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

SIAM Journal on Scientific Computing

Tuminaro, Raymond S.; Perego, Mauro P.; Kalashnikova, Irina; Salinger, Andrew G.; Price, Stephen

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.

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TYPE Journal Article YEAR 2016
DOIOSTI

The Aeras Next Generation Global Atmosphere Model

Bosler, Peter A.; Bova, S.W.; Demeshko, Irina P.; Fike, Jeffrey A.; Guba, Oksana G.; Overfelt, James R.; Roesler, Erika L.; Salinger, Andrew G.; Smith, Thomas M.; Kalashnikova, Irina; Watkins, Jerry E.

The Next Generation Global Atmosphere Model LDRD project developed a suite of atmosphere models: a shallow water model, an x-z hydrostatic model, and a 3D hydrostatic model, by using Albany, a finite element code. Albany provides access to a large suite of leading-edge Sandia high-performance computing technologies enabled by Trilinos, Dakota, and Sierra. The next-generation capabilities most relevant to a global atmosphere model are performance portability and embedded uncertainty quantification (UQ). Performance portability is the capability for a single code base to run efficiently on diverse set of advanced computing architectures, such as multi-core threading or GPUs. Embedded UQ refers to simulation algorithms that have been modified to aid in the quantifying of uncertainties. In our case, this means running multiple samples for an ensemble concurrently, and reaping certain performance benefits. We demonstrate the effectiveness of these approaches here as a prelude to introducing them into ACME.

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TYPE SAND Report YEAR 2016
DOIOSTI
Results 26–50 of 78
Results 26–50 of 78