高阶时域多分辨率算法在光子带隙结构中的应用  

Applying High-order MRTD(Multi-Resolution Time Domain) Theory to Photonic Band Gap Structure

作　　者：李源[1] 许家栋[1] 曾渊 罗永健[3] 

机构地区：[1]西北工业大学电子信息学院,陕西西安710072 [2]中航航空电子有限公司,北京100086 [3]西安通信学院,陕西西安710106

出　　处：《西北工业大学学报》2011年第4期608-613,共6页Journal of Northwestern Polytechnical University

基　　金：陕西省自然科学基础研究计划(2006F15);西北工业大学科技创新基金(2006CR11)资助

摘　　要：将具有强稳定特性的高阶龙格库塔方法和小波多分辨分析理论相结合,用于电磁场数值分析计算,消除了传统时域多分辨率算法中低阶时间微分离散格式对算法整体精度提高的制约,降低了由时间网格剖分引起的数值差分各向异性,并且通过选择龙格库塔方法迭代的误差阶数和空间场量的小波展开层数,可以得到算法在时域和空域上任意高阶的收敛特性,真正实现了电磁目标的多分辨率分析。通过一维电磁波传播和二维光子带隙结构的数值仿真,验证了改进策略提出的必要性和正确性。Aim. The introduction of the full paper reviews some papers in the open literature, points out what we believe to be their shortcomings, and then proposes applying MRTD theory to PBG （Photonic Band Gap） structure. Sections 1 through 4 explain our application, section 1 briefs MRTD theory. Section 2 explains HMRTD （ High-order MRTD） theory, its core consists of： ＂Combine the high-order strong stability preserving Runge-Kutta method and wavelet multi-resolution analysis theory in numerical simulation of electromagnetic field, and eliminate the constraints for improving the overall accuracy of traditional MRTD algorithm with low-order time differential discrete format. By selecting the order of iterative error for Runge-Kutta method and wavelet basis function, arbitrary high order convergence in time and space can be obtained and the truly multi-resolution analysis of objectives is achieved＂. Table 1 and Figs. 2 and 3 in section 3 show preliminarily that the performance of HMRTD algorithm is better than that of MRTD algorithm. Section 4 give the numerical simulation of one-dimensional electromagnetic wave propagation and two-dimensional photonic band gap structure;the simulation results in Figs. 5 and 6 verify preliminarity the necessity and correctness of the new HMRTD algorithm.

关 键 词：龙格库塔方法 小波变换 时域多分辨率算法 

分 类 号：TN253[电子电信—物理电子学]