Spectral mesh-free quadrature for planar regions bounded by rational parametric curves

@article{Gunderman2021SpectralMQ,
  title={Spectral mesh-free quadrature for planar regions bounded by rational parametric curves},
  author={D. Gunderman and K. Weiss and John A. Evans},
  journal={ArXiv},
  year={2021},
  volume={abs/2005.07780}
}
This work presents spectral, mesh-free, Green's theorem-based numerical quadrature schemes for integrating functions over planar regions bounded by rational parametric curves. Our algorithm proceeds in two steps: (1) We first find intermediate quadrature rules for line integrals along the region's boundary curves corresponding to Green's theorem. (2) We then use a high-order quadrature rule to compute the numerical antiderivative of the integrand along a coordinate axis, which is used to… Expand

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