Compact feature-aware Hermite-style high-order surface reconstruction

Journal Article · 02 July 2019 · Engineering with Computers

DOI: https://doi.org/10.1007/s00366-019-00815-z · OSTI ID:1557760

Li, Yipeng ^[1]; Zhao, Xinglin ^[2]; Ray, Navamita  ^[3]; Jiao, XIangmin  ^[1]

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1. Stony Brook Univ., NY (United States). Dept. of Applied Mathematics
2. Stony Brook Univ., NY (United States). Dept. of Applied Mathematics; Google Inc., Mountain View (United States)
3. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

High-order surface reconstruction is now a commonly used technique for mesh generation and adaptation, geometric and physical modeling, and high-order numerical methods for solving partial differential equations (PDEs). However, surface reconstruction from a relatively coarse mesh remained a challenging problem, especially for surfaces with sharp features. Here in this paper, we introduce a new method to address this challenge by improving the previous state of the art, including continuous moving frames (CMF) and weighted averaging of local fittings (WALF) (Eng Comput 28 (2012)), in two aspects. First, we significantly improve the robustness of reconstruction from coarse meshes using a Hermite-style least squares approximation to incorporate normals of the surface and tangents of the feature curves. Second, we ensure both G⁰ continuity and high-order accuracy of the reconstruction near sharp features by generating parametric surface elements with an iterative feature-aware parameterization. We present the theoretical framework of our method and compare it against point-based methods in terms of accuracy and stability. We demonstrate the use of the proposed technique in generating high-order meshes for finite element methods, and show that it enables nearly identical solutions as using the meshes generated from exact geometry, while allowing additional flexibility.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA)
• Grant/Contract Number: 89233218CNA000001; AC02-06CH11357
• OSTI ID: 1557760
• Report Number(s): LA-UR--19-20389
• Journal Information: Engineering with Computers, Journal Name: Engineering with Computers Journal Issue: 1 Vol. 37; ISSN 0177-0667
• Publisher: SpringerCopyright Statement
• Country of Publication: United States
• Language: English