triangle-cubature 0.0.2

cubature rules on triangles

Triangle Cubature Rules

This repo serves as a collection of well-tested triangle cubature rules, i.e. numerical integration schemes for integrals of the form

$$ \int_K f(x, y) ~\mathrm{d}x ~\mathrm{d}y, $$

where $K \subset \mathbb{R}^2$ is a triangle. All cubature rules are based on [1].

(Unit) Tests

To run auto tests, you do

python -m unittest discover tests/auto/

The unit tests use sympy to verify the degree of exactness of the implemented cubature rules, i.e. creates random polynomials $p_d$ of the expected degree of exactness $d$ and compares the exact result of $\int_K p_d(x, y) ~\mathrm{d}x ~\mathrm{d}y$ to the value obtained with the cubature rule at hand.

References

• [1] Stenger, Frank. 'Approximate Calculation of Multiple Integrals (A. H. Stroud)'. SIAM Review 15, no. 1 (January 1973): 234-35. https://doi.org/10.1137/1015023. p. 306-315