Array-based, parallel hierarchical mesh refinement algorithms for unstructured meshes
Abstract
In this paper, we describe an array-based hierarchical mesh refinement capability through uniform refinement of unstructured meshes for efficient solution of PDE's using finite element methods and multigrid solvers. A multi-degree, multi-dimensional and multi-level framework is designed to generate the nested hierarchies from an initial coarse mesh that can be used for a variety of purposes such as in multigrid solvers/preconditioners, to do solution convergence and verification studies and to improve overall parallel efficiency by decreasing I/O bandwidth requirements (by loading smaller meshes and in memory refinement). We also describe a high-order boundary reconstruction capability that can be used to project the new points after refinement using high-order approximations instead of linear projection in order to minimize and provide more control on geometrical errors introduced by curved boundaries.The capability is developed under the parallel unstructured mesh framework "Mesh Oriented dAtaBase" (MOAB Tautges et al. (2004)). We describe the underlying data structures and algorithms to generate such hierarchies in parallel and present numerical results for computational efficiency and effect on mesh quality. Furthermore, we also present results to demonstrate the applicability of the developed capability to study convergence properties of different point projection schemes for various mesh hierarchies and to amore »
- Authors:
-
- Argonne National Lab. (ANL), Argonne, IL (United States)
- Stony Brook Univ., Stony Brook, NY (United States)
- Publication Date:
- Research Org.:
- Argonne National Laboratory (ANL), Argonne, IL (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
- OSTI Identifier:
- 1373943
- Alternate Identifier(s):
- OSTI ID: 1411844
- Grant/Contract Number:
- AC02-06CH11357
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Computer Aided Design
- Additional Journal Information:
- Journal Volume: 85; Journal Issue: C; Journal ID: ISSN 0010-4485
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 97 MATHEMATICS AND COMPUTING; half-facet; hierarchical meshes; high-order surface reconstruction; parallel computation; uniform mesh refinement
Citation Formats
Ray, Navamita, Grindeanu, Iulian, Zhao, Xinglin, Mahadevan, Vijay, and Jiao, Xiangmin. Array-based, parallel hierarchical mesh refinement algorithms for unstructured meshes. United States: N. p., 2016.
Web. doi:10.1016/j.cad.2016.07.011.
Ray, Navamita, Grindeanu, Iulian, Zhao, Xinglin, Mahadevan, Vijay, & Jiao, Xiangmin. Array-based, parallel hierarchical mesh refinement algorithms for unstructured meshes. United States. https://doi.org/10.1016/j.cad.2016.07.011
Ray, Navamita, Grindeanu, Iulian, Zhao, Xinglin, Mahadevan, Vijay, and Jiao, Xiangmin. Thu .
"Array-based, parallel hierarchical mesh refinement algorithms for unstructured meshes". United States. https://doi.org/10.1016/j.cad.2016.07.011. https://www.osti.gov/servlets/purl/1373943.
@article{osti_1373943,
title = {Array-based, parallel hierarchical mesh refinement algorithms for unstructured meshes},
author = {Ray, Navamita and Grindeanu, Iulian and Zhao, Xinglin and Mahadevan, Vijay and Jiao, Xiangmin},
abstractNote = {In this paper, we describe an array-based hierarchical mesh refinement capability through uniform refinement of unstructured meshes for efficient solution of PDE's using finite element methods and multigrid solvers. A multi-degree, multi-dimensional and multi-level framework is designed to generate the nested hierarchies from an initial coarse mesh that can be used for a variety of purposes such as in multigrid solvers/preconditioners, to do solution convergence and verification studies and to improve overall parallel efficiency by decreasing I/O bandwidth requirements (by loading smaller meshes and in memory refinement). We also describe a high-order boundary reconstruction capability that can be used to project the new points after refinement using high-order approximations instead of linear projection in order to minimize and provide more control on geometrical errors introduced by curved boundaries.The capability is developed under the parallel unstructured mesh framework "Mesh Oriented dAtaBase" (MOAB Tautges et al. (2004)). We describe the underlying data structures and algorithms to generate such hierarchies in parallel and present numerical results for computational efficiency and effect on mesh quality. Furthermore, we also present results to demonstrate the applicability of the developed capability to study convergence properties of different point projection schemes for various mesh hierarchies and to a multigrid finite-element solver for elliptic problems.},
doi = {10.1016/j.cad.2016.07.011},
journal = {Computer Aided Design},
number = C,
volume = 85,
place = {United States},
year = {Thu Aug 18 00:00:00 EDT 2016},
month = {Thu Aug 18 00:00:00 EDT 2016}
}
Web of Science
Works referenced in this record:
Reconstructing high-order surfaces for meshing
journal, September 2011
- Jiao, Xiangmin; Wang, Duo
- Engineering with Computers, Vol. 28, Issue 4
Array-based Hierarchical Mesh Generation in Parallel
journal, January 2015
- Ray, Navamita; Grindeanu, Iulian; Zhao, Xinglin
- Procedia Engineering, Vol. 124
Parallel mesh refinement for 3-D finite element electromagnetics with tetrahedra: Strategies for optimizing system communication
journal, April 2006
- Ren, D. Q.; Giannacopoulos, D. D.
- IEEE Transactions on Magnetics, Vol. 42, Issue 4
Conformal and Non-conformal Adaptive Mesh Refinement with Hierarchical Array-based Half-Facet Data Structures
journal, January 2015
- Zhao, Xinglin; Conley, Rebecca; Ray, Navamita
- Procedia Engineering, Vol. 124
p4est : Scalable Algorithms for Parallel Adaptive Mesh Refinement on Forests of Octrees
journal, January 2011
- Burstedde, Carsten; Wilcox, Lucas C.; Ghattas, Omar
- SIAM Journal on Scientific Computing, Vol. 33, Issue 3
Parallel Adaptive Mesh Refinement
book, January 2006
- Diachin, Lori Freitag; Hornung, Richard; Plassmann, Paul
- Parallel Processing for Scientific Computing
Using generic programming for designing a data structure for polyhedral surfaces
journal, May 1999
- Kettner, Lutz
- Computational Geometry, Vol. 13, Issue 1
On the design of CGAL a computational geometry algorithms library
journal, January 2000
- Fabri, Andreas; Giezeman, Geert-Jan; Kettner, Lutz
- Software: Practice and Experience, Vol. 30, Issue 11
Design, Implementation, and Evaluation of the Surface_mesh Data Structure
book, January 2011
- Sieger, Daniel; Botsch, Mario
- Proceedings of the 20th International Meshing Roundtable
Compact Array-Based Mesh Data Structures
book, January 2005
- Alumbaugh, Tyler J.; Jiao, Xiangmin
- Proceedings of the 14th International Meshing Roundtable
OpenVolumeMesh – A Versatile Index-Based Data Structure for 3D Polytopal Complexes
book, January 2013
- Kremer, Michael; Bommes, David; Kobbelt, Leif
- Proceedings of the 21st International Meshing Roundtable
libMesh : a C++ library for parallel adaptive mesh refinement/coarsening simulations
journal, November 2006
- Kirk, Benjamin S.; Peterson, John W.; Stogner, Roy H.
- Engineering with Computers, Vol. 22, Issue 3-4
Stability of the 8-tetrahedra shortest-interior-edge partitioning method
journal, April 2008
- Kröger, Tim; Preusser, Tobias
- Numerische Mathematik, Vol. 109, Issue 3
Canonical numbering systems for finite‐element codes
journal, March 2009
- Tautges, Timothy J.
- International Journal for Numerical Methods in Biomedical Engineering, Vol. 26, Issue 12
Generating Unstructured Nuclear Reactor Core Meshes in Parallel
journal, January 2014
- Jain, Rajeev; Tautges, Timothy J.
- Procedia Engineering, Vol. 82
Works referencing / citing this record:
Distributed Combinatorial Maps for Parallel Mesh Processing
journal, July 2018
- Damiand, Guillaume; Gonzalez-Lorenzo, Aldo; Zara, Florence
- Algorithms, Vol. 11, Issue 7