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A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions

Authors:

Hong Xiao,

Zydrunas GimbutasAuthors Info & Claims

Computers & Mathematics with Applications, Volume 59, Issue 2

Pages 663 - 676

Published: 01 January 2010 Publication History

Abstract

We present a numerical algorithm for the construction of efficient, high-order quadratures in two and higher dimensions. Quadrature rules constructed via this algorithm possess positive weights and interior nodes, resembling the Gaussian quadratures in one dimension. In addition, rules can be generated with varying degrees of symmetry, adaptable to individual domains. We illustrate the performance of our method with numerical examples, and report quadrature rules for polynomials on triangles, squares, and cubes, up to degree 50. These formulae are near optimal in the number of nodes used, and many of them appear to be new.

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A numerical algorithm for the construction of efficient quadrature rules in two and higher dimensions
1. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis
2. Theory of computation

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cover image Computers & Mathematics with Applications

Computers & Mathematics with Applications Volume 59, Issue 2

January, 2010

446 pages

ISSN:0898-1221

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Pergamon Press, Inc.

United States

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Published: 01 January 2010

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Montoya TZingg D(2022)A Unifying Algebraic Framework for Discontinuous Galerkin and Flux Reconstruction Methods Based on the Summation-by-Parts PropertyJournal of Scientific Computing10.1007/s10915-022-01935-392:3Online publication date: 1-Sep-2022
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