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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
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.
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- Research Article
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- © The Author(s) 2016
References
Berntsen, J. and Espelid, T. O., ‘Algorithm 706, DCUTRI: an algorithm for adaptive cubature over a collection of triangles’, ACM TOMS
18 (1992) no. 3, 329–342.Google Scholar
Cools, R., ‘Monomial cubature rules since “Stroud”: a compilation—part 2’, J. Comput. Appl. Math.
112 (1999) 21–27.Google Scholar
Cools, R., Laurie, D. and Pluym, L., ‘Algorithm 764: Cubpack++: A C++ package for automatic two-dimensional cubature’, ACM TOMS
23 (1997) no. 1, 1–15.CrossRefGoogle Scholar
Cools, R. and Rabinowitz, P., ‘Monomial cubature rules since “Stroud”: a compilation’, J. Comput. Appl. Math.
48 (1993) 309–326.Google Scholar
Ritsema van Eck, H. J., Kors, J. A. and van Herpen, G., ‘The U wave in the electrocardiogram: a solution for a 100-year-old riddle’, Cardiovasc Res.
67 (2005) no. 2, 256–262.Google Scholar
Hahn, T., ‘CUBA – a library for multidimensional numerical integration’, Comput. Phys. Commun.
168 (2005) 78–95.CrossRefGoogle Scholar
Lee, D., Tien, H. C., Luo, C. P. and Luk, H.-N., ‘Hexagonal grid methods with applications to partial differential equations’, Int. J. Comput. Math.
91 (2014) 1986–2009.Google Scholar
Lyness, J. N. and Cools, R., ‘A survey of numerical cubature over triangles’, Preprint MCS-P410-0194, Argonne National Laboratory, Argonne, IL, 1994.Google Scholar
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