High-order numerical integration on regular embedded surfaces
<|reference_start|>High-order numerical integration on regular embedded surfaces: We present a high-order surface quadrature (HOSQ) for accurately approximating regular surface integrals on closed surfaces. The initial step of our approach rests on exploiting square-squeezing--a homeomorphic bilinear square-simplex transformation, re-parametrizing any surface triangulation to a quadrilateral mesh. For each resulting quadrilateral domain we interpolate the geometry by tensor polynomials in Chebyshev--Lobatto grids. Posterior the tensor-product Clenshaw-Curtis quadrature is applied to compute the resulting integral. We demonstrate efficiency, fast runtime performance, high-order accuracy, and robustness for complex geometries.<|reference_end|>
@article{zavalani2024high-order,
    title={High-order numerical integration on regular embedded surfaces},
    author={Gentian Zavalani and Michael Hecht},
    journal={arXiv preprint arXiv:2403.09178},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.09178},
    primaryClass={math.NA cs.NA}
}