Rapid Ascent-Entry Vehicle Mission Optimization Using hp-Adaptive Gaussian Quadrature Collocation

2017 ◽  
Author(s):  
Alexander T. Miller ◽  
Anil V. Rao
Keyword(s):  
Gaussian Quadrature ◽  
Rapid Ascent ◽  
Adaptive Gaussian Quadrature

Static deformation of a multilayered magneto-electro-elastic half-space structures due to vertical inner loading

2021 ◽  
pp. 108128652110495
Author(s):  
Peizhuo Wang ◽  
Dongchen Qin ◽  
Peng Shen ◽  
Jiangyi Chen
Keyword(s):  
Half Space ◽  
Vector Function ◽  
Stiffness Matrix ◽  
Matrix Method ◽  
Gaussian Quadrature ◽  
Elastic Half Space ◽  
Point Load ◽  
Static Deformation ◽  
Function System ◽  
Adaptive Gaussian Quadrature

The static deformation in a multilayered magneto-electro-elastic half-space under vertical inner loading is calculated using a vector function system approach and a stiffness matrix method. Firstly, the displacement, stress, and inner loading are expanded using the vector function system, and the N-type and L&M-type problems related to the expansion coefficient are constructed. Secondly, the stable stiffness matrix method is used to solve the expansion coefficients of the L&M-type problem. After introducing the boundary condition and the discontinuity of the stress caused by inner loading, the displacement and stress are calculated through adaptive Gaussian quadrature. Finally, the numerical examples considering the circular load and point load are designed and analyzed, respectively.

scholarly journals On Some Mixture Models for Over-dispersed Binary Data

2017 ◽  
Vol 6 (2) ◽  
pp. 134
Author(s):  
Bayo H. Lawal
Keyword(s):  
Mixture Models ◽  
Binary Data ◽  
Mixed Model ◽  
Gaussian Quadrature ◽  
Optimization Methods ◽  
Data Sets ◽  
Binomial Mixture ◽  
Adaptive Gaussian Quadrature ◽  
Quasi Newton ◽  
Proc Nlmixed

In this paper, we consider several binomial mixture models for fitting over-dispersed binary data. The models range from the binomial itself, to the beta-binomial (BB), the Kumaraswamy distributions I and II (KPI \& KPII) as well as the McDonald generalized beta-binomial mixed model (McGBB). The models are applied to five data sets that have received attention in various literature. Because of convergence issues, several optimization methods ranging from the Newton-Raphson to the quasi-Newton optimization algorithms were employed with SAS PROC NLMIXED using the Adaptive Gaussian Quadrature as the integral approximation method within PROC NLMIXED. Our results differ from those presented in Li, Huang and Zhao (2011) for the example data sets in that paper but agree with those presented in Manoj, Wijekoon and Yapa (2013). We also applied these models to the case where we have a $k$ vector of covariates $(x_1, x_2, \ldots, x_k)^{'}$. Our results here suggest that the McGBB performs better than the other models in the GLM framework. All computations in this paper employed PROC NLMIXED in SAS. We present in the appendix a sample of the SAS program employed for implementing the McGBB model for one of the examples.

Implementation of Adaptive Gaussian Quadrature for Improved Accuracy of Boundary Element Methods Applied to Three Dimensional Geometries

2019 ◽  
Author(s):  
Michael Davies ◽  
Joseph Saverin
Keyword(s):  
Boundary Element ◽  
State Of The Art ◽  
Gaussian Quadrature ◽  
Three Dimensional ◽  
Boundary Element Methods ◽  
Quadrilateral Elements ◽  
Adaptive Gaussian Quadrature ◽  
Improved Accuracy ◽  
Actual Geometry ◽  
Constant Source

Abstract An adaptive Gaussian quadrature method for characterizing flow over three dimensional bodies via a boundary element method using isoparametric quadrilateral elements with non-constant source and dipole strengths has been developed and tested. This method is compared to state-of-the-art methods: flat elements with constant strengths, flat elements with bilinear strengths, and twisted elements with constant dipole strengths. As such, an overview of current boundary element methods is provided. The method developed here for twisted elements with non-constant source and dipole strengths is advantageous in that it both better approximates the actual geometry of the surface and the distribution of the dipole and source strengths. The majority of current methods are lacking at least one of these attributes. The developed method has been validated by comparison to two known analytical solutions: a non-lifting ellipsoid and a Kármán-Trefftz airfoil. The flexible and robust procedure presented here results in improved accuracy of the solution to the Laplace equation around three dimensional bodies.

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