skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

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}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Save / Share:
  • Standard and goal-oriented adaptive mesh refinement (AMR) techniques are presented for the linear Boltzmann transport equation. A posteriori error estimates are employed to drive the AMR process and are based on angular-moment information rather than on directional information, leading to direction-independent adapted meshes. An error estimate based on a two-mesh approach and a jump-based error indicator are compared for various test problems. In addition to the standard AMR approach, where the global error in the solution is diminished, a goal-oriented AMR procedure is devised and aims at reducing the error in user-specified quantities of interest. The quantities of interest aremore » functionals of the solution and may include, for instance, point-wise flux values or average reaction rates in a subdomain. A high-order (up to order 4) Discontinuous Galerkin technique with standard upwinding is employed for the spatial discretization; the discrete ordinates method is used to treat the angular variable.« less
  • Standard and goal-oriented adaptive mesh refinement (AMR) techniques are presented for the linear Boltzmann transport equation. A posteriori error estimates are employed to drive the AMR process and are based on angular-moment information rather than on directional information, leading to direction-independent adapted meshes. An error estimate based on a two-mesh approach and a jump-based error indicator are compared for various test problems. In addition to the standard AMR approach, where the global error in the solution is diminished, a goal-oriented AMR procedure is devised and aims at reducing the error in user-specified quantities of interest. The quantities of interest aremore » functionals of the solution and may include, for instance, point-wise flux values or average reaction rates in a subdomain. A high-order (up to order 4) Discontinuous Galerkin technique with standard upwinding is employed for the spatial discretization; the discrete ordinates method is used to treat the angular variable.« less
  • In this paper, we describe an array-based hierarchical mesh generation 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 mesh that can be used for a number of purposes such as multi-level methods to generating large meshes. The capability is developed under the parallel mesh framework “Mesh Oriented dAtaBase” a.k.a MOAB. We describe the underlying data structures and algorithms to generate such hierarchies and present numerical results for computational efficiency and mesh quality. Inmore » conclusion, we also present results to demonstrate the applicability of the developed capability to a multigrid finite-element solver.« less
  • Here, the efficiency of discrete ordinates transport sweeps depends on the scheduling algorithm, the domain decomposition, the problem to be solved, and the computational platform. Sweep scheduling algorithms may be categorized by their approach to several issues. In this paper we examine the strategy of domain overloading for mesh partitioning as one of the components of such algorithms. In particular, we extend the domain overloading strategy, previously defined and analyzed for structured meshes, to the general case of unstructured meshes. We also present computational results for both the structured and unstructured domain overloading cases. We find that an appropriate amountmore » of domain overloading can greatly improve the efficiency of parallel sweeps for both structured and unstructured partitionings of the test problems examined on up to 10 5 processor cores.« less