03 October 2016

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

improved algebraic multigrid for ice sheet modeling.


A new, multigrid method was developed specifically for three-dimensional, finite-element-based ice sheet model applications.


When applied to realistic problems of modeling the Greenland and Antarctic ice sheets, the new solver has demonstrated extreme efficiency, robustness, and scalability; it is generally 10 times faster than the previous solver and has demonstrated good weak scalabilty out to approximately 1 billion unkowns.


A multigrid method is proposed that combines ideas from matrix depen- dent 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 ele- ments 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 sucient struc- tured coarsening, the resulting mesh contains only a single layer correspond- ing 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 di↵erent extruded mesh applications.

Ray Tuminaro
Sandia National Laboratories (SNL)
  • Advanced Scientific Computing Research