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Tuminaro, Raymond S.

Publications and source records attributed to Tuminaro, Raymond S..

At least 55 records · Page 3
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DOE OSTI2017

An algebraic multigrid method for Q 2 - Q 1 mixed discretizations of the Navier-Stokes equations: AMG for Q 2 - Q 1 discretization

Algebraic multigrid (AMG) preconditioners are considered for discretized systems of partial differential equations (PDEs) where unknowns associated with different physical quantities are not necessarily colocated at mesh points. Specifically, we investigate a Q 2 -Q 1 mixed finite element discretization of the incompressible Navier–Stokes equations where the number of velocity nodes is much greater than the number of pressure nodes. Consequently, some velocity degrees of freedom (DOFs) are defined at spatial locations where there are no corresponding pressure DOFs. Thus, AMG approaches leveraging this colocated structure are not applicable. This article instead proposes an automatic AMG coarsening that mimics certain pressure/velocity DOF relationships of the Q 2 -Q 1 discretization. The main idea is to first automatically define coarse pressures in a somewhat standard AMG fashion and then to carefully (but automatically) choose coarse velocity unknowns so that the spatial location relationship between pressure and velocity DOFs resembles that on the finest grid. To define coefficients within the intergrid transfers, an energy minimization AMG (EMIN-AMG) is utilized. EMIN-AMG is not tied to specific coarsening schemes and grid transfer sparsity patterns, and so it is applicable to the proposed coarsening. Numerical results highlighting solver performance are given on Stokes and incompressible Navier–Stokes problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

An ice sheet model validation framework for the Greenland ice sheet

We propose a new ice sheet model validation framework the Cryospheric Model Comparison Tool (CMCT) that takes advantage of ice sheet altimetry and gravimetry observations collected over the past several decades and is applied here to modeling of the Greenland ice sheet. We use realistic simulations performed with the Community Ice Sheet Model (CISM) along with two idealized, non-dynamic models to demonstrate the framework and its use. Dynamic simulations with CISM are forced from 1991 to 2013 using combinations of reanalysis-based surface mass balance and observations of outlet glacier flux change. We propose and demonstrate qualitative and quanti- tative metrics for use in evaluating the different model simulations against the observations. We find 10 that the altimetry observations used here are largely ambiguous in terms of their ability to distinguish one simulation from another. Based on basin- and whole-ice-sheet scale metrics, the model initial condition as well as output from idealized and dynamic models all provide an equally reasonable representation of the ice sheet surface (mean elevation differences of <1 m). This is likely due to their short period of record, biases inherent to digital elevation models used for model initial conditions, and biases resulting from firn dynamics, which are not explicitly accounted for in the models or observations. On the other hand, we find that the gravimetry observations used here are able to unambiguously distinguish between simulations of varying complexity, and along with the CMCT, can provide a quantitative score for assessing a particular model and/or simulation. The new framework demonstrates that our proposed metrics can distinguish relatively better from relatively worse simulations and that dynamic ice sheet models, when appropriately initialized and forced with the right boundary conditions, demonstrate predictive skill with respect to observed dynamic changes occurring on Greenland over the past few decades. An extensible design will allow for continued use of the CMCT as future altimetry, gravimetry, and other remotely sensed data become available for use in ice sheet model validation.

58 GEOSCIENCES↗
DOE OSTI2016

Teko: A block preconditioning capability with concrete example applications in Navier--Stokes and MHD

This study describes the design of Teko, an object-oriented C++ library for implementing advanced block preconditioners. Mathematical design criteria that elucidate the needs of block preconditioning libraries and techniques are explained and shown to motivate the structure of Teko. For instance, a principal design choice was for Teko to strongly reflect the mathematical statement of the preconditioners to reduce development burden and permit focus on the numerics. Additional mechanisms are explained that provide a pathway to developing an optimized production capable block preconditioning capability with Teko. Finally, Teko is demonstrated on fluid flow and magnetohydrodynamics applications. In addition to highlighting the features of the Teko library, these new results illustrate the effectiveness of recent preconditioning developments applied to advanced discretization approaches.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

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

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.

97 MATHEMATICS AND COMPUTING↗