Two approaches compute symmetric triangle quadrature rules that exactly integrate chosen sequences of singular functions; on a test electromagnetic integral, they reduce relative error by up to two orders of magnitude versus polynomial rules.
Analytical computation of moderate-degree fully-symmetric cubature rules on the triangle
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abstract
A method is developed to compute analytically fully symmetric cubature rules on the triangle by using symmetric polynomials to express the two kinds of invariance inherent in these rules. Rules of degree up to 15, some of them new and of good quality, are computed and presented.
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Symmetric Triangle Quadrature Rules for Arbitrary Functions
Two approaches compute symmetric triangle quadrature rules that exactly integrate chosen sequences of singular functions; on a test electromagnetic integral, they reduce relative error by up to two orders of magnitude versus polynomial rules.