A new method for gravity modeling using tesseroids and 2D Gauss-Legendre quadrature rule

2019 ◽  
Vol 164 ◽  
pp. 53-64 ◽  
Author(s):  
Yiyuan Zhong ◽  
Zhengyong Ren ◽  
Chaojian Chen ◽  
Huang Chen ◽  
Zhi Yang ◽  
...  
Keyword(s):  
Quadrature Rule ◽  
New Method ◽  
Gravity Modeling ◽  
Legendre Quadrature

scholarly journals Gauss-Legendre Numerical Integrations over a Quadrilateral Element in Closed Form

1970 ◽  
Vol 46 (3) ◽  
pp. 399-405 ◽  
Author(s):  
MS Islam ◽  
G Saha ◽  
N Akter
Keyword(s):  
Closed Form ◽  
Coordinate Transformation ◽  
Stiffness Matrix ◽  
Quadrature Rule ◽  
Computational Time ◽  
Quadrilateral Element ◽  
Memory Space ◽  
The Matrix ◽  
Quadrilateral Finite Element ◽  
Legendre Quadrature

In this paper we investigate the stiffness matrix of a general quadrilateral element in closed form using n x n Gauss-Legendre quadrature rule. For this, we propose four types of nodal coordinate transformation. The terms of the matrix are divided into two groups, namely - diagonal and non-diagonal. Only one term (called leading) from each group is computed, and then the remaining fourteen terms are computed from these two leading terms exploited one of the proposed types of coordinate transformation. This leads us a great savings in computational time and memory space. In order to compute the matrix we use these transformations in two ways, and thus two algorithms are given to generate the matrix. Finally, numerical example is given to verify the effectiveness of the present formulation. Keywords: Gauss-Legendre quadrature; Numerical integration; Quadrilateral finite element; Stiffness matrix; Closed form. DOI: http://dx.doi.org/10.3329/bjsir.v46i3.9050 BJSIR 2011; 46(3): 399-405

scholarly journals A Mixed Quadrature Rule by Blending Clenshaw-Curtis and Gauss-Legendre Quadrature Rules for Approximate Evaluation of Real Definite Integrals

2012 ◽  
Vol 2 ◽  
pp. 10-15
Author(s):  
Anasuya Pati ◽  
Rajani B. Dash ◽  
Pritikanta Patra
Keyword(s):  
Quadrature Rule ◽  
Quadrature Rules ◽  
Approximate Evaluation ◽  
Definite Integrals ◽  
Legendre Quadrature

A mixed quadrature rule blending Clenshaw-Curtis five point rule and Gauss-Legendre three point rule is formed. The mixed rule has been tested and found to be more effective than that of its constituent Clenshaw-Curtis five point rule.

scholarly journals A New Application of Gauss Quadrature Method for Solving Systems of Nonlinear Equations

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 432
Author(s):  
Hari M. Srivastava ◽  
Javed Iqbal ◽  
Muhammad Arif ◽  
Alamgir Khan ◽  
Yusif S. Gasimov ◽  
...  
Keyword(s):  
Nonlinear Equations ◽  
Nonlinear Boundary ◽  
Quadrature Rule ◽  
Gauss Quadrature ◽  
New Method ◽  
Systems Of Nonlinear Equations ◽  
System Of Nonlinear Equations ◽  
Numerical Comparison ◽  
Nonlinear Boundary Value Problems ◽  
Gauss Quadrature Rule

In this paper, we introduce a new three-step Newton method for solving a system of nonlinear equations. This new method based on Gauss quadrature rule has sixth order of convergence (with n=3). The proposed method solves nonlinear boundary-value problems and integral equations in few iterations with good accuracy. Numerical comparison shows that the new method is remarkably effective for solving systems of nonlinear equations.

scholarly journals New error bounds for Gauss-Legendre quadrature rules

Filomat ◽  
2014 ◽  
Vol 28 (6) ◽  
pp. 1281-1293 ◽  
Author(s):  
Mohammad Masjed-Jamei
Keyword(s):  
Quadrature Formula ◽  
Error Bounds ◽  
Quadrature Rule ◽  
Order Derivative ◽  
Quadrature Rules ◽  
Linear Kernel ◽  
Large N ◽  
Interpolatory Quadrature ◽  
Integrand Function ◽  
Legendre Quadrature

It is well-known that the remaining term of any n-point interpolatory quadrature rule such as Gauss-Legendre quadrature formula depends on at least an n-order derivative of the integrand function, which is of no use if the integrand is not smooth enough and requires a lot of differentiation for large n. In this paper, by defining a specific linear kernel, we resolve this problemand obtain new bounds for the error of Gauss-Legendre quadrature rules. The advantage of the obtained bounds is that they do not depend on the norms of the integrand function. Some illustrative examples are given in this direction.

Selective Sampling and Orientation of Non-Homogeneous Tissues

1968 ◽  
Vol 26 ◽  
pp. 98-99
Author(s):  
C. C. Clawson ◽  
L. W. Anderson ◽  
R. A. Good
Keyword(s):  
Electron Microscopy ◽  
Electron Microscope ◽  
Light Microscopy ◽  
Random Sampling ◽  
New Method ◽  
Microscope Examination ◽  
Small Areas ◽  
Selective Sampling ◽  
Large Numbers ◽  
Specific Orientation

Investigations which require electron microscope examination of a few specific areas of non-homogeneous tissues make random sampling of small blocks an inefficient and unrewarding procedure. Therefore, several investigators have devised methods which allow obtaining sample blocks for electron microscopy from region of tissue previously identified by light microscopy of present here techniques which make possible: 1) sampling tissue for electron microscopy from selected areas previously identified by light microscopy of relatively large pieces of tissue; 2) dehydration and embedding large numbers of individually identified blocks while keeping each one separate; 3) a new method of maintaining specific orientation of blocks during embedding; 4) special light microscopic staining or fluorescent procedures and electron microscopy on immediately adjacent small areas of tissue.

A new method for the determination of nitrates

1960 ◽  
Vol 23 ◽  
pp. 227-232 ◽  
Author(s):  
P WEST ◽  
G LYLES
Keyword(s):  
New Method
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