No CrossRef data available.
Article contents
A fourth-order seven-point cubature on regular hexagons
Part of:
Numerical approximation and computational geometry
Elliptic equations and systems
Basic linear algebra
Published online by Cambridge University Press: 01 April 2016
Abstract
Core share and HTML view are not possible as this article does not have html content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
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.
- Type
- Research Article
- Information
- Copyright
- © 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.CrossRefGoogle Scholar
Cools, R., ‘Monomial cubature rules since “Stroud”: a compilation—part 2’, J. Comput. Appl. Math.
112 (1999) 21–27.CrossRefGoogle Scholar
Cools, R., ‘An encyclopaedia of cubature formulas’, J. Complexity
19 (2003) 445–453.CrossRefGoogle 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.CrossRefGoogle 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.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle 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