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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, R.; Perego, Mauro P.; Tezaur, I.; Salinger, Andrew G.; Price, S.

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. This facilitates integration of the solver with a variety of different extruded mesh applications.

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TYPE Journal Article YEAR 2016
ScopusOSTIDOI

A performance-portable nonhydrostatic atmospheric dycore for the energy exascale earth system model running at cloud-resolving resolutions

International Conference for High Performance Computing, Networking, Storage and Analysis, SC

Bertagna, Luca B.; Guba, Oksana G.; Taylor, Mark A.; Foucar, James G.; Larkin, Jeff; Bradley, Andrew M.; Rajamanickam, Sivasankaran R.; Salinger, Andrew G.

We present an effort to port the nonhydrostatic atmosphere dynamical core of the Energy Exascale Earth System Model (E3SM) to efficiently run on a variety of architectures, including conventional CPU, many-core CPU, and GPU. We specifically target cloud-resolving resolutions of 3 km and 1 km. To express on-node parallelism we use the C++ library Kokkos, which allows us to achieve a performance portable code in a largely architecture-independent way. Our C++ implementation is at least as fast as the original Fortran implementation on IBM Power9 and Intel Knights Landing processors, proving that the code refactor did not compromise the efficiency on CPU architectures. On the other hand, when using the GPUs, our implementation is able to achieve 0.97 Simulated Years Per Day, running on the full Summit supercomputer. To the best of our knowledge, this is the most achieved to date by any global atmosphere dynamical core running at such resolutions.

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TYPE Conference Presenation YEAR 2020
ScopusOSTIDOI
Results 1–25 of 135
Results 1–25 of 135