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DOE OSTI2022

Assessing the large-scale drivers of precipitation in the northeastern United States via linear orthogonal decomposition

This study examines the linear orthogonal modes associated with monthly precipitation in the northeastern United States, from CESM1 LENS (35 ensemble members, 1979–2005) and two reanalysis datasets (ERA5, 1950–2018 and NOAA-CIRES-DOE 20CRv3, 1950–2015). Calendar months are aggregated together, and any linear trends in data are removed. Using region-averaged precipitation anomaly time series and monthly anomalies for several global 2D atmospheric fields, a linear orthogonal decomposition method is implemented to iteratively extract time series (based on field and geographic location) of absolute maximum correlation. Linear modes associated with this method are then projected onto the full set of 2D fields to provide physical insight into the mechanisms involved in generating precipitation. In this region, the first mode is associated with vapor transport from the Atlantic seaboard, the second mode is characterized by westward vapor transport associated with extratropical cyclones, and the third mode captures vapor transport from the Gulf of Mexico during the fall and winter. However, the third mode is less robust in the spring and summer. Results are generally consistent across the datasets, and applying multiple linear regression with the linear modes to predict the precipitation anomalies produces R-squared values of around 0.54–0.65 for CESM1 LENS, and around 0.58–0.88 for reanalysis, with the lowest values generally in the spring and late summer. The influence of low-frequency climate variability on the modes is considered for CESM1 LENS, and the modes in late winter can be predicted with some success via a combination of several, prominent large-scale teleconnection patterns.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

An efficient method to identify uncertainties of WRF-Solar variables in forecasting solar irradiance using a tangent linear sensitivity analysis

Uncertainty in predicting solar energy resources introduces major challenges in power system management and necessitates the development of reliable probabilistic solar forecasts. As the first part of the development of probabilistic forecasts based on the Weather Research and Forecasting model with solar extensions (WRF-Solar), this study presents a tangent linear approach to identify input variables responsible for the largest uncertainties in predicting surface solar irradiance and clouds. A tangent linear analysis is capable of efficiently investigating sensitivities of output variables with respect to various input variables of WRF-Solar because this approach avoids the computational burden of perturbing the initial conditions of individual input variables. We develop tangent linear models (TLMs) for six WRF-Solar physics packages that control the formation and dissipation of clouds and solar radiation, and we evaluate the validity of TLMs using a linearity test. The tangent linear sensitivity analysis is conducted under various scenarios based on satellite observations and model simulations to consider realistic input conditions. A simple method is used to quantify the impact of the uncertainty of input variables on the output variables from the TLMs. The results demonstrate that uncertainties in the output variables that are the focus of this study—including global horizontal irradiance, direct normal irradiance, cloud mixing ratio, cloud tendency, cloud fraction, and sensible and latent heat fluxes—are highly sensitive to uncertainties in 14 input variables. This study indicates that the tangent linear method can identify key variables of physics modules in WRF-Solar that can be stochastically perturbed to generate ensemble-based probabilistic forecasts.

14 SOLAR ENERGY↗

DOE OSTI2019

Verification of Floating Offshore Wind Linearization Functionality in OpenFAST

The wind engineering community relies on multiphysics engineering software to run nonlinear time-domain simulations, e.g., for design standards-based loads analysis. Although most physics involved in wind energy are nonlinear, linearization of the underlying nonlinear system equations is often advantageous to understand the system properties and exploit well-established methods and tools for analyzing linear systems. Previous work in this area has focused on the development of the new linearization functionality of the open-source engineering tool OpenFAST for floating offshore wind turbines, as well as the concepts and mathematical background needed to understand and apply it correctly. This paper focuses on the verification of this new linearization functionality, which is carried out by comparing results to previous stable versions of FAST. A nonlinear time-domain simulation for a floating offshore platform is also compared to the time-domain response of the linearized state-space model. The linearized results show good alignment between OpenFAST and previous versions of FAST, as well as with the time-domain simulations, thereby showing the accuracy of the new features in OpenFAST.

17 WIND ENERGY↗

DOE OSTI2015

SU-E-T-136: Assessment of Seasonal Linear Accelerator Output Variations and Associated Impacts

Purpose: Application of process control theory in quality assurance programs promises to allow earlier identification of problems and potentially better quality in delivery than traditional paradigms based primarily on tolerances and action levels. The purpose of this project was to characterize underlying seasonal variations in linear accelerator output that can be used to improve performance or trigger preemptive maintenance. Methods: Review of runtime plots of daily (6 MV) output data acquired using in house ion chamber based devices over three years and for fifteen linear accelerators of varying make and model were evaluated. Shifts in output due to known interventions with the machines were subtracted from the data to model an uncorrected scenario for each linear accelerator. Observable linear trends were also removed from the data prior to evaluation of periodic variations. Results: Runtime plots of output revealed sinusoidal, seasonal variations that were consistent across all units, irrespective of manufacturer, model or age of machine. The average amplitude of the variation was on the order of 1%. Peak and minimum variations were found to correspond to early April and September, respectively. Approximately 48% of output adjustments made over the period examined were potentially avoidable if baseline levels had corresponded to the mean output, rather than to points near a peak or valley. Linear trends were observed for three of the fifteen units, with annual increases in output ranging from 2–3%. Conclusion: Characterization of cyclical seasonal trends allows for better separation of potentially innate accelerator behaviour from other behaviours (e.g. linear trends) that may be better described as true out of control states (i.e. non-stochastic deviations from otherwise expected behavior) and could indicate service requirements. Results also pointed to an optimal setpoint for accelerators such that output of machines is maintained within set tolerances and interventions are required less frequently.

07 ISOTOPE AND RADIATION SOURCES↗

DOE OSTI2016

TU-H-BRA-06: Characterization of a Linear Accelerator Operating in a Compact MRIGuided Radiation Therapy System

Purpose: To describe the performance of a linear accelerator operating in a compact MRI-guided radiation therapy system. Methods: A commercial linear accelerator was placed in an MRI unit that is employed in a commercial MR-based image guided radiation therapy (IGRT) system. The linear accelerator components were placed within magnetic field-reducing hardware that provided magnetic fields of less than 40 G for the magnetron, gun driver, and port circulator, with 1 G for the linear accelerator. The system did not employ a flattening filter. The test linear accelerator was an industrial 4 MV model that was employed to test the ability to run an accelerator in the MR environment. An MR-compatible diode detector array was used to measure the beam profiles with the accelerator outside and inside the MR field and with the gradient coils on and off to examine if there was any effect on the delivered dose distribution. The beam profiles and time characteristics of the beam were measured. Results: The beam profiles exhibited characteristic unflattened Bremsstrahlung features with less than ±1.5% differences in the profile magnitude when the system was outside and inside the magnet and less than 1% differences with the gradient coils on and off. The central axis dose rate fluctuated by less than 1% over a 30 second period when outside and inside the MRI. Conclusion: A linaccompatible MR design has been shown to be effective in not perturbing the operation of a commercial linear accelerator. While the accelerator used in the tests was 4MV, there is nothing fundamentally different with the operation of a 6MV unit, implying that the design will enable operation of the proposed clinical unit. Research funding provided by ViewRay, Inc.

60 APPLIED LIFE SCIENCES↗

NASA NTRS2012

Linear Estimation of Particle Bulk Parameters from Multi-Wavelength Lidar Measurements

An algorithm for linear estimation of aerosol bulk properties such as particle volume, effective radius and complex refractive index from multiwavelength lidar measurements is presented. The approach uses the fact that the total aerosol concentration can well be approximated as a linear combination of aerosol characteristics measured by multiwavelength lidar. Therefore, the aerosol concentration can be estimated from lidar measurements without the need to derive the size distribution, which entails more sophisticated procedures. The definition of the coefficients required for the linear estimates is based on an expansion of the particle size distribution in terms of the measurement kernels. Once the coefficients are established, the approach permits fast retrieval of aerosol bulk properties when compared with the full regularization technique. In addition, the straightforward estimation of bulk properties stabilizes the inversion making it more resistant to noise in the optical data. Numerical tests demonstrate that for data sets containing three aerosol backscattering and two extinction coefficients (so called 3 + 2 ) the uncertainties in the retrieval of particle volume and surface area are below 45% when input data random uncertainties are below 20 %. Moreover, using linear estimates allows reliable retrievals even when the number of input data is reduced. To evaluate the approach, the results obtained using this technique are compared with those based on the previously developed full inversion scheme that relies on the regularization procedure. Both techniques were applied to the data measured by multiwavelength lidar at NASA/GSFC. The results obtained with both methods using the same observations are in good agreement. At the same time, the high speed of the retrieval using linear estimates makes the method preferable for generating aerosol information from extended lidar observations. To demonstrate the efficiency of the method, an extended time series of observations acquired in Turkey in May 2010 was processed using the linear estimates technique permitting, for what we believe to be the first time, temporal-height distributions of particle parameters.

linear estimation↗

DOE OSTI2017

Radiocarbon Suggests the Hemiparasitic Annual Melampyrum Lineare Desr. May Acquire Carbon from Stressed Hosts

Abstract Hemiparasitic plants obtain water and solutes from their hosts, but much remains to be learned about these transfers. We used a forest girdling experiment to investigate how leaf gas exchange, carbon and nitrogen cycling in the root hemiparasite Melampyrum lineare Desr. responded to disturbance and changes in physiology of potential host trees. By preventing belowground C allocation by 35% of the canopy, girdling decreased the starch and soluble sugar contents of bulk forest floor fine roots. Photosynthetic rates of M. lineare were statistically significantly lower in the girdled plot, but their hypothesized drivers (foliar N, stomatal conductance and transpiration) had no statistically significant differences between girdled and non-girdled plots. However, M. lineare in the girdled plot had higher foliar C concentrations and Δ 14 C than in the control plot, suggesting possible photosynthetic down-regulation in the girdled plot due to influx of older (e.g., host-derived) C into the leaves of M. lineare . Within the girdled plot (but not the control plot), M. lineare foliar C concentrations were positively correlated with foliar Δ 14 C and δ 15 N, suggesting that M. lineare may respond to changes in both C and N biogeochemistry during the decline of dominant canopy species.

Geochemistry & Geophysics↗

DOE OSTI2023

Gelation and Re-entrance in Mixtures of Soft Colloids and Linear Polymers of Equal Size

Liquid mixtures composed of colloidal particles and much smaller non-adsorbing linear homopolymers can undergo a gelation transition due to polymer-mediated depletion forces. We now show that the addition of linear polymers to suspensions of soft colloids having the same hydrodynamic size yields a liquid-togel-to-re-entrant liquid transition. In particular, the dynamic state diagram of 1,4-polybutadiene star-linear polymer mixtures was determined with the help of linear viscoelastic and small-angle Xray scattering experiments. While keeping the star polymers below their nominal overlap concentration, a gel was formed upon increasing the linear polymer content. Further addition of linear chains yielded a re-entrant liquid. This unexpected behavior was rationalized by the interplay of three possible phenomena: (i) depletion interactions, driven by the size disparity between the stars and the polymer length scale which is the mesh size of its entanglement network; (ii) colloidal deswelling due to the increased osmotic pressure exerted onto the stars; and (iii) a concomitant progressive suppression of the depletion efficiency on increasing the polymer concentration due to reduced mesh size, hence a smaller range of attraction. Our results unveil an exciting new way to tailor the flow of soft colloids and highlight a largely unexplored path to engineer soft colloidal mixtures.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2015

The effect of changes in sea surface temperature on linear growth of Porites coral in Ambon Bay

Coral is one of the most important organisms in the coral reef ecosystem. There are several factors affecting coral growth, one of them is changes in sea surface temperature (SST). The purpose of this research is to understand the influence of SST variability on the annual linear growth of Porites coral taken from Ambon Bay. The annual coral linear growth was calculated and compared to the annual SST from the Extended Reconstructed Sea Surface Temperature version 3b (ERSST v3b) model. Coral growth was calculated by using Coral X-radiograph Density System (CoralXDS) software. Coral sample X-radiographs were used as input data. Chronology was developed by calculating the coral’s annual growth bands. A pair of high and low density banding patterns observed in the coral’s X-radiograph represent one year of coral growth. The results of this study shows that Porites coral extents from 2001-2009 and had an average growth rate of 1.46 cm/year. Statistical analysis shows that the annual coral linear growth declined by 0.015 cm/year while the annual SST declined by 0.013°C/year. SST and the annual linear growth of Porites coral in the Ambon Bay is insignificantly correlated with r=0.304 (n=9, p>0.05). This indicates that annual SST variability does not significantly influence the linear growth of Porites coral from Ambon Bay. It is suggested that sedimentation load, salinity, pH or other environmental factors may affect annual linear coral growth.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2015

The origin of linear scaling Fock matrix calculation with density prescreening

A theorem was proven, which reads that the number of nonzero two-electron integrals scales linearly with respect to the number of basis functions for large molecular systems. This permits to show that linear scaling property of the Fock matrix calculation with using density prescreening arises due to linear scaling properties of the number of nonzero two-electron integrals and the number of leading matrix elements of density matrix. This property is reinforced by employing the density prescreening technique. The use of the density difference prescreening further improves the linear scaling property of the Fock matrix calculation method. As a result, the linear scaling regime of the Fock matrix calculation can begin from the number of basis functions of 2000–3000 in dependence on the basis function type in molecular calculations. It was also shown that the conventional algorithm of Fock matrix calculation from stored nonzero two-electron integrals with density prescreening possesses linear scaling property.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2016

Non-Condon equilibrium Fermi’s golden rule electronic transition rate constants via the linearized semiclassical method

In this paper, we test the accuracy of the linearized semiclassical (LSC) expression for the equilibrium Fermi’s golden rule rate constant for electronic transitions in the presence of non-Condon effects. We do so by performing a comparison with the exact quantum-mechanical result for a model where the donor and acceptor potential energy surfaces are parabolic and identical except for shifts in the equilibrium energy and geometry, and the coupling between them is linear in the nuclear coordinates. Since non-Condon effects may or may not give rise to conical intersections, both possibilities are examined by considering: (1) A modified Garg-Onuchic-Ambegaokar model for charge transfer in the condensed phase, where the donor-acceptor coupling is linear in the primary mode coordinate, and for which non-Condon effects do not give rise to a conical intersection; (2) the linear vibronic coupling model for electronic transitions in gas phase molecules, where non-Condon effects give rise to conical intersections. We also present a comprehensive comparison between the linearized semiclassical expression and a progression of more approximate expressions. The comparison is performed over a wide range of frictions and temperatures for model (1) and over a wide range of temperatures for model (2). The linearized semiclassical method is found to reproduce the exact quantum-mechanical result remarkably well for both models over the entire range of parameters under consideration. In contrast, more approximate expressions are observed to deviate considerably from the exact result in some regions of parameter space.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2016

Non-Condon nonequilibrium Fermi’s golden rule rates from the linearized semiclassical method

The nonequilibrium Fermi’s golden rule describes the transition between a photoexcited bright donor electronic state and a dark acceptor electronic state, when the nuclear degrees of freedom start out in a nonequilibrium state. In a previous paper [X. Sun and E. Geva, J. Chem. Theory Comput. 12, 2926 (2016)], we proposed a new expression for the nonequilibrium Fermi’s golden rule within the framework of the linearized semiclassical approximation and based on the Condon approximation, according to which the electronic coupling between donor and acceptor is assumed constant. In this paper we propose a more general expression, which is applicable to the case of non-Condon electronic coupling. We test the accuracy of the new non-Condon nonequilibrium Fermi’s golden rule linearized semiclassical expression on a model where the donor and acceptor potential energy surfaces are parabolic and identical except for shifts in the equilibrium energy and geometry, and the coupling between them is linear in the nuclear coordinates. Since non-Condon effects may or may not give rise to conical intersections, both possibilities are examined by considering the following: (1) A modified Garg-Onuchic-Ambegaokar model for charge transfer in the condensed phase, where the donor-acceptor coupling is linear in the primary-mode coordinate, and for which non-Condon effects do not give rise to a conical intersection; (2) the linear vibronic coupling model for electronic transitions in gas phase molecules, where non-Condon effects give rise to conical intersections. We also present a comprehensive comparison between the linearized semiclassical expression and a progression of more approximate expressions, in both normal and inverted regions, and over a wide range of initial nonequilibrium states, temperatures, and frictions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Linearized frequency domain Landau-Lifshitz-Gilbert equation formulation

We present a general finite element linearized Landau-Lifshitz-Gilbert equation (LLGE) solver for magnetic systems under weak time-harmonic excitation field. The linearized LLGE is obtained by assuming a small deviation around the equilibrium state of the magnetic system. Inserting such expansion into LLGE and keeping only first order terms gives the linearized LLGE, which gives a frequency domain solution for the complex magnetization amplitudes under an external time-harmonic applied field of a given frequency. We solve the linear system with an iterative solver using generalized minimal residual method. We construct a preconditioner matrix to effectively solve the linear system. The validity, effectiveness, speed, and scalability of the linear solver are demonstrated via numerical examples.

36 MATERIALS SCIENCE↗

DOE OSTI2014

MULTI-SPACECRAFT OBSERVATIONS OF LINEAR MODES AND SIDEBAND WAVES IN ION-SCALE SOLAR WIND TURBULENCE

In the scenario of weak turbulence, energy is believed to be cascaded from smaller to larger wave numbers and frequencies due to weak wave-wave interactions. Based on its perturbative treatment one may regard plasma turbulence as a superposition of linear modes (or normal modes) and sideband waves (or nonlinear modes). In this study, we use magnetic field and plasma measurements of nine solar wind events obtained by the Cluster spacecraft and make extensive use of a high-resolution wave vector analysis method, the Multi-point Signal Resonator technique, to find frequencies and wave vectors of discrete modes on ion kinetic scales in the plasma rest frame. The primarily unstructured wave observations in the frequency-wave number diagram are classified into three distinct linear modes (proton Bernstein modes, helium-alpha Bernstein modes, and kinetic Alfvén waves) and the sideband waves by comparing with the dispersion relations derived theoretically from linear Vlasov theory using observational values of the plasma parameter beta and the propagation angle from the mean magnetic field. About 60% of the observed discrete modes can be explained by the linear modes, primarily as the proton Bernstein and the kinetic Alfvén waves, within the frequency uncertainties, while the rest of the population (about 40%) cannot be classified as linear modes due to the large deviation from dispersion relations. We conclude that both the linear modes and sideband wave components are needed to construct the wave picture of solar wind turbulence on ion-kinetic scales.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Linear magnetoresistance with a universal energy scale in the strong-coupling superconductor Mo8Ga41 without quantum criticality

The recent discovery of a nonsaturating linear magnetoresistance in several correlated electron systems near a quantum critical point has revealed an interesting interplay between the linear magnetoresistance and the zero-field linear-in-temperature resistivity. These studies suggest a possible role of quantum criticality on the observed linear magnetoresistance. Here we report our discovery of a nonsaturating, linear magnetoresistance in Mo 8 Ga 41 , a nearly isotropic strong electron-phonon coupling superconductor with a linear-in-temperature resistivity from the transition temperature to ~ 55 K. The growth of the resistivity in field is comparable to that in temperature, provided that both quantities are measured in the energy unit. Overall, our data sets are remarkably similar to magnetoresistance data of the optimally doped La 2 - x Sr x CuO 4 , despite the clearly different crystal and electronic structures, and the apparent absence of quantum critical physics in Mo 8 Ga 41 . A new empirical scaling formula is developed, which is able to capture the key features of the low-temperature magnetoresistance data of Mo 8 Ga 41 , as well as the data of La 2 - x Sr x CuO 4 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2014

SU-E-T-475: An Accurate Linear Model of Tomotherapy MLC-Detector System for Patient Specific Delivery QA

Purpose: An accurate leaf fluence model can be used in applications such as patient specific delivery QA and in-vivo dosimetry for TomoTherapy systems. It is known that the total fluence is not a linear combination of individual leaf fluence due to leakage-transmission, tongue-and-groove, and source occlusion effect. Here we propose a method to model the nonlinear effects as linear terms thus making the MLC-detector system a linear system. Methods: A leaf pattern basis (LPB) consisting of no-leaf-open, single-leaf-open, double-leaf-open and triple-leaf-open patterns are chosen to represent linear and major nonlinear effects of leaf fluence as a linear system. An arbitrary leaf pattern can be expressed as (or decomposed to) a linear combination of the LPB either pulse by pulse or weighted by dwelling time. The exit detector responses to the LPB are obtained by processing returned detector signals resulting from the predefined leaf patterns for each jaw setting. Through forward transformation, detector signal can be predicted given a delivery plan. An equivalent leaf open time (LOT) sinogram containing output variation information can also be inversely calculated from the measured detector signals. Twelve patient plans were delivered in air. The equivalent LOT sinograms were compared with their planned sinograms. Results: The whole calibration process was done in 20 minutes. For two randomly generated leaf patterns, 98.5% of the active channels showed differences within 0.5% of the local maximum between the predicted and measured signals. Averaged over the twelve plans, 90% of LOT errors were within +/−10 ms. The LOT systematic error increases and shows an oscillating pattern when LOT is shorter than 50 ms. Conclusion: The LPB method models the MLC-detector response accurately, which improves patient specific delivery QA and in-vivo dosimetry for TomoTherapy systems. It is sensitive enough to detect systematic LOT errors as small as 10 ms.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2019

Fast and Robust Linear Solvers based on Hierarchical Matrices (LDRD Final Report)

This report is the final report for the LDRD project "Fast and Robust Linear Solvers using Hierarchical Matrices". The project was a success. We developed two novel algorithms for solving sparse linear systems. We demonstrated their effectiveness on ill-conditioned linear systems from ice sheet simulations. We showed that in many cases, we can obtain near-linear scaling. We believe this approach has strong potential for difficult linear systems and should be considered for other Sandia and DOE applications. We also report on some related research activities in dense solvers and randomized linear algebra.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Compare linear-system solver and preconditioner stacks with emphasis on GPU performance and propose phase-2 NGP solver development pathway

The goal of the ExaWind project is to enable predictive simulations of wind farms comprised of many megawatt-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. The primary physics codes in the ExaWind project are Nalu-Wind, which is an unstructured-grid solver for the acoustically incompressible Navier-Stokes equations, and OpenFAST, which is a whole-turbine simulation code. The Nalu-Wind model consists of the mass-continuity Poisson-type equation for pressure and a momentum equation for the velocity. For such modeling approaches, simulation times are dominated by linear-system setup and solution for the continuity and momentum systems. For the ExaWind challenge problem, the moving meshes greatly affect overall solver costs as reinitialization of matrices and recomputation of preconditioners is required at every time step. In this report we evaluated GPU-performance baselines for the linear solvers in the Trilinos and hypre solver stacks using two representative Nalu-Wind simulations: an atmospheric boundary layer precursor simulation on a structured mesh, and a fixed-wing simulation using unstructured overset meshes. Both strong-scaling and weak-scaling experiments were conducted on the OLCF supercomputer Summit and similar proxy clusters. We focused on the performance of multi-threaded Gauss-Seidel and two-stage Gauss-Seidel that are extensions of classical Gauss-Seidel; of one-reduce GMRES, a communication-reducing variant of the Krylov GMRES; and algebraic multigrid methods that incorporate the afore-mentioned methods. The team has established that AMG methods are capable of solving linear systems arising from the fixed-wing overset meshes on CPU, a critical intermediate result for ExaWind FY20 Q3 and Q4 milestones. For the fixed-wing strong-scaling study (model with 3M grid-points), the team identified that Nalu-Wind simulations with the new Trilinos and hypre solvers scale to modest GPU counts, maintaining above 70% efficiency up to 6 GPUs. However, there still remain significant bottlenecks to performance: matrix assembly (hypre), AMG setup (hypre and Trilinos) In the weak-scaling experiments (going from 0.4M to 211M gridpoints), it's shown that the solver apply phases are faster on GPUs, but that Nalu-Wind simulation times grow, primarily due to the multigrid-setup process. Finally, based on the report outcomes, we propose a linear solver path-forward for the remainder of the ExaWind project. Near term, the NREL team will continue their work on GPU-based linear-system assembly. They will also investigate how the use of alternatives to the NVIDIA UVM (unified virtual memory) paradigm affects performance. Longer term, the NREL team will evaluate algorithmic performance on other types of accelerators and merge their improvements back to the main hypre repository branch. Near term, the Trilinos team will address performance bottlenecks identified in this milestone, such as implementing a GPU-based segregated momentum solve and reusing matrix graphs across linear-system assembly phases. Longer term, the Trilinos team will do detailed analysis and optimization of multigrid setup.

17 WIND ENERGY↗