Results 141 to 150 of about 434 (170)

Numerical Approximation of Surface Integrals Using Mixed Cubature Adaptive Scheme

Annals of Pure and Applied Mathematics, 2020
This research described the development of a new mixed cubature rule for evaluation of surface integrals over rectangular domains. Taking the linear combination of Clenshaw-Curtis 5- point rule and Gauss-Legendre 3-point rule ( each rule is of same precision i.e. precision 5) in two dimensions the mixed cubature rule of higher precision was formed (i.e.
Pritikanta Patra, Debasish Das, Rajani Ballav Dash   +2 more
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On numerical cubatures of nearly singular surface integrals arising in BEM collocation

Computing, 1994
The discretization of the boundary element method (BEM) in \(\mathbb{R}^ 3\) using collocation requires the numerical estimation of numerous nearly singular surface integrals. Efficient computational methods tailored to this application are developed. Local polar coordinates with a corner of the triangular surface elements as origin are used, and the ...
Hackbusch, W, Sauter, S A
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Numerical Simulation by the Quadrature and Cubature Methods

Proceedings of International Petroleum Conference and Exhibition of Mexico, 1994
ABSTRACT In this paper, practical quadrature and cubature formulae for numerical differentiation, integration, interpolation, and extrapolation purposes are derived; the method for determination of the quadrature and cubature weights is given, and the procedure for development of finite-analytic quadrature and cubature schemes is ...
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Parallel Algorithms of Numeric Integration Using Lattice Cubature Formulas

2009
The results of theory and applications of optimal lattice cubature formulas are described. The approximate integration program based on lattice formulas is considered. It has sufficiently high precision for complicated domains with smooth boundaries and dimensions up to 10 and high efficiency of paralleling.
Marat D. Ramazanov, Dzhangir Y. Rakhmatullin   +1 more
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On the numerical solution of non-linear equation characterizing minimal cubature formulae

Computing, 1980
A cubature formula with degree of exactness ≦2k−2 has at leastk(k+1)/2 knots. The existence of such minimal formulae is equivalent to the existence of solutions of a system of quadratic equations. Each solution of such a system generates in a uniquely determined way a minimal formula. For the square [−1, 1]2 as domain of integration and for some weight-
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Multidimensional Euler Summation Formulas and Numerical Cubature

1982
The purpose of the present paper is the study of formulas and methods for numerical computation of multidimensional integrals. The entire discussion is based on multidimensional generalizations of Euler summation formula. Cubature formulas are considered, estimates of the truncation error are given. The theory of Green’s (lattice) functions to elliptic
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Learning Curves for Gaussian Processes via Numerical Cubature Integration

2011
This paper is concerned with estimation of learning curves for Gaussian process regression with multidimensional numerical integration. We propose an approach where the recursion equations for the generalization error are approximately solved using numerical cubature integration methods. The advantage of the approach is that the eigenfunction expansion
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Finite-Analytic Cubature Based Numerical Method for Reservoir Simulation

ECMOR III - 3rd European Conference on the Mathematics of Oil Recovery, 1992
This paper presents the application of the method of integro-differential cubature for efficient solution of reservoir models. The application of this method is illustrated by solving the Buckley-Leverett model for water flooding of naturally fractured oil reservoirs.
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Numerical integration in the virtual element method with the scaled boundary cubature scheme

International Journal for Numerical Methods in Engineering
AbstractThe virtual element method (VEM) is a stabilized Galerkin method on meshes that consist of arbitrary (convex and nonconvex) polygonal and polyhedral elements. A crucial ingredient in the implementation of low‐ and high‐order VEM is the numerical integration of monomials and nonpolynomial functions over such elements.
Eric B. Chin, Franco Dassi, Gianmarco Manzini, N. Sukumar   +3 more
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Numerical Quadrature and Cubature.

Mathematics of Computation, 1982
Philip Rabinowitz, H. Engels
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