Gauss-Green cubature and moment computation over arbitrary geometries

Authors:
Alvise Sommariva;Marco Vianello
Affiliations:
Department of Pure and Applied Mathematics, University of Padua, Italy;Department of Pure and Applied Mathematics, University of Padua, Italy
Venue:
Journal of Computational and Applied Mathematics
Year:
2009

Citing 10
Cited 1

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Abstract

We have implemented in Matlab a Gauss-like cubature formula over arbitrary bivariate domains with a piecewise regular boundary, which is tracked by splines of maximum degree p (spline curvilinear polygons). The formula is exact for polynomials of degree at most 2n-1 using N~cmn^2 nodes, 1@?c@?p, m being the total number of points given on the boundary. It does not need any decomposition of the domain, but relies directly on univariate Gauss-Legendre quadrature via Green's integral formula. Several numerical tests are presented, including computation of standard as well as orthogonal moments over a nonstandard planar region.