We propose a finite element method to compute the band structures of dispersive photonic crystals in 3D.The nonlinear Maxwell’s eigenvalue problem is formulated as the eigenvalue problem of a holomorphic operator fun...We propose a finite element method to compute the band structures of dispersive photonic crystals in 3D.The nonlinear Maxwell’s eigenvalue problem is formulated as the eigenvalue problem of a holomorphic operator function.The N´ed´elec edge elements are employed to discretize the operators,where the divergence free condition for the electric field is realized by a mixed form using a Lagrange multiplier.The convergence of the eigenvalues is proved using the abstract approximation theory for holomorphic operator functions with the regular approximation of the edge elements.The spectral indicator method is then applied to compute the discrete eigenvalues.Numerical examples are presented demonstrating the effectiveness of the proposed method.展开更多
针对机械故障振动信号的非线性与非平稳特征,提出一种基于复数微分算子的最优化分解(Optimization Decomposition Based on Complex Differential Operators,CDOOD)方法。该方法通过优化滤波器的参数将非线性信号分解,以得到的非线性信...针对机械故障振动信号的非线性与非平稳特征,提出一种基于复数微分算子的最优化分解(Optimization Decomposition Based on Complex Differential Operators,CDOOD)方法。该方法通过优化滤波器的参数将非线性信号分解,以得到的非线性信号分解余量能量最小为优化目标,在优化过程中运用复数微分算子约束得到多个内禀窄带分量(Intrinsic Narrow-Band Components,简称INBC)。将CDOOD方法应用于仿真信号和机械复合故障信号分析,并与自适应最稀疏时频分析(Adaptive Sparsest Time Frequency Analysis,简称ASTFA)方法和经验模态分解(Empirical Mode Decomposition,简称EMD)方法进行对比。结果表明,CDOOD能够有效抑制端点效应和模态混淆,并且在提高分量准确性和正交性等方面具有一定优势,同时可以有效应用于旋转机械复合故障的诊断。展开更多
基金China Postdoctoral Science Foundation Grant 2019M650460the NSF grant DMS-2011148.The research of J.Sun is supported partially by the Simons Foundation Grant 711922.
文摘We propose a finite element method to compute the band structures of dispersive photonic crystals in 3D.The nonlinear Maxwell’s eigenvalue problem is formulated as the eigenvalue problem of a holomorphic operator function.The N´ed´elec edge elements are employed to discretize the operators,where the divergence free condition for the electric field is realized by a mixed form using a Lagrange multiplier.The convergence of the eigenvalues is proved using the abstract approximation theory for holomorphic operator functions with the regular approximation of the edge elements.The spectral indicator method is then applied to compute the discrete eigenvalues.Numerical examples are presented demonstrating the effectiveness of the proposed method.
基金Supported by the National Natural Science Foundation of China(11171103)the Hunan Education Office Science Foundation of China(13C624)the Construction Program of the Key Discipline in Hunan University of Arts and Science-Applied Mathematics
文摘针对机械故障振动信号的非线性与非平稳特征,提出一种基于复数微分算子的最优化分解(Optimization Decomposition Based on Complex Differential Operators,CDOOD)方法。该方法通过优化滤波器的参数将非线性信号分解,以得到的非线性信号分解余量能量最小为优化目标,在优化过程中运用复数微分算子约束得到多个内禀窄带分量(Intrinsic Narrow-Band Components,简称INBC)。将CDOOD方法应用于仿真信号和机械复合故障信号分析,并与自适应最稀疏时频分析(Adaptive Sparsest Time Frequency Analysis,简称ASTFA)方法和经验模态分解(Empirical Mode Decomposition,简称EMD)方法进行对比。结果表明,CDOOD能够有效抑制端点效应和模态混淆,并且在提高分量准确性和正交性等方面具有一定优势,同时可以有效应用于旋转机械复合故障的诊断。
