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A fourth-order seven-point cubature on regular hexagons

Part of: Elliptic equations and systems Numerical approximation and computational geometry Basic linear algebra

Published online by Cambridge University Press:  01 April 2016

Daniel Lee  and
Hui-Chun Tien
Daniel Lee
Affiliation:
Department of Applied Mathematics, Tunghai University, Taichung 40704, Taiwan email danlee@thu.edu.tw
Hui-Chun Tien
Affiliation:
Department of Financial and Computational Mathematics, Providence University, Taichung 40704, Taiwan email hctien@pu.edu.tw

Abstract

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We investigate the central moments of (regular) hexagons and derive accordingly a discrete approximation to definite integrals on hexagons. The seven-point cubature rule makes use of interior and neighbor center nodes, and is of fourth order by construction. The result is expected to be useful in two-dimensional (open-field) applications of integral equations or image processing.

MSC classification

Primary: 65D32: Quadrature and cubature formulas 35J05: Laplacian operator, reduced wave equation (Helmholtz equation), Poisson equation 15A06: Linear equations
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 19 , Issue 1 , 2016 , pp. 175 - 185
Copyright
© The Author(s) 2016 

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