Results for “Linear systems solvers” — Page 20

DOE OSTI2022

Robust estimation of charge carrier diffusivity using transient photoluminescence microscopy

Transient microscopy has emerged as a powerful tool for imaging the diffusion of excitons and free charge carriers in optoelectronic materials. In many excitonic materials, extraction of diffusion coefficients can be simplified because of the linear relationship between signal intensity and local excited state population. However, in materials where transport is dominated by free charge carriers, extracting diffusivities accurately from multidimensional data is complicated by the nonlinear dependence of the measured signal on the local charge carrier density. To obtain accurate estimates of charge carrier diffusivity from transient microscopy data, statistically robust fitting algorithms coupled to efficient 3D numerical solvers that faithfully relate local carrier dynamics to raw experimental measurables are sometimes needed. Here, we provide a detailed numerical framework for modeling the spatiotemporal dynamics of free charge carriers in bulk semiconductors with significant solving speed reduction and for simulating the corresponding transient photoluminescence microscopy data. To demonstrate the utility of this approach, we apply a fitting algorithm using a Markov chain Monte Carlo sampler to experimental data on bulk CdS and methylammonium lead bromide (MAPbBr 3 ) crystals. Parameter analyses reveal that transient photoluminescence microscopy can be used to obtain robust estimates of charge carrier diffusivities in optoelectronic materials of interest, but that other experimental approaches should be used for obtaining carrier recombination constants. Additionally, simplifications can be made to the fitting model depending on the experimental conditions and material systems studied. Our open-source simulation code and fitting algorithm are made freely available to the scientific community.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

A Comprehensive Review of Latent Space Dynamics Identification Algorithms for Intrusive and Non-Intrusive Reduced-Order-Modeling

Numerical solvers of partial differential equations (PDEs) have been widely employed for simulating physical systems. However, the computational cost remains a major bottleneck in various scientific and engineering applications, which has motivated the development of reduced-order models (ROMs). Recently, machine-learning-based ROMs have gained significant popularity and are promising for addressing some limitations of traditional ROM methods, especially for advection dominated systems. In this chapter, we focus on a particular framework known as Latent Space Dynamics Identification (LaSDI), which transforms the high-fidelity data, governed by a PDE, to simpler and low-dimensional latent-space data, governed by ordinary differential equations (ODEs). These ODEs can be learned and subsequently interpolated to make ROM predictions. Each building block of LaSDI can be easily modulated depending on the application, which makes the LaSDI framework highly flexible. In particular, we present strategies to enforce the laws of thermodynamics into LaSDI models (tLaSDI), enhance robustness in the presence of noise through the weak form (WLaSDI), select high-fidelity training data efficiently through active learning (gLaSDI, GPLaSDI), and quantify the ROM prediction uncertainty through Gaussian processes (GPLaSDI). We demonstrate the performance of different LaSDI approaches on Burgers equation, a non-linear heat conduction problem, and a plasma physics problem, showing that LaSDI algorithms can achieve relative errors of less than a few percent and up to thousands of times speed-ups.

Computational Engineering, Finance, and Science (c↗

NASA NTRS2023

Measurements and Computations of Natural Transition on the NASA Juncture-Flow Model with a Symmetric Wing

Experiments were performed in the 14- by 22-Foot Subsonic Tunnel to assess natural transition on the symmetric-airfoil wings of the NASA Juncture-Flow Model. Infrared thermography was used to visualize the heating on the upper surface of both wings of the full-span model, and on the fuselage, for angles of incidence ranging from -10° to 10° at a fixed Reynolds number of 2.4E6 based on the chord length at the wing planform break. The fuselage boundary layer transitioned well upstream of the wing-root leading edge for all conditions. Transition fronts were identified by a steep rise in the surface temperature, and the transition coordinates were transformed from an image-based to a body-fixed system. Additionally, the state of the boundary layer was estimated at pressure ports distributed on the wings through observation of the pressure coefficient as a function of the angle of incidence. For increasing angles of incidence, the transition front was observed to advance upstream, in a mostly spanwise-uniform fashion, from near midchord at α = 0°; however, for increasingly negative angles of incidence, the transition front first receded and then advanced in a nonuniform jagged manner that is typically observed with stationary crossflow. The transition wedges first appeared inboard of the wing break and then spread outboard to near the tip by α = -6°. The upstream shift in transition at positive angles of incidence and the outboard progression of crossflow-dominated transition at increasingly negative angles of incidence are consistent with trends identified in a computational assessment of the boundary-layer transition based on both linear stability analysis and Reynolds-averaged-Navier-Stokes-based transition models. The stability results obtained from the Langley Stability and Transition Analysis Code were used to recalibrate a dual N-factor criterion, which allowed for the prediction of transition fronts that showed excellent agreement with the experiment. The Reynolds-averaged-Navier-Stokes-based models, from the NASA OVERFLOW 2.3 solver, that accounted for the crossflow instability showed mixed results in comparison with the experiment, with the helicity-based Langtry-Menter model performing the best. The experimental data, particularly the cases involving strong influence from both Tollmien-Schlichting and crossflow instabilities, will be valuable for the continued validation and improvement of transition models.

Boundary layer transition↗

NASA NTRS2023

Measurements and Computations of Natural Transition on the NASA Juncture-Flow Model with a Symmetric Wing

Experiments were performed in the 14- by 22-Foot Subsonic Tunnel to assess natural transition on the symmetric-airfoil wings of the NASA Juncture-Flow Model. Infrared thermography was used to visualize the heating on the upper surface of both wings of the full-span model, and on the fuselage, for angles of incidence ranging from -10° to 10° at a fixed Reynolds number of 2.4E6 based on the chord length at the wing planform break. The fuselage boundary layer transitioned well upstream of the wing-root leading edge for all conditions. Transition fronts were identified by a steep rise in the surface temperature, and the transition coordinates were transformed from an image-based to a body-fixed system. Additionally, the state of the boundary layer was estimated at pressure ports distributed on the wings through observation of the pressure coefficient as a function of the angle of incidence. For increasing angles of incidence, the transition front was observed to advance upstream, in a mostly spanwise-uniform fashion, from near midchord at α = 0°; however, for increasingly negative angles of incidence, the transition front first receded and then advanced in a nonuniform jagged manner that is typically observed with stationary crossflow. The transition wedges first appeared inboard of the wing break and then spread outboard to near the tip by α = -6°. The upstream shift in transition at positive angles of incidence and the outboard progression of crossflow-dominated transition at increasingly negative angles of incidence are consistent with trends identified in a computational assessment of the boundary-layer transition based on both linear stability analysis and Reynolds-averaged-Navier-Stokes-based transition models. The stability results obtained from the Langley Stability and Transition Analysis Code were used to recalibrate a dual N-factor criterion, which allowed for the prediction of transition fronts that showed excellent agreement with the experiment. The Reynolds-averaged-Navier-Stokes-based models, from the NASA OVERFLOW 2.3 solver, that accounted for the crossflow instability showed mixed results in comparison with the experiment, with the helicity-based Langtry-Menter model performing the best. The experimental data, particularly the cases involving strong influence from both Tollmien-Schlichting and crossflow instabilities, will be valuable for the continued validation and improvement of transition models.

boundary layer transition↗

NASA NTRS2023

Measurements and Computations of Natural Transition on the NASA Juncture-Flow Model with a Symmetric Wing

Experiments were performed in the 14- by 22-Foot Subsonic Tunnel to assess natural transition on the symmetric-airfoil wings of the NASA Juncture-Flow Model. Infrared thermography was used to visualize the heating on the upper surface of both wings of the full-span model, and on the fuselage, for angles of incidence ranging from -10° to 10° at a fixed Reynolds number of 2.4E6 based on the chord length at the wing planform break. The fuselage boundary layer transitioned well upstream of the wing-root leading edge for all conditions. Transition fronts were identified by a steep rise in the surface temperature, and the transition coordinates were transformed from an image-based to a body-fixed system. Additionally, the state of the boundary layer was estimated at pressure ports distributed on the wings through observation of the pressure coefficient as a function of the angle of incidence. For increasing angles of incidence, the transition front was observed to advance upstream, in a mostly spanwise-uniform fashion, from near midchord at α = 0°; however, for increasingly negative angles of incidence, the transition front first receded and then advanced in a nonuniform jagged manner that is typically observed with stationary crossflow. The transition wedges first appeared inboard of the wing break and then spread outboard to near the tip by α = -6°. The upstream shift in transition at positive angles of incidence and the outboard progression of crossflow-dominated transition at increasingly negative angles of incidence are consistent with trends identified in a computational assessment of the boundary-layer transition based on both linear stability analysis and Reynolds-averaged-Navier-Stokes-based transition models. The stability results obtained from the Langley Stability and Transition Analysis Code were used to recalibrate a dual N-factor criterion, which allowed for the prediction of transition fronts that showed excellent agreement with the experiment. The Reynolds-averaged-Navier-Stokes-based models, from the NASA OVERFLOW 2.3 solver, that accounted for the crossflow instability showed mixed results in comparison with the experiment, with the helicity-based Langtry-Menter model performing the best. The experimental data, particularly the cases involving strong influence from both Tollmien-Schlichting and crossflow instabilities, will be valuable for the continued validation and improvement of transition models.

boundary layer transition↗

NASA NTRS2003

Aeroelastic System Development Using Proper Orthogonal Decomposition and Volterra Theory

This research combines Volterra theory and proper orthogonal decomposition (POD) into a hybrid methodology for reduced-order modeling of aeroelastic systems. The out-come of the method is a set of linear ordinary differential equations (ODEs) describing the modal amplitudes associated with both the structural modes and the POD basis functions for the uid. For this research, the structural modes are sine waves of varying frequency, and the Volterra-POD approach is applied to the fluid dynamics equations. The structural modes are treated as forcing terms which are impulsed as part of the uid model realization. Using this approach, structural and uid operators are coupled into a single aeroelastic operator. This coupling converts a free boundary uid problem into an initial value problem, while preserving the parameter (or parameters) of interest for sensitivity analysis. The approach is applied to an elastic panel in supersonic cross ow. The hybrid Volterra-POD approach provides a low-order uid model in state-space form. The linear uid model is tightly coupled with a nonlinear panel model using an implicit integration scheme. The resulting aeroelastic model provides correct limit-cycle oscillation prediction over a wide range of panel dynamic pressure values. Time integration of the reduced-order aeroelastic model is four orders of magnitude faster than the high-order solution procedure developed for this research using traditional uid and structural solvers.

Lucia, David J.↗

NASA NTRS2014

High-Lift OVERFLOW Analysis of the DLR-F11 Wind Tunnel Model

In response to the 2nd AIAA CFD High Lift Prediction Workshop, the DLR-F11 wind tunnel model is analyzed using the Reynolds-averaged Navier-Stokes flow solver OVERFLOW. A series of overset grids for a bracket-off landing configuration is constructed and analyzed as part of a general grid refinement study. This high Reynolds number (15.1 million) analysis is done at multiple angles-of-attack to evaluate grid resolution effects at operational lift levels as well as near stall. A quadratic constitutive relation recently added to OVERFLOW for improved solution accuracy is utilized for side-of-body separation issues at low angles-of-attack and outboard wing separation at stall angles. The outboard wing separation occurs when the slat brackets are added to the landing configuration and is a source of discrepancy between the predictions and experimental data. A detailed flow field analysis is performed at low Reynolds number (1.35 million) after pressure tube bundles are added to the bracket-on medium grid system with the intent of better understanding bracket/bundle wake interaction with the wing's boundary layer. Localized grid refinement behind each slat bracket and pressure tube bundle coupled with a time accurate analysis are exercised in an attempt to improve stall prediction capability. The results are inconclusive and suggest the simulation is missing a key element such as boundary layer transition. The computed lift curve is under-predicted through the linear range and over-predicted near stall, and the solution from the most complete configuration analyzed shows outboard wing separation occurring behind slat bracket 6 where the experiment shows it behind bracket 5. These results are consistent with most other participants of this workshop.

High-lift↗

DOE OSTI2026

Integrated Transmission-Distribution Multi-Period Switching for Wildfire Risk Mitigation: Improving Speed and Scalability with Distributed Optimization: Preprint

With increasingly severe wildfire conditions driven by climate change, utilities must manage the risk of wildfire ignitions from electric power lines. During "public safety power shutoff'" events, utilities de-energize power lines to reduce wildfire ignition risk, which may result in load shedding. Distributed energy resources provide flexibility that can help support the system to reduce load shedding when lines are de-energized. We investigate a coordinated transmission-distribution optimization problem that balances wildfire risk mitigation and load shedding. We model distribution systems that include battery energy storage systems which may support loads when transmission lines are de-energized. This multi-period integrated transmission-distribution optimal switching problem jointly optimizes line switching decisions, the generators' setpoints, load shedding, and the batteries' states of charge, resulting in significant computational challenges. To improve scalability, we decompose the problem over both space and time and apply a distributed optimization algorithm. Using a large-scale synthetic California test case with realistic distribution models and real wildfire risk data, we show that distributed optimization can solve large-scale multi-period switching problems that are otherwise intractable for centralized solvers. We also discuss challenges and future directions for improving the distributed algorithm's convergence performance as the number of time periods increases.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2020

DESC: A stellarator equilibrium solver

In this paper, the new code DESC is presented to solve for fixed-boundary ideal magnetohydrodynamic equilibria in stellarators. The approach directly solves the equilibrium force balance as a system of nonlinear equations in the form f(x) = 0. The independent variables x represent nested magnetic flux surfaces expressed in the inverse representation with toroidal flux coordinates, and the equations f(x) quantify equilibrium force balance errors at discrete points in real space. Discretizing with global Fourier–Zernike basis functions properly treats the magnetic axis and minimizes the number of coefficients needed to describe the flux surfaces. The pseudospectral method provides great flexibility in where the errors are evaluated, and the system of equations is efficiently solved with a Newton–Raphson iteration. Equilibria are computed and compared against VMEC for both axisymmetric and non-axisymmetric examples. The results show fast convergence rates and solutions with low errors throughout the plasma volume.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2026

Regional surrogates for predictive control of digital twins

Digital twins of complex systems must involve a model that is fast, generalizable, and usable for real-time control. For example, high-fidelity nonlinear multiphysics simulations can capture laser-material interactions, but are too slow for optimization or model predictive control (MPC). Reduced-order models, used to accelerate such computation, frequently fail to generalize to unseen inputs or control states. We show theoretically that this failure is intrinsic, i.e., that a learned model is non-unique outside the sampled subspace when its low-rank structure arises from limited excitation and clustered eigenvalues, rather than from a user-imposed truncation alone. Motivated by this result, we propose a control-ready regional surrogate-construction framework for both autonomous and nonautonomous dynamics; it employs Koopman lifting to represent nonlinearities, while preserving spatial locality. We illustrate our approach by constructing a control-ready surrogate for the digital twin of a thermal component of additive-manufacturing process. Our surrogate, localized in space through a von Neumann stencil, is learned from noisy high-fidelity simulations that emulate thermal-camera images collected during the manufacturing. It is linear in thermo-physically augmented states so that MPC reduces to a convex quadratic program. The surrogate requires no online correction, generalizes to unseen scan paths and power profiles of the laser, and is more than three orders of magnitude faster than a finite-difference solver. Furthermore, when the MPC sequence computed on the digital twin is applied to this solver, closed-loop temperature regulation is recovered, showing that the surrogate preserves control-relevant input-output behavior.

Data-driven model↗

DOE OSTI2025

Computational Algorithms for Unit Commitment with AC Power Flows (Final Report)

Security-constrained unit commitment (SCUC) is a key component in power system operations. When AC power flow constraints are considered in the SCUC model (AC-SCUC), the problem becomes extremely difficult due to its discrete and non-convex nature, as described in “Grid Optimization Competition Challenge 3 Problem Formulation (GOCC)”. There are four main challenges: (i) Discrete decisions regarding unit online/offline status and start-up/shut-down procedures for every single unit. The number of discrete decision variables increases considerably when a system integrates multiple generators; (ii) Configuration-based combined-cycle formulations, and multi-commodity models that include ramping products, spin/non-spin products, and regulation up/down products. The combined-cycle units introduce additional discrete decision variables and auxiliary service products further complicate the model by connecting multi-commodity products’ continuous and discrete variables; (iii) SCUC models with AC power flow constraints are far more complex due to massive bilinear terms in the large-scale nonlinear power balance equations. The nonlinear power balance equations are further complicated by the discrete step control variables of shunts; (iv) N − 1 contingency analysis. The size of the model increases linearly with the number of contingencies considered, greatly increasing the size of the optimization model. Accordingly, there is an emergent need to develop a robust algorithm capable of deriving a high-quality solution in a short time and passing through contingency tests simultaneously. In this project, we explore innovative techniques to address this challenging problem by integrating advanced polyhedral theory, approximation methods, relaxation strategies, decomposition techniques, and parallel computing. Each technique approaches the problem from a different perspective, leveraging its specific strengths to tackle distinct challenges. Each individual method has demonstrated its effectiveness in the PI’s previous research. Their integration is expected to significantly reduce the computational time required to solve the proposed complex problem. Successful completion of this project has the potential to transform the industry by enhancing optimization solvers capable of handling large-scale day-ahead energy market clearing models within strict time constraints, while incorporating AC power flow constraints. This advancement will lead to reduced overall generation costs and, consequently, increased social welfare.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2024

ReEDS Performance Improvement

The Regional Energy Deployment System (ReEDS) is an open-source, spatially explicit, long-term capacity expansion model for the bulk electric power system of the contiguous United States, encompassing multiple scenarios with technological and political assumptions (see https://github.com/NREL/ReEDS-2.0). With the increased needs for capabilities, higher temporal and spatial resolutions to model the evolution of the power system with modern technologies and low-carbon pathways, ReEDS' model solution times have increased significantly from 4-6 hours in 2018 to 18-48+ hours in 2023 . Also, the model size for commonly-run ReEDS scenarios reached 22 and 28 million equations and variables, respectively. These runtimes can be especially challenging under certain scenario settings (e.g., very high temporal or spatial resolution) or with limited computational power. In this presentation, we will discuss several methods we used to improve model runtime, including data preparation, model modification, and solver tuning. The implementation of these methods shrank the model size to 7.2 and 7.3 million equations and variables, respectively. Furthermore, this led to a 77% reduction in the model's run time for commonly-run ReEDS scenarios. We will discuss the process of identifying areas for solve time improvements and how the specific enhancements for the ReEDS model might be applied to other similar large-scale models.

ENERGY PLANNING, POLICY, AND ECONOMY,MATHEMATICS A↗

DOE OSTI2023

Airfoil Computational Fluid Dynamics - 2k shapes, 25 AoA's, 3 Re numbers

This dataset contains aerodynamic quantities - including flow field values (momentum, energy, and vorticity) and summary values (coefficients of lift, drag, and momentum) - for 1,830 airfoil shapes computed using the HAM2D CFD (computational fluid dynamics) model. The airfoil shapes were designed using the separable shape tensor parameterization that encodes two-dimensional shapes as elements of the Grassmann manifold. This data-driven approach learns two independent spaces of parameter from a collection of sample airfoils. The first captures large-scale, linear perturbations, and the second defines small-scale, higher-order perturbations. For this dataset, we used the G2Aero database of over 19,000 airfoil shapes to learn a parameter space that captured a wide array of shape characteristics. We sampled airfoil designs over both parameter spaces to explore the full range of possible shape variations. The aerodynamic quantities for the generated airfoil were obtained using the HAM2D code, which is a finite-volume Reynolds-averaged Navier-Stokes (RANS) flow solver. We employ a fifth-order WENO scheme for spatial reconstruction with Roe's flux difference scheme for inviscid flux and second-order central differencing for viscous flux. A preconditioned GMRES method is applied for implicit integration. The Spalart-Allmaras 1-eq turbulence model is used for the turbulence closure, and the Medida-Baeder 2-eq transition model is applied to account for the effects of laminar turbulent transition. The airfoil grid is generated with a total of 400 points on the airfoil surface, the initial wall-normal spacing of y+ = 1, and an outer boundary located at 300 chord lengths away from the wall. The CFD simulations are performed at a freestream Mach number of 0.1, for or three different Reynolds' numbers (3M, 6M, and 9M), and for 25 angles of attack from -4 deg. to 20 deg. with 1 degree increments. Across all these various parameters, this dataset includes the results from over 250,000 CFD simulations. The simulations were performed using the Bridges-2 system at the Pittsburgh Supercomputing Center in February 2023 as part of the INTEGRATE project funded by the Advanced Research Projects Agency - Energy, in the U.S. Department of Energy. The data was collected, reformatted, and preprocessed for this OEDI submission in July 2023 under the Foundational AI for Wind Energy project funded by the U.S. Department of Energy Wind Energy Technologies Office. This dataset is intended to serve as a benchmark against which new artificial intelligence (AI) or machine learning (ML) tools may be tested. Baseline AI/ML methods for analyzing this dataset have been implemented, and a link to their repository containing those models has been provided. The .h5 data file structure can be found in the GitHub Repository resource under explore_airfoil_2k_data.ipynb.

2k↗

NASA NTRS2018

Computational Investigation of Nominally-Orthogonal Pneumatic Active Flow Control for High-Lift Systems

We explore the feasibility of using nominally-orthogonal jets as active aerodynamic load control for multi-element high-lift systems, and whether the nominally-orthogonal jets can offer a variety of performance improvements. These nominally-orthogonal jets inject momentum normal to the airfoil surface near the flap trailing edge, where they create a vortex that entrains flow from the opposing side and change the airfoil circulation. Lift-enhancement opportunities of trailing edge nominally-orthogonal jets have previously been studied by Malavard et al. and Blaylock et al. on single-element airfoils; however, their effect on drag was not thoroughly investigated. In this study, we investigate two- dimensional nominally-orthogonal jet effects on both lift and drag on a two-element airfoil, NLR7301. We utilize Chimera Grid Tools to generate structured curvilinear overset grids, and the Reynolds-averaged Navier-Stokes solver OVERFLOW-2 to solve for the flow field around the airfoil. We perform various computational sensitivity studies on the baseline airfoil without a jet to validate computational results against benchmark experimental data. Using a Chimera overset grid topology, we demonstrate a similar lift-enhancement effect between a nominally-orthogonal jet and a nominally-orthogonal physical tab employed at the same location on the studied airfoil. After we introduce the nominally-orthogonal jet concept, we investigate nominally-orthogonal jets with various momentum coefficient settings, C(sub µ) = 0.00 − 0.04 and present a lift-enhancement relationship ∆C(sub l) ≃ 3.59 (C(sub µ)) for this airfoil. We discuss that utilizing a nominally-orthogonal jet with C(sub µ) = 0.01 can shift the linear region of the lift curve by a ∆C(sub l) = 0.36 for the pressure side jet and by a ∆C(sub l) = −0.27 for the suction side jet. Employing a nominally-orthogonal jet is also shown effective in altering the drag. To study the impact, we carry out a drag decomposition study in the form of drag polars. We show for a given C(sub l) = 2.50, a nominally-orthogonal jet with C(sub µ) = 0.01 on the pressure and suction side of the airfoil results in 113 drag count decrements and 41 drag count increments, respectively, compared to the baseline airfoil with no jet. These results show that large and controllable changes in aerodynamic performance can be achieved by relatively small active flow control inputs using the nominally-orthogonal jets presented in this study.

Nominally-Orthogonal↗

DOE OSTI2022

SNICAR-ADv4: a physically based radiative transfer model to represent the spectral albedo of glacier ice

Abstract. Accurate modeling of cryospheric surface albedo is essential for our understanding of climate change as snow and ice surfaces regulate the global radiative budget and sea-level through their albedo and mass balance. Although significant progress has been made using physical principles to represent the dynamic albedo of snow, models of glacier ice albedo tend to be heavily parameterized and not explicitly connected with physical properties that govern albedo, such as the number and size of air bubbles, specific surface area (SSA), presence of abiotic and biotic light absorbing constituents (LACs), and characteristics of any overlying snow. Here, we introduce SNICAR-ADv4, an extension of the multi-layer two-stream delta-Eddington radiative transfer model with the adding–doubling solver that has been previously applied to represent snow and sea-ice spectral albedo. SNICAR-ADv4 treats spectrally resolved Fresnel reflectance and transmittance between overlying snow and higher-density glacier ice, scattering by air bubbles of varying sizes, and numerous types of LACs. SNICAR-ADv4 simulates a wide range of clean snow and ice broadband albedo (BBA), ranging from 0.88 for (30 µm) fine-grain snow to 0.03 for bare and bubble-free ice under direct light. Our results indicate that representing ice with a density of 650 kg m−3 as snow with no refractive Fresnel layer, as done previously, generally overestimates the BBA by an average of 0.058. However, because most naturally occurring ice surfaces are roughened “white ice”, we recommend modeling a thin snow layer over bare ice simulations. We find optimal agreement with measurements by representing cryospheric media with densities less than 650 kg m−3 as snow and larger-density media as bubbly ice with a Fresnel layer. SNICAR-ADv4 also simulates the non-linear albedo impacts from LACs with changing ice SSA, with peak impact per unit mass of LACs near SSAs of 0.1–0.01 m2 kg−1. For bare, bubble-free ice, LACs actually increase the albedo. SNICAR-ADv4 represents smooth transitions between snow, firn, and ice surfaces and accurately reproduces measured spectral albedos of a variety of glacier surfaces. This work paves the way for adapting SNICAR-ADv4 to be used in land ice model components of Earth system models.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

GPU-acceleration of the ELPA2 distributed eigensolver for dense symmetric and hermitian eigenproblems

The solution of eigenproblems is often a key computational bottleneck that limits the tractable system size of numerical algorithms, among them electronic structure theory in chemistry and in condensed matter physics. Large eigenproblems can easily exceed the capacity of a single compute node, thus must be solved on distributed-memory parallel computers. We here present GPU-oriented optimizations of the ELPA two-stage tridiagonalization eigensolver (ELPA2). On top of cuBLAS-based GPU offloading, we add a CUDA kernel to speed up the back-transformation of eigenvectors, which can be the computationally most expensive part of the two-stage tridiagonalization algorithm. Furthermore, we benchmark the performance of this GPU-accelerated eigensolver on two hybrid CPU–GPU architectures, namely a compute cluster based on Intel Xeon Gold CPUs and NVIDIA Volta GPUs, and the Summit supercomputer based on IBM POWER9 CPUs and NVIDIA Volta GPUs. Consistent with previous benchmarks on CPU-only architectures, the GPU-accelerated two-stage solver exhibits a parallel performance superior to the one-stage counterpart. Finally, we demonstrate the performance of the GPU-accelerated eigensolver developed in this work for routine semi-local KS-DFT calculations comprising thousands of atoms.

97 MATHEMATICS AND COMPUTING↗

NASA NTRSDate not supplied

Preliminary Results Cycling GEOS-JEDI with GSI-based Background Errors

The first phase of transitioning the NASA GMAO GEOS atmospheric data assimilation capabilities to JEDI involves the replacement of the Grid-point Statistical Interpolation (GSI) with a corresponding JEDI analysis. This includes taking JEDI's Unified Observation Operator (UFO), its underlying dependencies, and the JEDI solver that enables a hybrid 4DEnVar strategy similar to what is used in the current GEOS-GSI system. Variational analysis involves at least two main components associated with the observation and background cost function terms. The first is directly related to the UFO, which is being carefully validated in a joint collaboration between GMAO and NCEP to demonstrate consistency with corresponding observations usage in GSI. The second component is the background term, which in a hybrid system involves the ability to set up both a climatologically-based term and an ensemble-based term. JEDI provides the means to implement both terms through its BUMP component. Use of BUMP would require a complete re-tune of both climatological and ensemble, which is a non-trivial exercise we would prefer to avoid. As an alternative, the work here studies the results of interfacing the GSI-background error capability (GSIBEC) into JEDI through SABER. With this, the exact same background error covariance formulation used in GSI can be employed in JEDI without need for re-tuning. This brief summary covers the work done to interface GSIBEC into JEDI and shows preliminary results where the background error covariances of the control (GEOS-GSI) and experiment (GEOS-JEDI) are identical in corresponding cycling experiments. The cycling exercise is obviously preliminary and so much can be expected from GEOS-JEDI when compared to GEOS-GSI. There is still a number of features that need closer attention and although in some cases in principle ready to cycle have been intentionally either turned off or not fully exercised (e.g., VarBC is applied but not cycled). Other features are still pending implementation, one such example is the implementation of the Tangent Linear Normal Mode Constraint. Still, results are quite encouraging as hopefully the discussion here illustrates.

Ricardo Todling↗

DOE OSTI2020

An Algebraic Sparsified Nested Dissection Algorithm Using Low-Rank Approximations

Here, we propose a new algorithm for the fast solution of large, sparse, symmetric positive-definite linear systems, spaND (sparsified Nested Dissection). It is based on nested dissection, sparsification, and low-rank compression. After eliminating all interiors at a given level of the elimination tree, the algorithm sparsifies all separators corresponding to the interiors. This operation reduces the size of the separators by eliminating some degrees of freedom but without introducing any fill-in. This is done at the expense of a small and controllable approximation error. The result is an approximate factorization that can be used as an efficient preconditioner. We then perform several numerical experiments to evaluate this algorithm. We demonstrate that a version using orthogonal factorization and block-diagonal scaling takes fewer CG iterations to converge than previous similar algorithms on various kinds of problems. Furthermore, this algorithm is provably guaranteed to never break down and the matrix stays symmetric positive-definite throughout the process. We evaluate the algorithm on some large problems show it exhibits near-linear scaling. The factorization time is roughly $\mathcal{O}$(N), and the number of iterations grows slowly with N.

97 MATHEMATICS AND COMPUTING↗