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the expansion order
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     For different values of the propagation distance z,the expansion order M can be chosen according to the inequality proposed.
     对于不同的传输距离z,可根据不等式来选择合适的阶数M。
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  the expansion order
The expansion coefficients are polynomials in the space variable of a degree increasing linearly with the expansion order.
      
Use of a Taylor series expansion of the body deformation in the kinematical model presents a way to refine the deformation description by increasing the expansion order.
      
The presence in the list is a function of the evaluation measure and defines the expansion order.
      
The expansion order is chosen to get an error close to that of the wavelet method.
      
The expansion order in the x-direction for both elements is kept constant at 16.
      
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In order to simulate the diffraction field of apertured beam more precisely,the higher-order field can simulate the diffraction field of apertured beam by an appropriate increase of the expansion order M as the propagation distance z decreases.For different values of the propagation distance z,the expansion order M can be chosen according to the inequality proposed.Taking the super-Gaussian beam as an example,numerical calculation is performed to illustrate the application of the theoretical formulations.The...

In order to simulate the diffraction field of apertured beam more precisely,the higher-order field can simulate the diffraction field of apertured beam by an appropriate increase of the expansion order M as the propagation distance z decreases.For different values of the propagation distance z,the expansion order M can be chosen according to the inequality proposed.Taking the super-Gaussian beam as an example,numerical calculation is performed to illustrate the application of the theoretical formulations.The results obtained in this paper are useful for studying the propagation of optical beam diffracted by an aperture.

为了模拟受光阑限制光束衍射场的分布,利用泰勒展开得到了一系列的高阶修正场。随着传输距离z的减少,只需增大到合适的阶数M即可模拟衍射场分布。对于不同的传输距离z,可根据不等式来选择合适的阶数M。以超高斯光束为例,用数值计算例说明理论公式的应用。所得结果对于研究通过光阑衍射光束的传输是有用的。

A class of hybrid basis are designed for Legengre spectral element method and it's linear independence is proved.As a result,a new Legendre spectral element scheme is developed.The local lagrangian basis are used at the boundaries of the element,and the modified Legendre polynomials are adopted interiorly.Numerical tests show that high accuracy can be obtained with the hybrid local basis like the traditional spectral element method.What's more,the element matrices have sparsity characteristic and can be reused...

A class of hybrid basis are designed for Legengre spectral element method and it's linear independence is proved.As a result,a new Legendre spectral element scheme is developed.The local lagrangian basis are used at the boundaries of the element,and the modified Legendre polynomials are adopted interiorly.Numerical tests show that high accuracy can be obtained with the hybrid local basis like the traditional spectral element method.What's more,the element matrices have sparsity characteristic and can be reused when the expansion order are different.

针对勒让德谱元方法,构造了一类混合局部基函数,并证明了其线性无关特点。在此基础上,给出了一种勒让德谱元计算格式:在元素端点采用局部拉格朗日基函数,在元素内部采用调整后的局部勒让德多项式。进行了正确性和精度测试,数值实验结果表明该方法能够有效地实现高计算精度,且其计算矩阵比经典谱元方法更为简单,并具有良好的数据重用性和稀疏特点。

 
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