A matrix dependent/algebraic multigrid approach for extruded meshes with applications to ice sheet modeling
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 threedimensional mesh can be viewed as an extrusion of a twodimensional, 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 twodimensional, 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:

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 Sandia National Lab. (SNLNM), Albuquerque, NM (United States)
 Sandia National Lab. (SNLCA), Livermore, CA (United States)
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Publication Date:
 Report Number(s):
 SAND20158309J
Journal ID: ISSN 10648275; 606326
 Grant/Contract Number:
 AC0494AL85000
 Type:
 Accepted Manuscript
 Journal Name:
 SIAM Journal on Scientific Computing
 Additional Journal Information:
 Journal Volume: 38; Journal Issue: 5; Journal ID: ISSN 10648275
 Publisher:
 SIAM
 Research Org:
 Sandia National Lab. (SNLCA), Livermore, CA (United States); Sandia National Lab. (SNLNM), Albuquerque, NM (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), Biological and Environmental Research (BER) (SC23)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS AND COMPUTING; ice sheets; iterative solvers; algebraic method
 OSTI Identifier:
 1334163
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.,
Web. doi: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. doi:10.1137/15m1040839.
Tuminaro, Raymond S., Perego, Mauro, Tezaur, Irina Kalashnikova, Salinger, Andrew G., and Price, Stephen. 2016.
"A matrix dependent/algebraic multigrid approach for extruded meshes with applications to ice sheet modeling". United States.
doi: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 threedimensional mesh can be viewed as an extrusion of a twodimensional, 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 twodimensional, 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}
}