Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
469340 | Computers & Mathematics with Applications | 2010 | 14 Pages |
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.
Related Topics
Physical Sciences and Engineering
Computer Science
Computer Science (General)
Authors
Hong Xiao, Zydrunas Gimbutas,