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

Journal Article · · SIAM Journal on Scientific Computing
DOI:https://doi.org/10.1137/15m1040839· OSTI ID:1334163
 [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)
+ Show Author Affiliations
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.
Research Organization:
Sandia National Laboratories (SNL-CA), Livermore, CA (United States); Sandia National Laboratories, Albuquerque, NM (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Biological and Environmental Research (BER) (SC-23)
Grant/Contract Number:
AC04-94AL85000
OSTI ID:
1334163
Report Number(s):
SAND--2015-8309J; 606326
Journal Information:
SIAM Journal on Scientific Computing, Journal Name: SIAM Journal on Scientific Computing Journal Issue: 5 Vol. 38; ISSN 1064-8275
Publisher:
SIAMCopyright Statement
Country of Publication:
United States
Language:
English

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Cited By (3)

Exploring basal sliding with a fluidity-based, ice-sheet model using FOSLS: Fluidity-Based Ice-Sheet Models journal March 2018
A Study on the Performance Portability of the Finite Element Assembly Process Within the Albany Land Ice Solver book February 2020
MPAS-Albany Land Ice (MALI): a variable-resolution ice sheet model for Earth system modeling using Voronoi grids journal January 2018

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Related Subjects

97 MATHEMATICS AND COMPUTING
algebraic method
ice sheets
iterative solvers