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:
-
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
- Sandia National Lab. (SNL-CA), Livermore, CA (United States)
- 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. 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. 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 = {Thu Oct 06 00:00:00 EDT 2016},
month = {Thu Oct 06 00:00:00 EDT 2016}
}
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Works referencing / citing this record:
Exploring basal sliding with a fluidity-based, ice-sheet model using FOSLS: Fluidity-Based Ice-Sheet Models
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