Journal
COMPUTER-AIDED DESIGN
Volume 141, Issue -, Pages -Publisher
ELSEVIER SCI LTD
DOI: 10.1016/j.cad.2021.103093
Keywords
Quadrature; High-order; Trimmed; Immersed
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Funding
- U.S. Department of Energy by Lawrence Livermore National Laboratory [DE-AC52-07NA27344]
- HEDP Fellowship program within the WCI directorate at Lawrence Livermore National Laboratory
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This work presents a high-accuracy numerical quadrature scheme that achieves exponential convergence by iteratively reducing integration dimensionality and employing high-order numerical integration rules, with applications in geometric moments calculation, immersogeometric analysis, and other fields.
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. (C) 2021 Elsevier Ltd. All rights reserved.
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