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

Journal Article · · Engineering with Computers
 [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)

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

References (21)

Optimal Isoparametric Finite Elements and Error Estimates for Domains Involving Curved Boundaries journal June 1986
Anisotropic mesh adaptation for evolving triangulated surfaces journal December 2009
The Finite Element Method for Elliptic Problems book January 2002
Automated low-order to high-order mesh conversion journal March 2018
Higher-Order Mesh Generation Using Linear Meshes [EM Programmer's Notebook] journal April 2019
Identification of and discontinuities for surface meshes in CAD journal February 2008
Condition numbers and equilibration of matrices journal December 1969
Interpolation theory over curved elements, with applications to finite element methods journal August 1972
A novel cubic-order algorithm for approximating principal direction vectors journal January 2004
Accuracy-preserving source term quadrature for third-order edge-based discretization journal September 2017
NURBS-enhanced finite element method (NEFEM)
  • Sevilla, Ruben; Fernández-Méndez, Sonia; Huerta, Antonio
  • International Journal for Numerical Methods in Engineering, Vol. 76, Issue 1 https://doi.org/10.1002/nme.2311
journal October 2008
A triangular G1 patch from boundary curves journal February 1996
Robust moving least-squares fitting with sharp features journal July 2005
On the generation of symmetric Lebesgue-like points in the triangle journal December 2012
Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement journal October 2005
Gmsh: A 3-D finite element mesh generator with built-in pre- and post-processing facilities journal September 2009
Reconstructing high-order surfaces for meshing journal September 2011
Consistent computation of first- and second-order differential quantities for surface meshes conference January 2008
Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree journal December 1995
The Mathematical Theory of Finite Element Methods book January 2008
Curved PN triangles conference January 2001

Cited By (1)

Surface reconstruction based on CAD model driven priori templates journal December 2019