Biological and Environmental Research - Earth and Environmental System Sciences
Earth and Environmental System Modeling

A Matrix Dependent/Algebraic Multigrid Approach for Extruded Meshes With Applications to Ice Sheet Modeling

TitleA Matrix Dependent/Algebraic Multigrid Approach for Extruded Meshes With Applications to Ice Sheet Modeling
Publication TypeJournal Article
Year of Publication2016
Authors, Perego Mauro, Tezaur Irina, Salinger Andy, and Price Stephen F.
JournalSIAM Journal of Scientific Computing
Volume38
Number5
PagesC504–C532
Abstract / Summary

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 semi-coarsen 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 multi-grid 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. This facilitates integration of the solver with a variety of different extruded mesh applications.

URLhttp://dx.doi.org/10.1137/15M1040839
DOI10.1137/15M1040839
Journal: SIAM Journal of Scientific Computing
Year of Publication: 2016
Volume: 38
Number: 5
Pages: C504–C532
Publication Date: 10/2016

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 semi-coarsen 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 multi-grid 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. This facilitates integration of the solver with a variety of different extruded mesh applications.

DOI: 10.1137/15M1040839
Citation:
2016.  "A Matrix Dependent/Algebraic Multigrid Approach for Extruded Meshes With Applications to Ice Sheet Modeling."  SIAM Journal of Scientific Computing 38(5): C504–C532.  https://doi.org/10.1137/15M1040839.