时域有限差分法(FDTD)是计算电磁领域中的一类非常重要的研究工具。而 Taylor 级数展开定理是构造差分格式的一种重要方法,例如 Yee 格式采用二阶 Taylor 格式,Fang 格式采用四阶 Taylor 格式。本文借助于采样定理,详细分析了不同阶 Tay...时域有限差分法(FDTD)是计算电磁领域中的一类非常重要的研究工具。而 Taylor 级数展开定理是构造差分格式的一种重要方法,例如 Yee 格式采用二阶 Taylor 格式,Fang 格式采用四阶 Taylor 格式。本文借助于采样定理,详细分析了不同阶 Taylor 中心差分格式的谱特性以及计算误差,并将任意阶 Taylor 中心差分格式用于数值求解麦克斯韦方程中,严格导出了稳定性条件和数值色散关系的表达式,引入了新的误差定义来衡量算法的好坏。详细地研究了 Courant 数、网格分辨率 CPW 和网格长度比率等因素对于数值色散误差的影响,为基于 Taylor 差分格式的 FDTD 算法的研究提供了有用的参考。展开更多
By analyzing the structure of the objective function based on error sum of squares and the information provided by the objective function, the essential problems in the current parameter estimation methods are summari...By analyzing the structure of the objective function based on error sum of squares and the information provided by the objective function, the essential problems in the current parameter estimation methods are summarized: (1) the information extracted from the objective function based on error sum of squares is unreasonable or even wrong for parameter estimation; and (2) the surface of the objective function based on error sum of squares is more complex than that of the parameter function, which indicates that the optimal parameter values should be searched on the surface of the parameter function instead of the objective function. This paper proposes the concept of sample intersection and demonstrates the uniqueness theorem of intersection point (namely the uniqueness of optimal parameter values). According to the characteristics of parameter function surface and Taylor series expansion, a parameter estimation method based on the sample intersection information extracted from parameter function surface (PFS method) was constructed. The results of theoretical analysis and practical application show that the proposed PFS method can avoid the problems in the current automatic parameter calibration, and has fast convergence rate and good performance in parameter calibration.展开更多
The following coupled Schrodinger system with a small perturbationis considered, where β and ε are small parameters. The whole system has a periodic solution with the aid of a Fourier series expansion technique, and...The following coupled Schrodinger system with a small perturbationis considered, where β and ε are small parameters. The whole system has a periodic solution with the aid of a Fourier series expansion technique, and its dominant system has a heteroclinic solution. Then adjusting some appropriate constants and applying the fixed point theorem and the perturbation method yield that this heteroclinic solution deforms to a heteroclinic solution exponentially approaching the obtained periodic solution （called the generalized heteroclinic solution thereafter）.展开更多
文摘时域有限差分法(FDTD)是计算电磁领域中的一类非常重要的研究工具。而 Taylor 级数展开定理是构造差分格式的一种重要方法,例如 Yee 格式采用二阶 Taylor 格式,Fang 格式采用四阶 Taylor 格式。本文借助于采样定理,详细分析了不同阶 Taylor 中心差分格式的谱特性以及计算误差,并将任意阶 Taylor 中心差分格式用于数值求解麦克斯韦方程中,严格导出了稳定性条件和数值色散关系的表达式,引入了新的误差定义来衡量算法的好坏。详细地研究了 Courant 数、网格分辨率 CPW 和网格长度比率等因素对于数值色散误差的影响,为基于 Taylor 差分格式的 FDTD 算法的研究提供了有用的参考。
基金supported by the National Natural Science Foundation of China (Grant No. 51279057)the Major Program of National Natural Science Foundation of China (Grant Nos. 51190090 and 51190091)+1 种基金the Ph.D. Programs Foundation of Ministry of Education of China (Grant No.20120094120018)the Fundamental Research Funds for the Central Universities of China (Grant No. 2012B00214)
文摘By analyzing the structure of the objective function based on error sum of squares and the information provided by the objective function, the essential problems in the current parameter estimation methods are summarized: (1) the information extracted from the objective function based on error sum of squares is unreasonable or even wrong for parameter estimation; and (2) the surface of the objective function based on error sum of squares is more complex than that of the parameter function, which indicates that the optimal parameter values should be searched on the surface of the parameter function instead of the objective function. This paper proposes the concept of sample intersection and demonstrates the uniqueness theorem of intersection point (namely the uniqueness of optimal parameter values). According to the characteristics of parameter function surface and Taylor series expansion, a parameter estimation method based on the sample intersection information extracted from parameter function surface (PFS method) was constructed. The results of theoretical analysis and practical application show that the proposed PFS method can avoid the problems in the current automatic parameter calibration, and has fast convergence rate and good performance in parameter calibration.
基金supported by the National Natural Science Foundation of China(Nos.11126292,11201239,11371314)the Guangdong Natural Science Foundation(No.S2013010015957)the Project of Department of Education of Guangdong Province(No.2012KJCX0074)
文摘The following coupled Schrodinger system with a small perturbationis considered, where β and ε are small parameters. The whole system has a periodic solution with the aid of a Fourier series expansion technique, and its dominant system has a heteroclinic solution. Then adjusting some appropriate constants and applying the fixed point theorem and the perturbation method yield that this heteroclinic solution deforms to a heteroclinic solution exponentially approaching the obtained periodic solution （called the generalized heteroclinic solution thereafter）.
