDTD相比節(jié)約了最多達(dá)1/3(三維)或2/5(二維)的內(nèi)存。與基于零散度關(guān)系的ADI/R-FDTD相比，該算法避免了采用長時間步長計(jì)算時的發(fā)散現(xiàn)象。應(yīng)用所提出的ADI/R-FDTD算法計(jì)算了二維自由空間波的傳播及一維頻率選擇表面垂直入射的問題，計(jì)算結(jié)果與ADI-FDTD計(jì)算結(jié)果完全一致，驗(yàn)證了ADI/R-FDTD的正確性和有效性。
-
關(guān)鍵詞:
- FDTD;減縮時域有限差分法(R-FDTD);交替方向隱式(ADI)技術(shù)
Abstract: In this paper, it is proven that the divergence relationship of electric-field and magnetic-field is non-zero even in charge-free regions, when the electric-field and magnetic-field are calculated with Alternating Direction Implicit Finite-Difference Time-Domain (ADI-FDTD) method, and the concrete expression of the divergence relationship is derived. Based on the non-zero divergence relationship, the ADI-FDTD which is unconditionally stable is combined with the Reduced Finite-Difference Time-Domain(R-FDTD). In the proposed method (ADI/R-FDTD), the merit of ADI-FDTD, e.g. increasing time step size and decreasing calculation time, is kept, at the same time, the memory requirement is reduced by 1/3(3-D) or 2/5(2-D) of the memory requirement of ADI-FDTD. Compare to the ADI/R-FDTD based on regular zero divergence relationship, the proposed algorithm is more stable when lager time step size is used. Wave propagation in 2-D free space and the scattered field of a 1-D Frequency Selective Surface(FSS) is simulated by the proposed hybrid method. Compared with ADI-FDTD，perfect agreement of numerical results indicates that ADI/R-FDTD method is correct and efficient. -
Namiki T. A new FDTD algorithm based on alternating direction implicit method [J]. IEEE Trans. on Microwave Theory and Techniques, 1999, 47(10): 20032007 .[2]Zheng F, Chen Z, Zhang J. Toward the development of a three-dimensional unconditionally stable Finite-Difference Time-Domain method [J]. IEEE Trans. on Microwave Theory and Techniques, 2000, 48(9): 19501958. .[3]George D K, Franco D F, Gregory J O, et al.. A memory-efficient formulation of the Finite-Difference Time-Domain method for the solution of Maxwell equation [J].IEEE Trans. on Microwave Theory and Techniques.2001, 49(7):1310-[4]周永剛，徐金平. 減縮時域有限差分法在電磁干擾預(yù)測中的應(yīng)用[J]. 東南大學(xué)學(xué)報，2003, 33(4): 392.395.[5]Liu Bo.[J].Gao Benqing, Tan Wei, Ren Wu. A new FDTD algorithm ADI/R-FDTD. 2002 3rd International Symposium onElectromagnetic Compatibility, Beijing, China.2002,:-[6]Tsay Wen-Jiunn, Pozar D M. Application of the FDTD technique to periodic problems in scattering and radiation [J].IEEE Microwave and Guided Wave Letters.1993, 3(8):250- -
計(jì)量
- 文章訪問數(shù): 2550
- HTML全文瀏覽量: 90
- PDF下載量: 840
- 被引次數(shù): 0
下載:
