Gauss-Green cubature over spline curvilinear polygons
نویسندگان
چکیده
We have implemented in Matlab a Gauss-like cubature formula over 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 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 area moments over a nonstandard planar region. 2000 AMS subject classification: 65D32.
منابع مشابه
Gauss-Green cubature and moment computation over arbitrary geometries
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 ∼ cmn2 nodes, 1 ≤ c ≤ p, m being the total number of points given on the boundary. It does not need any decomposition of ...
متن کاملAn algebraic cubature formula on curvilinear polygons
We implement in Matlab a Gauss-like cubature formula on bivariate domains whose boundary is a piecewise smooth Jordan curve (curvilinear polygons). The key tools are Green’s integral formula, together with the recent software package chebfun to approximate the boundary curve close to machine precision by piecewise Chebyshev interpolation. Several tests are presented, including some comparisons ...
متن کاملPolynomial interpolation and cubature over polygons
We have implemented a Matlab code to compute Discrete Extremal Sets (of Fekete and Leja type) on convex or concave polygons, together with the corresponding interpolatory cubature formulas. The method works by QR and LU factorizations of rectangular Vandermonde matrices on Weakly Admissible Meshes (WAMs) of polygons, constructed by polygon quadrangulation. 2000 AMS subject classification: 65D05...
متن کاملCubature rule associated with a discrete blending sum of quadratic spline quasi-interpolants
A new cubature rule for a parallelepiped domain is defined by integrating a discrete blending sum of C1 quadratic spline quasi-interpolants in one and two variables. We give the weights and the nodes of this cubature rule and we study the associated error estimates for smooth functions. We compare our method with cubature rules based on tensor products of spline quadratures and classical compos...
متن کاملChapter 5: Derivatives and Integration
2 Numerical and Symbolic Integration 2 2.1 Cubature Formulae Notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 2.2 Constructing Cubature Formulae . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2.1 Interpolatory Cubature Formulae . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2.2 Ideal Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....
متن کامل