2021/01/31 by David Gunderman, Kenneth Weiss, John A. Evans · 1 citation
Mathematics · Computer Science · #math.NA #cs.NA #msc:65D30 #msc:65D17
paper · pdf · doi:10.1016/j.cad.2021.103093
published as Computer-Aided Design 141 (2021) 103093 · 19 pages, 17 figures, submitted to Computer-Aided Design
arxiv created 2022/01/02 · arxiv updated 2022/01/04
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 the generalized Stokes theorem to line integrals over trimming curves, and (2) we employ numerical antidifferentiation in the generalized Stokes theorem using high-order quadrature rules. The scheme achieves exponential convergence up to trimming curve approximation error and has applications to computation of geometric moments, immersogeometric analysis, conservative field transfer between high-order curvilinear meshes, and initialization of multi-material simulations. We compare the quadrature scheme to commonly-used quadrature schemes in the literature and show that our scheme is much more efficient in terms of number of quadrature points used. We provide an open-source implementation of the scheme in MATLAB as part of QuaHOG, a software package for Quadrature of High-Order Geometries.