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spherical harmonic synthesis
相关语句
  球谐综合
     The problem of spherical harmonic synthesis for the gravitational field realized directly by the Walsh transform in sequency domain is put forward in this paper.
     提出直接在序率域内用Walsh变换实现引力场球谐综合的问题。
短句来源
     The values of spherical harmonic synthesis obtained by using three methods are always indentical for a given order and altitude.
     对于给定的阶数和飞行高度,3种方法求得的球谐综合值总是完全一致的;
短句来源
     The conclusions are useful for selecting computing methods of ALFs in spherical harmonic synthesis and analysis.
     文中结论为超高阶次球谐综合与球谐分析的数值计算提供了可靠的依据。
短句来源
  “spherical harmonic synthesis”译为未确定词的双语例句
     A WALSH TRANSFORM METHOD OF SPHERICAL HARMONIC SYNTHESIS FOR GRAVITATIONAL FIELD
     引力场球谐综合的Walsh变换方法
短句来源
     In this paper,a numerical computing principle of spherical harmonic synthesis and analysis is introduced,and its inherent parallelizability is studied. Then a parallel computing strategy of domain division and collective communication is proposed.
     本文介绍了球谐合成和分析问题的数值计算原理,研究分析了其内在的并行性,提出了区域划分和聚合通信的并行计算策略。
短句来源
  相似匹配句对
     The Improvement on Spherical Harmonic Expansion
     球谐函数级数式的改化形式
短句来源
     The spherical harmonic analysis in geomagnetism and gravitation
     在地磁学与地球重力学中的球谐分析
短句来源
     Parallel computation of spherical harmonic analysis and synthesis
     球谐分析及合成并行计算
短句来源
     Harmonic and Administration
     谐波及其治理
短句来源
     ON HARMONIC OF VVVF
     交流变频调速(VVVF)的谐波问题
短句来源
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  spherical harmonic synthesis
We present software for spherical harmonic analysis (SHA) and spherical harmonic synthesis (SHS), which can be used for essentially arbitrary degrees and all co-latitudes in the interval (0°, 180°).
      
Simplified techniques for high-degree spherical harmonic synthesis are extended to include gravitational potential second derivatives with respect to latitude.
      


The problem of spherical harmonic synthesis for the gravitational field realized directly by the Walsh transform in sequency domain is put forward in this paper. The Walsh transform of spherical harmonic expansion and fast algorithm is presented. The differences between the Walsh transform and the Walsh-Fourier transform, and the Fourier transform are discussed. The results of the Walsh transform and the Fourier transform made by the geopotential coefficients of the Earth's gravity field model...

The problem of spherical harmonic synthesis for the gravitational field realized directly by the Walsh transform in sequency domain is put forward in this paper. The Walsh transform of spherical harmonic expansion and fast algorithm is presented. The differences between the Walsh transform and the Walsh-Fourier transform, and the Fourier transform are discussed. The results of the Walsh transform and the Fourier transform made by the geopotential coefficients of the Earth's gravity field model OSU81 are analysed. The results of research show that the differences of corresponding vector between the Walsh transform and the Walsh-Fourier transform, and the Fourier transform are usually less than±10~(-5) in quantities. The values of spherical harmonic synthesis obtained by using three methods are always indentical for a given order and altitude. The data of grid for 1°×1°etc are similar to the Walsh functions in shape. The Walsh series will converge much faster than the Fourier series in research of gravity field. The Walsh transform can be better than the Fourier transform in computation speed, computational accuracy, data storage, convergence rate, and simplicity in method.

提出直接在序率域内用Walsh变换实现引力场球谐综合的问题。给出球谐函数展开式的Walsh变换及快速算法,讨论了Walsh变换和Walsh-Fourier变换、Fourier变换之间的差异,分析了用地球重力场模型OSU81的位系数作出的Walsh变换和Fourier变换的结果。研究表明:Walsh变换与Walsh-Fourier变换、Fourier变换对应向量在数量方面的差值通常都小于士10~(-5);对于给定的阶数和飞行高度,3种方法求得的球谐综合值总是完全一致的;1°×1°等网格数据和Walsh函数形状相近。在重力场研究中Walsh级数会比Fourier级数收敛得更快;Walsh变换在计算速度、计算准确度、数据储存、收敛速度和方法简单方面都好于Fourier变换。

The numerical stability of the construction and application of the ultra-high degree and order the Earth's gravity models lies on the computing methods of the ultra-high degree and order fully normalized associated Legendre functions(ALFs).In this paper,a lot of computing methods of ALFs including standard forward column method,standard forward row method,recursive method between every other order and degree,and Belikov column method,are detailedly discussed.Advantages and disadvantages of these methods are...

The numerical stability of the construction and application of the ultra-high degree and order the Earth's gravity models lies on the computing methods of the ultra-high degree and order fully normalized associated Legendre functions(ALFs).In this paper,a lot of computing methods of ALFs including standard forward column method,standard forward row method,recursive method between every other order and degree,and Belikov column method,are detailedly discussed.Advantages and disadvantages of these methods are analyzed and compared from three aspects: numerical efficiency,numerical precision and arithmetic overflow,when the degree and order are up to 2 160.The Belikov column method and recursive method between every other order and degree are proved to be excellent and others are not fit to compute the ultra-high degree and order ALFs by numerical tests.The conclusions are useful for selecting computing methods of ALFs in spherical harmonic synthesis and analysis.

扩展高阶和超高阶重力场模型的构制与应用的数值稳定性取决于超高阶次缔合勒让德函数的计算方法。文中详细介绍了现有的多种缔合勒让德函数的递推计算方法:标准前向列推法、标准前向行推法、跨阶次递推法和Belikov列推法。从计算速度、计算精度和计算溢出问题3个角度分析比较了阶次高至2 160阶的各种方法的优劣。通过数值试验证明,Belikov列推法和跨阶次递推法是计算超高阶次缔合勒让德函数较优的方法,而其他几种方法不能用于超高阶次缔合勒让德函数的计算。文中结论为超高阶次球谐综合与球谐分析的数值计算提供了可靠的依据。

In this paper,a numerical computing principle of spherical harmonic synthesis and analysis is introduced,and its inherent parallelizability is studied.Then a parallel computing strategy of domain division and collective communication is proposed.The parallelism of computation of spherical harmonic analysis and synthesis is achieved by applying MPI(Message Passing Interface)mode of parallel computing based on the Fourier transformation techniques.The experimental results indicate that...

In this paper,a numerical computing principle of spherical harmonic synthesis and analysis is introduced,and its inherent parallelizability is studied.Then a parallel computing strategy of domain division and collective communication is proposed.The parallelism of computation of spherical harmonic analysis and synthesis is achieved by applying MPI(Message Passing Interface)mode of parallel computing based on the Fourier transformation techniques.The experimental results indicate that the parallel implementation significantly reduces computing time,compared with serial implementation,and obtains a linear speedup and high parallel performance

本文介绍了球谐合成和分析问题的数值计算原理,研究分析了其内在的并行性,提出了区域划分和聚合通信的并行计算策略。基于傅立叶变换技术,应用MPI(消息传递接口)并行编程模式,实现了球谐分析及合成计算的并行化。实验结果表明,较之串行实现,并行实现大大缩短了计算时间,获得了近似线形加速比,取得很高的并行效率。

 
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