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.

翻译：我们提出了一种高阶曲面求积法（HOSQ），用于精确逼近封闭曲面上的规则曲面积分。该方法的第一步基于利用方形压缩变换——一种同胚的双线性方形-单纯形变换，将任意曲面三角剖分重新参数化为四边形网格。对于每个生成的四边形域，我们通过切比雪夫-洛巴托网格上的张量多项式插值几何形状。随后应用张量积克伦肖-柯蒂斯求积法计算所得积分。我们展示了该方法在复杂几何形状上的高效性、快速运行性能、高阶精度及鲁棒性。