High-Accuracy Mesh-Free Quadrature for Trimmed Parametric Surfaces and Volumes

This work presents a high-accuracy, mesh-free, generalized Stokes theorem-based numerical quadrature scheme for integrating functions over trimmed parametric surfaces and volumes. The algorithm relies on two fundamental steps: (1) We iteratively reduce the dimensionality of integration using theorem to line integrals trimming curves, (2) we employ antidifferentiation in high-order rules. achieves exponential convergence up curve approximation error has applications computation geometric moments, immersogeometric analysis, conservative field transfer between curvilinear meshes, initialization multi-material simulations. compare commonly-used schemes literature show that our is much more efficient terms number points used. provide an open-source implementation MATLAB as part QuaHOG, software package Quadrature High-Order Geometries.