New fully symmetric and rotationally symmetric cubature rules on the triangle using minimal orthonormal bases

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• 作者：Stefanos-Aldo Papanicolopulos ; ^{S.Papanicolopulos@ed.ac.uk" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 65D32 ; secondary ; 65D30
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2016
• 出版时间：1 March 2016
• 年：2016
• 卷：294
• 期：Complete
• 页码：39-48
• 全文大小：758 K

文摘

Cubature rules on the triangle have been extensively studied, as they are of great practical interest in numerical analysis. In most cases, the process by which new rules are obtained does not preclude the existence of similar rules with better characteristics. There is therefore clear interest in searching for better cubature rules.

Here we present a number of new cubature rules on the triangle, exhibiting full or rotational symmetry, that improve on those available in the literature either in terms of number of points or in terms of quality. These rules were obtained by determining and implementing minimal orthonormal polynomial bases that can express the symmetries of the cubature rules. As shown in specific benchmark examples, this results in significantly better performance of the employed algorithm.