Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “linear optimization”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Earthquake Arrival Association with Backprojection and Graph Theory

The association of seismic-wave arrivals with causative earthquakes becomes progressively more challenging as arrival detection methods become more sensitive, and particularly when earthquake rates are high. For instance, seismic waves arriving across a monitoring network from several sources may overlap in time, false arrivals may be detected, and some arrivals may be of unknown phase (e.g., P or S waves). We propose an automated method to associate arrivals with earthquake sources and obtain source locations applicable to such situations. To do so, we use a pattern detection metric based on the principle of back-projection to reveal candidate sources followed by graph-theory-based clustering and an integer linear optimization routine to associate arrivals with the minimum number of sources necessary to explain the data. We find that this method solves for all sources and phase assignments simultaneously, rather than in a sequential greedy procedure as is common in other association routines. We demonstrate our method on both synthetic and real data from the Integrated Plate Boundary Observatory Chile seismic network of northern Chile. For the synthetic tests, we report results for cases with varying complexity, including rates of 500 earthquakes/day and 500 false arrivals/station/day, for which we measure true positive detection accuracy of >95%. For the real data, we develop a new catalog between 1 January 2010 and 31 December 2017 containing 817,548 earthquakes, with detection rates on average 279 earthquakes/day and a magnitude-of-completion of M~1.8. A subset of detections are identified as sources related to quarry and industrial site activity, and we also detect thousands of foreshocks and aftershocks of the 1 April 2014 Mw 8.2 Iquique earthquake. During the highest rate of aftershock activity, >600 earthquakes/day are detected in the vicinity of the Iquique earthquake rupture zone.

58 GEOSCIENCES↗
DOE OSTI2015

Using learning curves on energy-efficient technologies to estimate future energy savings and emission reduction potentials in the U.S. iron and steel industry

Increasing concerns on non-sustainable energy use and climate change spur a growing research interest in energy efficiency potentials in various critical areas such as industrial production. This paper focuses on learning curve aspects of energy efficiency measures in the U.S iron and steel sector. A number of early-stage efficient technologies (i.e., emerging or demonstration technologies) are technically feasible and have the potential to make a significant contribution to energy saving and CO 2 emissions reduction, but fall short economically to be included. However, they may also have the cost effective potential for significant cost reduction and/or performance improvement in the future under learning effects such as ‘learning-by-doing’. The investigation is carried out using ISEEM, a technology oriented, linear optimization model. We investigated how steel demand is balanced with/without the availability learning curve, compared to a Reference scenario. The retrofit (or investment in some cases) costs of energy efficient technologies decline in the scenario where learning curve is applied. The analysis also addresses market penetration of energy efficient technologies, energy saving, and CO 2 emissions in the U.S. iron and steel sector with/without learning impact. Accordingly, the study helps those who use energy models better manage the price barriers preventing unrealistic diffusion of energy-efficiency technologies, better understand the market and learning system involved, predict future achievable learning rates more accurately, and project future savings via energy-efficiency technologies with presence of learning. We conclude from our analysis that, most of the existing energy efficiency technologies that are currently used in the U.S. iron and steel sector are cost effective. Penetration levels increases through the years, even though there is no price reduction. However, demonstration technologies are not economically feasible in the U.S. iron and steel sector with the current cost structure. In contrast, some of the demonstration technologies are adapted in the mid-term and their penetration levels increase as the prices go down with learning curve. We also observe large penetration of 225kg pulverized coal injection with the presence of learning.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2018

NA-22 Particle Classifier Quarterly Report FY18 Q1 [Automated Particle Classifier]

This is the first quarter of the third and final year of this project. Much of this quarter was taken up with preparing the comprehensive paper that details the collection of appropriate data, the pre-processing of data, the forms and development of the algorithms, and the scoring of performance. These four processes were still a bit unpolished among the different algorithms, so by synergy the paper raised the quality of performance of each algorithm. For completeness, the group implemented two more kinds of algorithms for performance comparison: Gatti-DeMartini’s optimal linear filter, and a more straightforward (and more effective) implementation of principal component analysis (PCA) than we had previously built.

47 OTHER INSTRUMENTATION↗
DOE OSTI2019

Workshop Report on Basic Research Needs for Scientific Machine Learning: Core Technologies for Artificial Intelligence

Scientific Machine Learning (SciML) and Artificial Intelligence (AI) will have broad use and transformative effects across the Department of Energy. Accordingly, the January 2018 Basic Research Needs workshop identified six Priority Research Directions (PRDs). The first three PRDs describe foundational research themes that correspond to the need for domain-awareness (PRD #1), interpretability (PRD #2), and robustness (PRD #3). The other three PRDs describe capability research themes and correspond to the three major use cases for massive scientific data analysis (PRD #4), machine learning-enhanced modeling and simulation (PRD #5), and intelligent automation and decision-support for complex systems (PRD #6). The Priority Research Directions provide a sound basis for a coherent, long-term research and development strategy in SciML and AI. Over the last decade, DOE investments in applied mathematics have laid the groundwork for the type of basic research that will underpin key advances in the six PRDs. Such advances will build on the work from leading researchers in optimization, linear algebra, high-performance solvers and algorithms, multiscale modeling and simulation, complex systems research, uncertainty quantification, and the new basic research areas that will emerge from the pursuit of transformative technologies.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Brochure on Basic Research Needs for Scientific Machine Learning: Core Technologies for Artificial Intelligence [Slides]

Scientific Machine Learning (SciML) and Artificial Intelligence (AI) will have broad use and transformative effects across the Department of Energy. Accordingly, the January 2018 Basic Research Needs workshop identified six Priority Research Directions (PRDs). The first three PRDs describe foundational research themes that correspond to the need for domain-awareness (PRD #1), interpretability (PRD #2), and robustness (PRD #3). The other three PRDs describe capability research themes and correspond to the three major use cases for massive scientific data analysis (PRD #4), machine learning-enhanced modeling and simulation (PRD #5), and intelligent automation and decision-support for complex systems (PRD #6). The Priority Research Directions provide a sound basis for a coherent, long-term research and development strategy in SciML and AI. Over the last decade, DOE investments in applied mathematics have laid the groundwork for the type of basic research that will underpin key advances in the six PRDs. Such advances will build on the work from leading researchers in optimization, linear algebra, high-performance solvers and algorithms, multiscale modeling and simulation, complex systems research, uncertainty quantification, and the new basic research areas that will emerge from the pursuit of transformative technologies.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Are coupled renewable-battery power plants more valuable than independently sited installations?

Coupled renewable-battery powerplants differ from the traditional concept of independent siting of electricity resources within transmission networks. Prior research on the value proposition and cost savings from coupling did not consider the geographic constraint of co-location. This paper fills the gap by assessing how pricing volatility differences between nodes within electricity markets impact the system value of coupled renewable-battery projects as compared to independent VRE and battery installations. We use wholesale power market prices from 2012–2019 across the seven main U.S. independent system operators (ISOs) with a linear optimization program to compare the electricity market value of coupled projects to the value of the same underlying sub-components, deployed separately. We find that additional value from adding a 4-hour battery sized to 50% of renewable-plant nameplate capacity is $\$$10/MWh across ISOs on average. The highest boost occurs in California ($\$$15/MWh), where the value of adding storage to solar rises over time in tandem with increased solar penetration in the region. If renewables and batteries are deployed independently, we estimate that $\$$12.5/MWh of additional value could be achieved because of more flexibility on battery siting and operation. The $\$$12.5/MWh coupling penalty is reduced to $\$$1.6/MWh when considering alternative approaches to integrating battery storage. This result implies that renewable-battery power plants will play an increasing role in electricity systems if they can be built for $\$$2–$\$$13/MWh less than independent projects of comparable size. However, the wide regional variation in coupling penalties, along with the importance of conditions captured in our sensitivity cases, suggests the tradeoff between coupling penalties and savings will vary by situation. Therefore, roles exist for independent and coupled projects from a system optimization perspective.

14 SOLAR ENERGY↗
DOE OSTI2021

Keep it short: Exploring the impacts of configuration choices on the recent economics of solar-plus-battery and wind-plus-battery hybrid energy plants

Coupled renewable-battery powerplants differ from the traditional concept of independent siting of electricity resources within transmission networks. Prior research on the value proposition and cost savings from coupling did not consider the geographic constraint of co-location. This paper fills the gap by assessing how pricing volatility differences between nodes within electricity markets impact the system value of coupled renewable-battery projects as compared to independent VRE and battery installations. We use wholesale power market prices from 2012–2019 across the seven main U.S. independent system operators (ISOs) with a linear optimization program to compare the electricity market value of coupled projects to the value of the same underlying sub-components, deployed separately. We find that additional value from adding a 4-hour battery sized to 50% of renewable-plant nameplate capacity is $\$10$/MWh across ISOs on average. The highest boost occurs in California ($\$15$/MWh), where the value of adding storage to solar rises over time in tandem with increased solar penetration in the region. If renewables and batteries are deployed independently, we estimate that $\$12.5$/MWh of additional value could be achieved because of more flexibility on battery siting and operation. The $\$12.5$/MWh coupling penalty is reduced to $\$1.6$/MWh when considering alternative approaches to integrating battery storage. This result implies that renewable-battery power plants will play an increasing role in electricity systems if they can be built for $\$2$–$\$13$/MWh less than independent projects of comparable size. However, the wide regional variation in coupling penalties, along with the importance of conditions captured in our sensitivity cases, suggests the tradeoff between coupling penalties and savings will vary by situation. Therefore, roles exist for independent and coupled projects from a system optimization perspective.

14 SOLAR ENERGY↗
DOE OSTI2019

Measurement of CH{sub 3}D on Titan at Submillimeter Wavelengths

We present the first radio/submillimeter detection of monodeuterated methane (CH{sub 3}D) in Titan’s atmosphere, using archival data from of the Atacama Large Millimeter/submillimeter Array (ALMA). The J {sub K} = 2{sub 1}−1{sub 1} and J {sub K} = 2{sub 0}−1{sub 0} transitions at 465.235 and 465.250 GHz (∼0.644 mm) were measured at significance levels of 4.6σ and 5.7σ, respectively. These two lines were modeled using the Non-linear optimal Estimator for MultivariatE spectral analySIS (NEMESIS) radiative transfer code to determine the disk-averaged CH{sub 3}D volume mixing ratio = 6.157 × 10{sup −6} in Titan’s stratosphere (at altitudes >130 km). By comparison with the CH{sub 4} vertical abundance profile measured by Cassini–Huygens mass spectrometry, the resulting value for D/H in CH{sub 4} is (1.033 ± 0.081) × 10{sup −4}. This is consistent with previous ground-based and in situ measurements from the Cassini–Huygens mission, though slightly lower than the average of the previous values. Additional CH{sub 3}D observations at higher spatial resolution will be required to determine a value truly comparable with the Cassini–Huygens CH{sub 4} measurements, by measuring CH{sub 3}D with ALMA close to Titan’s equator. In the post-Cassini era, spatially resolved observations of CH{sub 3}D with ALMA will enable the latitudinal distribution of methane to be determined, making this an important molecule for further studies.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

A General Method for Estimating Zonal Transmission Interface Limits from Nodal Network Data: Preprint

Capacity expansion models for the electric power system often employ zonal (rather than nodal) resolution, necessitating estimates of aggregate power transfer limits across the interfaces between model zones. Interface limits between planning areas are sometimes published, but they are not generalizable to arbitrary zone shapes. There is thus a need for a reproducible method for estimating interface transfer limits (ITLs) between user-defined zones directly from nodal transmission system data. Here, we present a simple method for estimating ITLs using a DC power flow approximation via the power transfer distribution factor (PTDF) matrix. Linear optimization is performed to identify the distribution of power flows that maximizes the total flow on interface-crossing lines, subject to individual line ratings, limits on bus injection/withdrawal, and the relationships among flows, injections, and withdrawals imposed by the PTDF matrix. We demonstrate the application of the method on a 134-zone ~65000-bus system, and we explore the influence of flow direction, contingency level, and zone size on the estimated ITLs. There is significant heterogeneity in the ratio of the ITL to the sum of interface-crossing line ratings, which highlights the importance of accounting for the physical constraints on power flows imposed by Kirchhoff's laws when estimating zonal ITLs.

17 WIND ENERGY↗
DOE OSTI2021

Development of an in situ dual-channel thermal desorption gas chromatography instrument for consistent quantification of volatile, intermediate-volatility and semivolatile organic compounds

Abstract. Aerosols are a source of great uncertainty in radiative forcing predictions and have poorly understood health impacts. Most aerosol mass is formed in the atmosphere from reactive gas-phase organic precursors, forming secondary organic aerosol (SOA). Semivolatile organic compounds (SVOCs) (effective saturation concentration, C*, of 10−1–103 µg m−3) comprise a large fraction of organic aerosol, while intermediate-volatility organic compounds (IVOCs) (C* of 103–106 µg m−3) and volatile organic compounds (VOCs) (C* ≥ 106 µg m−3) are gas-phase precursors to SOA and ozone. The Comprehensive Thermal Desorption Aerosol Gas Chromatograph (cTAG) is the first single instrument simultaneously quantitative for a broad range of compound-specific VOCs, IVOCs and SVOCs. cTAG is a two-channel instrument which measures concentrations of C5–C16 alkane-equivalent-volatility VOCs and IVOCs on one channel and C14–C32 SVOCs on the other coupled to a single high-resolution time-of-flight mass spectrometer, achieving consistent quantification across 15 orders of magnitude of vapor pressure. cTAG obtains concentrations hourly and gas–particle partitioning for SVOCs every other hour, enabling observation of the evolution of these species through oxidation and partitioning into the particle phase. Online derivatization for the SVOC channel enables detection of more polar and oxidized species. In this work we present design details and data evaluating key parameters of instrument performance such as I/VOC collector design optimization, linearity and reproducibility of calibration curves obtained using a custom liquid evaporation system for I/VOCs and the effect of an ozone removal filter on instrument performance. Example timelines of precursors with secondary products are shown, and analysis of a subset of compounds detectable by cTAG demonstrates some of the analytical possibilities with this instrument.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Development of observation-based global multilayer soil moisture products for 1970 to 2016

Abstract. Soil moisture (SM) datasets are critical to understanding the global water, energy, and biogeochemical cycles and benefit extensive societal applications. However, individual sources of SM data (e.g., in situ and satellite observations, reanalysis, offline land surface model simulations, Earth system model – ESM – simulations) have source-specific limitations and biases related to the spatiotemporal continuity, resolutions, and modeling and retrieval assumptions. Here, we developed seven global, gap-free, long-term (1970–2016), multilayer (0–10, 10–30, 30–50, and 50–100 cm) SM products at monthly 0.5∘ resolution (available at https://doi.org/10.6084/m9.figshare.13661312.v1; Wang and Mao, 2021) by synthesizing a wide range of SM datasets using three statistical methods (unweighted averaging, optimal linear combination, and emergent constraint). The merged products outperformed their source datasets when evaluated with in situ observations (mean bias from −0.044 to 0.033 m3 m−3, root mean square errors from 0.076 to 0.104 m3 m−3, Pearson correlations from 0.35 to 0.67) and multiple gridded datasets that did not enter merging because of insufficient spatial, temporal, or soil layer coverage. Three of the new SM products, which were produced by applying any of the three merging methods to the source datasets excluding the ESMs, had lower bias and root mean square errors and higher correlations than the ESM-dependent merged products. The ESM-independent products also showed a better ability to capture historical large-scale drought events than the ESM-dependent products. The merged products generally showed reasonable temporal homogeneity and physically plausible global sensitivities to observed meteorological factors, except that the ESM-dependent products underestimated the low-frequency temporal variability in SM and overestimated the high-frequency variability for the 50–100 cm depth. Based on these evaluation results, the three ESM-independent products were finally recommended for future applications because of their better performances than the ESM-dependent ones. Despite uncertainties in the raw SM datasets and fusion methods, these hybrid products create added value over existing SM datasets because of the performance improvement and harmonized spatial, temporal, and vertical coverages, and they provide a new foundation for scientific investigation and resource management.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Robust historical evapotranspiration trends across climate regimes

Evapotranspiration (ET) links the hydrological, energy and carbon cycles on the land surface. Quantifying ET and its spatio-temporal changes is also key to understanding climate extremes such as droughts, heatwaves and flooding. Regional ET estimates require reliable observation-based gridded ET datasets, and while many have been developed using physically based, empirically based and hybrid techniques, their efficacy, and particularly the efficacy of their uncertainty estimates, is difficult to verify. In this work, we extend the methodology used in Hobeichi et al. (2018) to derive two new versions of the Derived Optimal Linear Combination Evapotranspiration (DOLCE) product, with observationally constrained spatio-temporally varying uncertainty estimates, higher spatial resolution, more constituent products and extended temporal coverage (1980–2018). After demonstrating the efficacy of these uncertainty estimates with out-of-sample testing, we derive novel ET climatology clusters for the land surface, based on the magnitude and variability of ET at each location on land. The new clusters include three wet and three dry regimes and provide an approximation of Köppen–Geiger climate classes. The verified uncertainty estimates and extended time period then allow us to examine the robustness of historical trends spatially and in each of these six ET climatology clusters. We find that despite robust decreasing ET trends in some regions these do not correlate with behavioural ET clusters. Each cluster, and the majority of the Earth's surface, shows clear robust increases in ET over the recent historical period. The new datasets DOLCE V2.1 and DOLCE V3 can be used for benchmarking global ET estimates and for examining ET trends respectively.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2017

A Life Cycle Analysis of Refinery Fuel Products Air Emissions Using Refinery Emissions Inventory Data

With the transportation sector being a major source of air pollutant emissions, this study seeks to evaluate criteria pollutant emissions associated with the use of petroleum fuels in vehicles using the GREET® (Greenhouse gases, Regulated Emissions, and Energy use in Transportation) well-to-wheel model. The life cycle of petroleum fuels includes the major stages of crude recovery, crude transportation, crude refining, fuel distribution and fuel combustion (vehicle operation). This study focuses on quantifying refinery emissions, in terms of both refinery throughput and various refinery fuel products, by matching a refinery emissions inventory dataset with refinery operation information, at various levels (national, regional, facility, and process unit). The refinery emissions in terms refinery throughput (per refinery crude input, in g/mmbtu crude) are developed at a regional level for various Petroleum Administration for Defense Districts (PADD), and also aggregated at the national level. To allocate refinery emissions to refinery products, a methodology is developed using a refinery operation optimization Linear Programming (LP) model for individual refineries. The results from individual refinery facilities are then aggregated to obtain statistical national average (capacity weighted) emissions for each product. Because refineries vary by complexity of operation, configuration, crude quality, and product slate, the derived emissions demonstrate large variation for each product and per unit of crude input. Relative to previous estimates used in the GREET model, the present research shows reductions in refinery (and life cycle) emissions for most criteria pollutants. The reduction is especially significant for sulfur dioxide (SOx) emissions.

Allocation↗
DOE OSTI2021

Resilient Operation of Power Distribution Systems Using MPC-Based Critical Service Restoration: Preprint

Power distribution systems are more prone to disruptions and cause most power system outages. We propose a service restoration technique to recover the system service (electricity delivery) following an extreme event-triggered substation outage. The proposed technique considers the problem of controlling distributed energy resources (DERs) of a distribution system with the objective of achieving maximum load pick up while satisfying network flow and voltage constraints. The problem is formulated as a model predictive control (MPC), where a linearized optimal power flow (OPF) model is employed to describe the network. The formulation is augmented with a ramping (up) reserve product for the DERs to ensure an upward monotonic load restoration as time evolves. We perform simulations considering the IEEE 13-bus test feeder integrated with wind, solar, microturbine, and energy storage devices. We demonstrate the efficacy of the devised technique in restoring the system loads monotonically, without shedding previously restored loads. We also show the benefit of co-optimization of power and reserve products for DERs on service restoration. In addition, the capability of the technique in regulating nodal voltages and reducing renewable power curtailment is demonstrated.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2021

Resilient Operation of Power Distribution Systems Using MPC-Based Critical Service Restoration

Power distribution systems are more prone to disruptions and cause most power system outages. We propose a service restoration technique to recover the system service (electricity delivery) following an extreme event-triggered substation outage. The proposed technique considers the problem of controlling distributed energy resources (DERs) of a distribution system with the objective of achieving maximum load pick up while satisfying network flow and voltage constraints. The problem is formulated as a model predictive control (MPC), where a linearized optimal power flow (OPF) model is employed to describe the network. The formulation is augmented with a ramping (up) reserve product for the DERs to ensure an upward monotonic load restoration as time evolves. We perform simulations considering the IEEE 13-bus test feeder integrated with wind, solar, microturbine, and energy storage devices. We demonstrate the efficacy of the devised technique in restoring the system loads monotonically, without shedding previously restored loads. We also show the benefit of co-optimization of power and reserve products for DERs on service restoration. In addition, the capability of the technique in regulating nodal voltages and reducing renewable power curtailment is demonstrated.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2020

Identification and Quantification of Beta-Emitters in Waste Packages by Segmented Gamma-Scanning - 20114

A commonly applied method for the non-destructive characterization of the radioactive inventory of waste packages (e.g. 200-l drums) is segmented gamma-scanning. The gamma-emitting inventory is identified via their characteristic lines in the measured spectra. The corresponding net peak areas allow for quantification applying appropriate models. The identification and quantification of beta-emitters present in the waste package require further evaluation. While some of them emit gamma-rays, too, which can be used for identification and quantification, pure beta-emitters contribute to the gamma-spectra only by their Bremsstrahlung-spectra. {sup 32}P, {sup 90}Sr and {sup 90}Y are typical representatives of these isotopes. A method is developed for identification and quantification of these pure beta-emitters in radioactive waste packages. Origin of the procedure is the evaluation of the measured gamma-spectrum. After the identification of all lines present in the spectrum (characteristic gamma-lines, single- and double-escape-lines, X-ray-lines, annihilation peak etc.) this information is used together with calibration data of the detection system and further a-priori information like matrix composition, cross-section data from databases etc. to simulate the spectra without the Bremsstrahlung-components by an appropriate method. This may be Monte Carlo simulations or, like in our case, a computer code taking into account mathematical descriptions of the physical effects like photo effect, (multiple) Compton scattering, backscattering etc. and the attenuation effects of the waste matrix. In any case, the resulting spectrum must simulate the real spectrum without its Bremsstrahlung-component as good as possible. Subtracting the simulated from the measured spectrum then results in the Bremsstrahlung-components caused by the beta-emitters. Prior to evaluation, a set of Bremsstrahlung-spectra is calculated and stored for different beta-emitters in different matrices using the Bethe-Heitler equation. This data set can be extended for new conditions, if necessary, and is allocated in a data base for future application. Applying a non-linear optimization using the generalized reduced gradient method for comparing the calculated with the derived Bremsstrahlung-spectra results in the identification of the beta-emitter and a factor, which is proportional to its activity. The proportionality is determined by previous calibration measurements. The application of the method is demonstrated by measurements on a 200-l mock-up drum and a real waste package. (authors)

07 ISOTOPE AND RADIATION SOURCES↗
DOE OSTI2016

A Full Multigrid Method for the Self-Adjoint Angular Flux Equation Based on Cellwise Block Jacobi Iteration

Previous work by Densmore et al. has demonstrated that multigrid methods for the self-adjoint angular flux (SAAF) equation with cellwise block Jacobi smoothing can be extremely effective at solving for the angular flux in one dimension. The extension of that work to two dimensions demonstrated that while the smoother works well, the use of a direct coarse-grid approximation can severely limit the rate of convergence for optically thin cells. In that paper, this convergence limit was evaded through the use of a partially Galerkin coarse-grid approximation. However, relying on a Galerkin coarse-grid approximation is not ideal as constructing the coarse-grid discretization in this approach is complicated. The motivation for this summary is to find a method that can work without the need for a Galerkin coarse-grid approximation. The Full Multigrid (FMG) method is well known as a method that can theoretically solve a problem to its discretization accuracy with optimal linear computational complexity, that is in just O(N) operations for N unknowns. Indeed, we develop an FMG method for the 2-D SAAF equation that yields discretization accuracy and does not require the use of a Galerkin coarse-grid approximation. Until recently, aside from proofs about the order of the error for FMG, little work had been done in quantifying when and how FMG can obtain discretization accuracy. However, recent work by Rodrigo et al. has introduced a Fourier analysis technique called worst-case right-hand side analysis used to calculate the FMG accuracy measure. The FMG accuracy measure is the upper bound on the constant of proportionality between the error of the FMG solution and the discretization error. In this summary, we develop and implement an FMG method for the 2-D Cartesian SAAF equations. We then perform worst-case right-hand side analysis and give numerical examples that demonstrate under what circumstances the method can solve the 2-D SAAF equations to discretization accuracy, for optically thin cells, without the need for a Galerkin coarse-grid approximation. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Approximating a linear multiplicative objective in watershed management optimization

Implementing management practices in a cost-efficient manner is critical for regional efforts to reduce the amount of pollutants entering the Chesapeake Bay. We study the problem of selecting a subset of practices that minimizes pollutant load—subject to budgetary and environmental constraints—as simulated in a widely used regulatory watershed model. Mimicking the computation of pollutant load in the regulatory model, we formulate this problem as a continuous optimization model with a linear multiplicative objective function and linear constraints. To lay the groundwork for incorporating additional stakeholder requirements in the future, especially those that would require integer variables, we present and study a continuous linear optimization model that approximates the nonlinear model. The linear model, which requires an exponential number of variables, arises naturally as an alternative model for the same underlying physical process. We examine the theoretical behavior of these optimization models and investigate restrictions of the linear model to handle its large number of variables. Through extensive computational tests on real and randomly generated instances, we demonstrate that the linear model and its restrictions provide optimal solutions close to those of the nonlinear model in practice, despite poor approximation properties in the worst case. We conclude that the linear model—together with our approach to handling its large number of variables—provides a viable framework from which to extend the optimization model to better meet the needs of the Chesapeake Bay watershed management stakeholders.

54 ENVIRONMENTAL SCIENCES↗