The goal of the ExaWind project is to enable predictive simulations of wind farms composed of many MW-scale turbines situated in complex terrain. Predictive simulations will require computational fluid dynamics (CFD) simulations for which the mesh resolves the geometry of the turbines, and captures the rotation and large deflections of blades. Whereas such simulations for a single turbine are arguably petascale class, multi-turbine wind farm simulations will require exascale-class resources. We describe in this report our efforts to decrease the setup and solution time for the mass-continuity Poisson system with respect to the benchmark timing results reported in FY18 Q1. In particular, we investigate improving and evaluating two types of algebraic multigrid (AMG) preconditioners: Classical Ruge-Stfiben AMG (C-AMG) and smoothed-aggregation AMG (SA-AMG), which are implemented in the Hypre and Trilinos/MueLu software stacks, respectively.
The goal of the ExaWind project is to enable predictive simulations of wind farms composed of many MW-scale turbines situated in complex terrain. Predictive simulations will require computational fluid dynamics (CFD) simulations for which the mesh resolves the geometry of the turbines, and captures the rotation and large deflections of blades. Whereas such simulations for a single turbine are arguably petascale class, multi-turbine wind farm simulations will require exascale-class resources.
When faced with a restrictive evaluation budget that is typical of today's highfidelity simulation models, the effective exploitation of lower-fidelity alternatives within the uncertainty quantification (UQ) process becomes critically important. Herein, we explore the use of multifidelity modeling within UQ, for which we rigorously combine information from multiple simulation-based models within a hierarchy of fidelity, in seeking accurate high-fidelity statistics at lower computational cost. Motivated by correction functions that enable the provable convergence of a multifidelity optimization approach to an optimal high-fidelity point solution, we extend these ideas to discrepancy modeling within a stochastic domain and seek convergence of a multifidelity uncertainty quantification process to globally integrated high-fidelity statistics. For constructing stochastic models of both the low-fidelity model and the model discrepancy, we employ stochastic expansion methods (non-intrusive polynomial chaos and stochastic collocation) computed by integration/interpolation on structured sparse grids or regularized regression on unstructured grids. We seek to employ a coarsely resolved grid for the discrepancy in combination with a more finely resolved Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the US Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000. Grid for the low-fidelity model. The resolutions of these grids may be defined statically or determined through uniform and adaptive refinement processes. Adaptive refinement is particularly attractive, as it has the ability to preferentially target stochastic regions where the model discrepancy becomes more complex, i.e., where the predictive capabilities of the low-fidelity model start to break down and greater reliance on the high-fidelity model (via the discrepancy) is necessary. These adaptive refinement processes can either be performed separately for the different grids or within a coordinated multifidelity algorithm. In particular, we present an adaptive greedy multifidelity approach in which we extend the generalized sparse grid concept to consider candidate index set refinements drawn from multiple sparse grids, as governed by induced changes in the statistical quantities of interest and normalized by relative computational cost. Through a series of numerical experiments using statically defined sparse grids, adaptive multifidelity sparse grids, and multifidelity compressed sensing, we demonstrate that the multifidelity UQ process converges more rapidly than a single-fidelity UQ in cases where the variance of the discrepancy is reduced relative to the variance of the high-fidelity model (resulting in reductions in initial stochastic error), where the spectrum of the expansion coefficients of the model discrepancy decays more rapidly than that of the high-fidelity model (resulting in accelerated convergence rates), and/or where the discrepancy is more sparse than the high-fidelity model (requiring the recovery of fewer significant terms).
Imported oil exacerabates our trade deficit and funds anti-American regimes. Nuclear Energy (NE) is a demonstrated technology with high efficiency. NE's two biggest political detriments are possible accidents and nuclear waste disposal. For NE policy, proliferation is the biggest obstacle. Nuclear waste can be reduced through reprocessing, where fuel rods are separated into various streams, some of which can be reused in reactors. Current process developed in the 1950s is dirty and expensive, U/Pu separation is the most critical. Fuel rods are sheared and dissolved in acid to extract fissile material in a centrifugal contactor. Plants have many contacts in series with other separations. We have taken a science and simulation-based approach to develop a modern reprocessing plant. Models of reprocessing plants are needed to support nuclear materials accountancy, nonproliferation, plant design, and plant scale-up.
In this report we summarize research into new parallel algebraic multigrid (AMG) methods. We first provide a introduction to parallel AMG. We then discuss our research in parallel AMG algorithms for very large scale platforms. We detail significant improvements in the AMG setup phase to a matrix-matrix multiplication kernel. We present a smoothed aggregation AMG algorithm with fewer communication synchronization points, and discuss its links to domain decomposition methods. Finally, we discuss a multigrid smoothing technique that utilizes two message passing layers for use on multicore processors.