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Showing 1 to 20 of 24 for “"Gaussian quadrature"”.
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Gaussian Quadrature for computer aided robust design
… required, but none have supplanted Monte Carlo. Gaussian Quadrature (GQ) is presented here as a new option with significant benefits for many types of engineering problems. Advantages of GQ include: as few as 2*(number of noise factors) simulation runs required to estimate performance mean and …
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Computation of nodes and weights of Gaussian Quadrature rule by using Jacobi method
… a useful connection between nodes and weights of Gaussian quadrature and eigenvalues and eigenvectors. Thus the need for faster methods to solve these larger eigenvalue problems has become very important. A standard textbook method for finding the eigenvalues of a matrix A is to solve for the …
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O método de Equação Integral com Quadratura Gaussiana para otimizar os parâmetros do gráfico de controle multivariado de Somas Acumuladas
… this work the method of Integral Equation with Gaussian Quadrature to optimize the main parameters ARL, k and h of the multivariate cumulative sum control chart (MCUSUM) is proposed. This method involves the derivation of an analytical integral equation, whose numerical resolution way Gaussian …
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The Boundary Integral Equation Method for Torsion of an Inhomogeneous Variable Diameter Shaft
… of the functions and the boundary. Gaussian quadrature with four Gaussian points are used for the numerical integration.
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An arbitrarily high-order, unstructured, free-wake panel solver
… curved, high-order panels using adaptive Gaussian quadrature is detailed. Furthermore, automated wake handling is addressed and a method to robustly solve for the steady-state free-wake rollup is proposed. Finally, a Fast Multipole Method with a complexity that scales as O(N) is also …
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Infinite Orthotropic plate on an elastic foundation with a traverse point load
… is carried out numerically, via the Gaussian Quadrature scheme, to obtain the real response. Symmetry of the transform response due to the material orthotropy has been used to reduce the effort involved in performing the integration. Results indicated a similar symmetric behavior for …
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Impact of Source Zone and Pumping Well Orientation on Dissolved Contaminant Dilution Factor
… with cases 4- 6 are solved in MATLAB using Gaussian quadrature and Gaussian Kronrod integration methods and demonstrate how each of these source types impacts the dilution factor calculation. After analyzing the results for the first analytical model, the overall conclusion is that the …
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Uma aplicação do Método dos Elementos de Contorno a problemas da elastodinâmica no domínio da frequência
… case is presented. The numerical integration (Gaussian Quadrature) is employed to evaluate all integrals except those in the Cauchy principal value sense which are performed analytically. The third order tensors needed for the evaluation of internal stresses are also derived. Finally, three …
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A quadrature-based technique for robust design with computer simulations
… simulations. This method is based on the Hermite-Gaussian quadrature for a single input. It is extended to multiple variables, in which case, for simulations with n randomly varying inputs, the method requires 4n + 1 samples. For situations in which the polynomial response is separable, it is …
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Percolação em barragens de terra em regime permanente e transiente com o método dos elementos de contorno
… in order to improve the accuracy of Gaussian quadrature schemes in the near-singularity range. An adequate treatment of discontinuities significantly reduces numerical oscillations along the free surface making smoothing procedures unnecessary, even if an explicit time marching scheme …
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Uma formulação de elementos de contorno para análise de vibrações livres
… functions over each boundary element. Gaussian Quadrature is used to compute integrals over non-singular elements. As usual in Boundary Element analysis, rigid body motion considerations are employed to evaluate the contributions of the Cauchy principal value integrals. Four examples …
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Mathematical modeling of adhesive layer cracks utilizing integral equations
… algorithm, Fast Fourier Transform techniques, Gaussian inversion, Gaussian quadrature and Romberg quadrature. The numerically sensitive regions were identified. Finally, recommendations for future work and possible solutions to handle the numerically sensitive regions were presented.
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Improved collocation methods with application to direct trajectory optimization
… methods are based on a family of modified Gaussian quadrature rules. This family of rules includes the basic trapezoid and Simpson quadrature rules. The collocation schemes derived from the trapezoid and Simpson rules are in use today for solving a variety of optimal control problems. These …
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A novel boundary element method for low Reynolds number external flow of biological fluid dynamics
… functions, linear shape functions, and two-point Gaussian quadrature with analytic removal of the Green's function singularity for the integrations.First, we compare against various methods for the benchmark problems of flow past a circular cylinder and also a cylinder with an elliptical …
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Towards Improvement of Numerical Accuracy for Unstructured Grid Flow Solver
… interpolation is introduced as a substitution to Gaussian quadrature to achieve the higher order surface integration on mixed element unstructured grids.</p><p>The proposed high order improvements for unstructured grid schemes have been tested for a wide range of flows from very low Mach number to …
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The use of stochastic collocation for sampling from expensive distributions with applications in finance
… first kind as collocation points, as opposed to Gaussian quadrature points used by Babuˇska et al. (2007), Loeven et al. (2007) and Grzelak et al. (2015). The roots of the Chebyshev polynomials are constrained to lie in a specified closed interval and hence are convenient to use when the …
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Numerical methods for systems of highly oscillatory ordinary differential equations
… and fluid dynamics. Classical methods based on Gaussian quadrature fail to approximate oscillatory integrals. In this work we introduce numerical methods which share the remarkable feature that the accuracy of approximation improves as the frequency of oscillation increases. Asymptotically, our …
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Impacts of Ignoring Nested Data Structure in Rasch/IRT Model and Comparison of Different Estimation Methods
… (PQL), Laplace approximation, and Adaptive Gaussian Quadrature (AGQ), commonly used in HGLM in terms of accuracy and efficiency in estimating parameters. As expected, PQL tended to produce seriously biased item difficulty estimates and ability variance estimates whereas almost unbiased for …
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Density estimation and some topics in multivariate analysis
… a comparison is made between the midpoint and Gaussian quadrature methods. FORTRAN programs are included. Part III - entitled "Non-parametric density estimation," begins with an extensive literature review of non-parametric methods for estimating probability densities based on a sample of N …
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