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Title: 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 » multigrid finite-element solver for elliptic problems.« less

Authors:
 [1];  [1];  [2];  [1];  [2]
  1. Argonne National Lab. (ANL), Argonne, IL (United States)
  2. Stony Brook Univ., Stony Brook, NY (United States)
Publication Date:
Research Org.:
Argonne National Lab. (ANL), Argonne, IL (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
OSTI Identifier:
1373943
Alternate Identifier(s):
OSTI ID: 1411844
Grant/Contract Number:  
AC02-06CH11357
Resource Type:
Journal Article: 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. doi: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. doi: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}
}

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