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

Abstract

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 G 0 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.

Authors:
 [1];  [2]; ORCiD logo [3]; ORCiD logo [1]
  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)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1557760
Report Number(s):
LA-UR-19-20389
Journal ID: ISSN 0177-0667
Grant/Contract Number:  
89233218CNA000001; AC02-06CH11357
Resource Type:
Accepted Manuscript
Journal Name:
Engineering with Computers
Additional Journal Information:
Journal Name: Engineering with Computers; Journal ID: ISSN 0177-0667
Publisher:
Springer
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING; Computer Science; Mathematics; high-order methods; surface reconstruction; weighted least squares; Hermite approximations; geometric discontinuities; finite element methods

Citation Formats

Li, Yipeng, Zhao, Xinglin, Ray, Navamita, and Jiao, XIangmin. Compact feature-aware Hermite-style high-order surface reconstruction. United States: N. p., 2019. Web. doi:10.1007/s00366-019-00815-z.
Li, Yipeng, Zhao, Xinglin, Ray, Navamita, & Jiao, XIangmin. Compact feature-aware Hermite-style high-order surface reconstruction. United States. doi:10.1007/s00366-019-00815-z.
Li, Yipeng, Zhao, Xinglin, Ray, Navamita, and Jiao, XIangmin. Wed . "Compact feature-aware Hermite-style high-order surface reconstruction". United States. doi:10.1007/s00366-019-00815-z.
@article{osti_1557760,
title = {Compact feature-aware Hermite-style high-order surface reconstruction},
author = {Li, Yipeng and Zhao, Xinglin and Ray, Navamita and Jiao, XIangmin},
abstractNote = {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.},
doi = {10.1007/s00366-019-00815-z},
journal = {Engineering with Computers},
number = ,
volume = ,
place = {United States},
year = {2019},
month = {7}
}

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