Recurrence Relations for a Family of Orthogonal Polynomials on a Triangle
Recurrence Relations for a Family of Orthogonal Polynomials on a Triangle
复制标题
三角形上的一族正交多项式的递推关系
DOI：
10.1007/978-3-030-39647-3_5
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
Geoff Vasil
中科院分区：
文献类型：
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作者：
S. Olver;Alex Townsend;Geoff Vasil
本文导出了三角形上正交多项式与其偏导数之间的稀疏递推关系，类似于雅可比多项式的递推关系。我们通过引入梯形运算符以系统的方式导出这些递归，这些梯形运算符通过递增或递减相关参数来将一个正交多项式映射到另一个。我们将结果应用于有效地计算三角形上函数的多项式逼近的拉普拉斯函数，使用数千个多项式的次数，即数百万个自由度。
This paper derives sparse recurrence relations between orthogonal polynomials on a triangle and their partial derivatives, which are analogous to recurrence relations for Jacobi polynomials. We derive these recurrences in a systematic fashion by introducing ladder operators that map an orthogonal polynomial to another by incrementing or decrementing its associated parameters by one. We apply the results to efficiently calculating the Laplacian of polynomial approximations of functions on the triangle, using polynomial degrees in the thousands, i.e., millions of degrees of freedom.