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Title: A matrix dependent/algebraic multigrid approach for extruded meshes with applications to ice sheet modeling

Abstract

A multigrid method is proposed that combines ideas from matrix dependent multigrid for structured grids and algebraic multigrid for unstructured grids. It targets problems where a three-dimensional mesh can be viewed as an extrusion of a two-dimensional, unstructured mesh in a third dimension. Our motivation comes from the modeling of thin structures via finite elements and, more specifically, the modeling of ice sheets. Extruded meshes are relatively common for thin structures and often give rise to anisotropic problems when the thin direction mesh spacing is much smaller than the broad direction mesh spacing. Within our approach, the first few multigrid hierarchy levels are obtained by applying matrix dependent multigrid to semicoarsen in a structured thin direction fashion. After sufficient structured coarsening, the resulting mesh contains only a single layer corresponding to a two-dimensional, unstructured mesh. Algebraic multigrid can then be employed in a standard manner to create further coarse levels, as the anisotropic phenomena is no longer present in the single layer problem. The overall approach remains fully algebraic, with the minor exception that some additional information is needed to determine the extruded direction. Furthermore, this facilitates integration of the solver with a variety of different extruded mesh applications.

Authors:
 [1];  [1];  [2];  [1];  [3]
  1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
  2. Sandia National Lab. (SNL-CA), Livermore, CA (United States)
  3. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Sandia National Lab. (SNL-CA), Livermore, CA (United States); Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Biological and Environmental Research (BER)
OSTI Identifier:
1334163
Report Number(s):
SAND-2015-8309J
Journal ID: ISSN 1064-8275; 606326
Grant/Contract Number:  
AC04-94AL85000
Resource Type:
Accepted Manuscript
Journal Name:
SIAM Journal on Scientific Computing
Additional Journal Information:
Journal Volume: 38; Journal Issue: 5; Journal ID: ISSN 1064-8275
Publisher:
SIAM
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; ice sheets; iterative solvers; algebraic method

Citation Formats

Tuminaro, Raymond S., Perego, Mauro, Tezaur, Irina Kalashnikova, Salinger, Andrew G., and Price, Stephen. A matrix dependent/algebraic multigrid approach for extruded meshes with applications to ice sheet modeling. United States: N. p., 2016. Web. https://doi.org/10.1137/15m1040839.
Tuminaro, Raymond S., Perego, Mauro, Tezaur, Irina Kalashnikova, Salinger, Andrew G., & Price, Stephen. A matrix dependent/algebraic multigrid approach for extruded meshes with applications to ice sheet modeling. United States. https://doi.org/10.1137/15m1040839
Tuminaro, Raymond S., Perego, Mauro, Tezaur, Irina Kalashnikova, Salinger, Andrew G., and Price, Stephen. Thu . "A matrix dependent/algebraic multigrid approach for extruded meshes with applications to ice sheet modeling". United States. https://doi.org/10.1137/15m1040839. https://www.osti.gov/servlets/purl/1334163.
@article{osti_1334163,
title = {A matrix dependent/algebraic multigrid approach for extruded meshes with applications to ice sheet modeling},
author = {Tuminaro, Raymond S. and Perego, Mauro and Tezaur, Irina Kalashnikova and Salinger, Andrew G. and Price, Stephen},
abstractNote = {A multigrid method is proposed that combines ideas from matrix dependent multigrid for structured grids and algebraic multigrid for unstructured grids. It targets problems where a three-dimensional mesh can be viewed as an extrusion of a two-dimensional, unstructured mesh in a third dimension. Our motivation comes from the modeling of thin structures via finite elements and, more specifically, the modeling of ice sheets. Extruded meshes are relatively common for thin structures and often give rise to anisotropic problems when the thin direction mesh spacing is much smaller than the broad direction mesh spacing. Within our approach, the first few multigrid hierarchy levels are obtained by applying matrix dependent multigrid to semicoarsen in a structured thin direction fashion. After sufficient structured coarsening, the resulting mesh contains only a single layer corresponding to a two-dimensional, unstructured mesh. Algebraic multigrid can then be employed in a standard manner to create further coarse levels, as the anisotropic phenomena is no longer present in the single layer problem. The overall approach remains fully algebraic, with the minor exception that some additional information is needed to determine the extruded direction. Furthermore, this facilitates integration of the solver with a variety of different extruded mesh applications.},
doi = {10.1137/15m1040839},
journal = {SIAM Journal on Scientific Computing},
number = 5,
volume = 38,
place = {United States},
year = {2016},
month = {10}
}

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    Works referencing / citing this record:

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