球面三角形上的数值积分公式的构造

Constructing Cubature Formulae on an Arbitrary Spherical Triangle

研究定义在球面三角形上函数的数值积分,通过积分的插值多项式函数构造具有多项式精度的插值型求积公式,以及给出精确计算球面三角形上多项式函数的方法.通过把其定义域上的积分化为平面单纯形{u=(u1,u2,u3):u1+u2+u3=1,u1,u2,u3≥0}上的积分,然后利用平面单纯形上数值积分公式给出其在球面三角形上的对d次齐次多项式精确成立Gauss求积分式的构造方法,给出了基于平面单纯形上Gauss型求积公式的一种近似求积公式,这种方法确定求积结点与求积系数比较简单,从而更具有应用前景.

The main purpose is to construct cubature formulae on an arbitrary spherical triangle. Firstly, a method for accurately computing the definite integral of spherical polynomial functions on a spherical triangle is proposed. Then interpolating cubature formulae is given based on La_grange interpolation formulae. Secondly, it makes use of the cubature formulac on the triangle to construct cubature formulae on the correspondent spherical triangle. Finally, some tables to show the exact points and correspondent coefficients are given in these formulae.