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Gauss quadrature 1

Gauss-Legendre quadrature 1

Hankel transformation 1

Hermite polynomial 1

Laguerre polynomial 1

Legendre polynomial 1

Rosenblatt transformation 1

anisotropic 1

extended Gauss integration 1

extended sparse grid 1

extract roots 1

high-order moments analysis 1

interlayer condition 1

maximum entropy principle 1

multi-layered structure 1

transversely isotropic 1

uncertainty propagation analysis 1

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High-precision Numerical Computation of High-degree Gauss quadrature Nodes

Zhang Qingli,Wang Xiaomei,Yin Shaotang,Jiang Haihe

Strategic Study of CAE 2008, Volume 10, Issue 2, Pages 35-40

Abstract:

Gauss quadrature is used widely in many fields such as the engineeringThe nodes and weight factors of Gauss-quadrature are essential data to the numerical integration.compute the zeroes of the high-degree Legendre, Laguerre and Hermite polynomials, which are the nodes of Gauss-Legendre, Gauss-Laguerre and Gauss-Hermite Quadrature, respectively, is studied, and a very efficient algorithm

Keywords： Gauss quadrature Legendre polynomial Laguerre polynomial Hermite polynomial extract roots

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Anisotropy of multi-layered structure with sliding and bonded interlayer conditions

Lingyun YOU, Kezhen YAN, Jianhong MAN, Nengyuan LIU

Frontiers of Structural and Civil Engineering 2020, Volume 14, Issue 3, Pages 632-645 doi: 10.1007/s11709-020-0617-4

Abstract: Gauss-Legendre quadrature is a key scheme in the numerical inversion process.

Keywords： multi-layered structure Hankel transformation anisotropic transversely isotropic interlayer condition Gauss-Legendre

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Uncertainty propagation analysis by an extended sparse grid technique

X. Y. JIA, C. JIANG, C. M. FU, B. Y. NI, C. S. WANG, M. H. PING

Frontiers of Mechanical Engineering 2019, Volume 14, Issue 1, Pages 33-46 doi: 10.1007/s11465-018-0514-x

Abstract: The proposed method incorporates the extended Gauss integration into the uncertainty propagation analysistransformation, the various types of extended integration points are transformed into the extended Gauss-Hermite

Keywords： uncertainty propagation analysis extended sparse grid maximum entropy principle extended Gauss integration