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DOE OSTI2026

Stochastic Thermo-Hydro Modeling and Neural Network Surrogate Development for Thermal Resource Assessment of the Galleries-to-Calories Geobattery

The Galleries-to-Calories Geobattery concept explores the use of abandoned coal mine workings for large-scale thermal energy transport and storage. The system involves injecting waste heat from a supercomputing facility into flooded mine galleries, where groundwater flow can store and transport thermal energy for potential recovery in downgradient district heating and cooling applications. To evaluate the feasibility and performance of the Geobattery under geological and operational uncertainty, we developed a suite of stochastic thermo-hydrological (TH) simulations using Monte Carlo sampling of key uncertain parameters (e.g., permeability, porosity, thermal conductivity, specific heat capacity) and operating conditions (e.g., injection rate, injection temperature). Results identified injection rate and temperature as the most influential parameters governing thermal front propagation, while the geometry of the room-and-pillar structure played a critical role in directing the extent and orientation of thermal advancement. Optimal combinations of material properties for maximizing heat recovery were also determined. To address the high computational cost of coupled-process stochastic modeling, we trained a neural network surrogate model on 24,000 physics-based realizations, achieving an R² > 0.99 and MAE < 0.1 for temperature predictions at monitoring locations. This surrogate enabled an additional 100,000 realizations for global sensitivity analysis and probabilistic thermal resource assessment. The integrated stochastic physics–surrogate modeling framework offers a computationally efficient tool for quantifying uncertainty, identifying key drivers, and informing early-stage design decisions for Geobattery systems.

15 - GEOTHERMAL ENERGY↗

DOE OSTI2021

Assessment of model parameters in MFiX particle-in-cell approach

The limitations in numerical treatment of solids-phase in conventional methods like Discrete Element Model and Two-Fluid Model have facilitated the development of alternative techniques such as Particle-In-Cell (PIC). However, a number of parameters are involved in PIC due to its empiricism. In this work, global sensitivity analysis of PIC model parameters is performed under three distinct operating regimes common in chemical engineering applications, viz. settling bed, bubbling fluidized bed and circulating fluidized bed. Simulations were performed using the PIC method in Multiphase Flow with Interphase eXchanges (MFiX) developed by National Energy Technology Laboratory (NETL). A non-intrusive uncertainty quantification (UQ) based approach is applied using Nodeworks to first construct an adequate surrogate model and then identify the most influential parameters in each case. This knowledge will aid in developing an effective design of experiments and determine optimal parameters through techniques such as deterministic or statistical calibration.

01 COAL, LIGNITE, AND PEAT↗

DOE OSTI2020

Simulations of activities, solubilities, transport properties, and nucleation rates for aqueous electrolyte solutions

This article reviews recent molecular simulation studies of "collective" properties of aqueous electrolyte solutions, specifically free energies and activity coefficients, solubilities, nucleation rates of crystals, and transport coefficients. These are important fundamental properties for biology and geoscience, but also relevant for many technological applications. Their determination from molecular-scale calculations requires large systems and long sampling times, as well as specialized sampling algorithms. As a result, such properties have not typically been taken into account during optimization of force field parameters; thus, they provide stringent tests for the transferability and range of applicability of proposed molecular models. There has been significant progress on simulation algorithms to enable the determination of these properties with good statistical uncertainties. Comparisons of simulation results to experimental data reveal deficiencies shared by many commonly used models. Moreover, there appear to exist specific tradeoffs within existing modeling frameworks, so that good prediction of some properties is linked to poor prediction for specific other properties. For example, non-polarizable models that utilize full charges on the ions generally fail to predict accurately both activity coefficients and solubilities; the concentration dependence of viscosity and diffusivity for these models is also incorrect. Scaled-charge models improve the dynamic properties and could also perform well for solubilities, but fail in the prediction of nucleation rates. Even models that do well at room temperature for some properties generally fail to capture their experimentally observed temperature dependence. Finally, the main conclusion from the present review is that qualitatively new physics will need to be incorporated in future models of electrolyte solutions to allow description of collective properties for broad ranges of concentrations, temperatures, and solvent conditions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2026

4D beam matrix reconstruction in particle accelerators

Transverse beam parameters in particle accelerators are commonly described using the Twiss parameters, which are experimentally accessible yet inherently limited because they neglect correlations between different transverse coordinates. Such correlations frequently arise from uncompensated cathode magnetic fields or misaligned focusing quadrupoles, affecting beam quality and accelerator performance. To address this limitation, we propose and validate a novel diagnostic method for the complete four-dimensional (4D) transverse beam matrix. Our method involves passing the beam through a beamline comprising both conventional and skew quadrupole magnets, followed by downstream measurements of the resulting two-dimensional (2D) beam profiles. These measurements represent distinct 2D projections of the underlying 4D transverse phase–space distribution. By systematically varying quadrupole strengths, multiple independent projections of the beam phase space are obtained. We reconstruct the original 4D beam matrix from these measured projections using an optimization-based least-square fit, providing fast and robust reconstruction regardless of the specific beamline configuration. Through extensive numerical simulations and realistic particle-tracking studies, we demonstrate the diagnostic’s accuracy, robustness, and capability to achieve reconstruction uncertainties smaller than measurement errors, particularly when employing sufficient numbers of quadrupole scans. This method presents a powerful and flexible approach for comprehensive beam characterization and accelerator tuning.

43 PARTICLE ACCELERATORS↗

DOE OSTI2023

Autonomous Cyber Defense Against Dynamic Multi-strategy Infrastructural DDoS Attacks

Dynamic Infrastructural Distributed Denial of Service (I-DDoS) attacks constantly change attack vectors to congest core backhaul links and disrupt critical network availability while evading end-system defenses. To effectively counter these highly dynamic attacks, defense mechanisms need to exhibit adaptive decision strategies for real-time mitigation. This paper presents a novel Autonomous DDoS Defense framework that employs model-based reinforcement agents. The framework continuously learns attack strategies, predicts attack actions, and dynamically determines the optimal composition of defense tactics such as filtering, limiting, and rerouting for flow diversion. Our contributions include extending the underlying formulation of the Markov Decision Process (MDP) to address simultaneous DDoS attack and defense behavior, and accounting for environmental uncertainties. We also propose a fine-grained action mitigation approach robust to classification inaccuracies in Intrusion Detection Systems (IDS). Additionally, our reinforcement learning model demonstrates resilience against evasion and deceptive attacks. Evaluation experiments using real-world and simulated DDoS traces demonstrate that our autonomous defense framework ensures the delivery of approximately 96 - 98% of benign traffic despite the diverse range of attack strategies.

Dutta, Ashutosh↗

DOE OSTI2022

LLNL 5-2428: Fracture Permeability and Seismic Slip Behavior

Our goal is to develop, apply and validate a holistic thermal, hydrologic, mechanical, and chemical (THMC) workflow that also includes evaluation of induced seismic slip in EGS reservoirs. We will integrate experimental and modelling approaches to reduce parameteruncertainty and better predict and mitigate seismic hazard at Utah FORGE and future EGS sites.We propose a novel approach that incorporates 3D physics-based Earthquake simulations in THMC models, herein referred to as “THMC+E” models. This capability will enable improvedengineering decisions at Utah FORGE and move EGS operations toward repeatable, robust, economically viable, and socially accepted development. Utah FORGE management and future EGS operators may employ results of THMC+E models for decision making purposes throughout the lifetime of the field operation. For example, before production well installation, our THMC+E models will predict circulation scenarios and related seismic hazard for a suite ofpossible well locations and flow rates, thus enabling evaluation of optimal production well placement. Such efforts will be conducted throughout the lifetime of the project, whereby additional laboratory experiments will constrain key model parameters and machine learning (ML) will reduce the size of the parameter space and the associated uncertainty. THMC+E simulations will enable exploration various circumstances that may hinder EGS success and develop mitigation strategies.

58 GEOSCIENCES↗

DOE OSTI2023

IER - 551: Experiment for Unresolved Resonance of Plutonium Actinides (EUROPA): CED-1 for True Intermediate Pu Benchmark

IER-551 or the Experiment for Unresolved Resonance Of Plutonium Actinides (EUROPA), is an experiment campaign to design and execute a series of true intermediate energy plutonium critical configurations. EUROPA is a collaboration between Los Alamos National Laboratory (LANL), Oak Ridge National Laboratory (ORNL), and the French Institut de Radioprotection et de Sûreté Nucléaire (IRSN) to validate current and future evaluations of 239,240 Pu isotopes. Preliminary designs were optimized using Particle Swarm Optimization to save on computation time and the configuration with highest percentage of intermediate neutrons causing fission found was BeO-Cd. This combination has over 70% of fissions occurring from intermediate energy neutrons. Secondary considerations regarding end benchmark uncertainties and quality of nuclear data resulted in a beryllium metal only experiment proposed as the final system. This final preliminary design achieves 68% intermediate fissions, sensitivities of fission and capture cross sections of 239 Pu of 0.3021 and -0.1610 respectively.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2026

Performance Enhancement of the Transcritical CO2 Cycle with a Near-Isothermal Liquid Piston Compression by an Ejector

This study investigates the use of an ejector in a transcritical CO2 cycle employing a near-isothermal liquid piston compressor, with the objective of mitigating refrigerant degassing in mineral oil. While the liquid piston compressor demonstrated high isothermal efficiency (˜90%), overall cycle performance was limited by CO2 degassing during chamber pressure fluctuations. A thermodynamic model was developed to compare baseline and ejector-assisted cycles, incorporating solubility correlations, entrainment ratio characteristics, and a degassing correction factor. Results indicate that the ejector increased suction pressure and reduced CO2–oil solubility variation, which improved refrigerant intake and reduced degassing losses. Despite these benefits, the ejector-assisted cycle showed a lower coefficient of performance (COP) than the baseline. Possible contributing factors include the limited marginal benefit of pressure reduction in a highly efficient isothermal compressor, reduced effectiveness of the separator due to the use of a suction-line heat exchanger in both cycles, and uncertainties in the solubility data under transient conditions. These findings suggest that degassing mitigation is essential for realizing the potential of liquid piston compression, but ejector integration alone is unlikely to enhance COP. Future work should focus on ejector optimization, improved oil–refrigerant management, introducing less-soluble working liquids, and experimental validation under realistic operating conditions.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2021

Impact of reservoir parameters and wellbore permeability uncertainties on CO 2 and brine leakage potential at the Shenhua CO 2 Storage Site, China

Here, this paper describes a system-level risk assessment for the Shenhua CO 2 storage site, China, using the National Risk Assessment Partnership Integrated Assessment Model for Carbon Storage (NRAP-IAM-CS). Here, we begin by determining the optimal number of Monte Carlo (MC) simulations to achieve CO 2 and brine leakage result convergence. Then, we calculate mass CO 2 and brine leakage to the atmosphere and a hypothetical shallow aquifer. Finally, we assess the geochemical impacts in the event of leakage as if there were a shallow freshwater aquifer at the Shenhua site. Simulation results show that leakage results tend to stabilize after 300 Monte Carlo simulations. When the three wells on site are assigned a permeability of 10 -11 m 2 (representing significantly leaking wells), moderate CO 2 and brine leakages occur, and the percentage of CO 2 leakage exceeds the threshold value we set based on the Intergovernmental Panel on Climate Change (IPCC). This is, however, unlikely to be the case for the Shenhua site. For all the other scenarios, the CO 2 leakage is trivial although there is still the possibility of CO 2 leakage into the groundwater aquifer exceeding the 1% threshold over 1000 years, assuming constant legacy wellbore permeability. For the significantly leaking scenario, there is a 10% probability to have a moderate (2.7 × 10 7 m 3 ) leakage-affected volume in the shallow aquifer with the pH below 6.5, and a large (1.4 × 10 8 m 3 ) volume with the total dissolved solids (TDS) above 500 ppm, hence pH and TDS may be considered for site monitoring plans. Based on the simulation results, there is a very low probability of significant CO 2 /brine leakage through the existing wells at the Shenhua CO 2 storage site.

58 GEOSCIENCES↗

DOE OSTI2022

A Multistage Stochastic Transmission Expansion Algorithm for Wide-Area Planning under Uncertainty

The overall objective for this project was to develop and demonstrate a set of methods for solving the transmission investment problem for a large network considering many possible scenarios of future conditions and multiple decision points when investments can be made. Project sub-objectives achieved this goal through a succession of extending the methods to apply to problems with increasing complexity or additional features, including the number of decision points, whether generation and transmission are co-optimized, and whether AC or DC power flow is used. A transmission model was developed for the Western Electric Coordinating Council (WECC) region, the high-voltage transmission system that serves the western third of the continental U.S. Using a dataset provided by WECC and by researchers from John Hopkins University, we have validated and demonstrated the model and used it to compare the new method for solving multi-stage stochastic transmission planning to several state-of-the-art techniques. The project has resulted in several key outcomes and achievements: The covariance-based method for choosing a small set of hours to represent short-term variability has superior performance in terms of accuracy to existing methods, including K-means clustering and Importance Sampling; The combined partitioning method for long-term uncertainty with the nested clustering approach for choosing representative hours for each long-term group has superior accuracy for equivalent computational effort compared with existing methods; Using the partitioning/clustering method combined with Sample Average Approximation provides both statistical bounds on the quality of the solution and at the same time, a complete investment plan for all contingencies in the full uncertainty set; no existing methods can provide both at the same time; The method is demonstrated to work well for choosing both transmission and generation investments; A variant on the method allows for both scenario selection and simultaneous correction for the error from the DC power flow approximation to provide a tractable method for AC power flow-based transmission planning under uncertainty; The method applied to the WECC case study demonstrates the additional value to the system operator and the consumer of identifying flexible investment options in the near-term decisions. In particular, the case study exhibits significant option value in postponing some transmission additions that appear useful but in some long-term system states create new congestion problems.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2020

Sensitivity Analysis and Effective Parametrization of PEM Fuel Cell Models

The cost of proton-exchange-membrane fuel cells (PEMFCs) remains a major hurdle in large-scale commercialization of this technology. To improve their performance and reduce cost, novel materials and electrode designs are continuously envisioned, e.g., non-PGM catalyst layers, ultra-thin Pt/Pt-Ni based catalyst layers, structured ionomer arrays or NSTF catalyst layers.1 Understanding the impact of these improvement strategies can be extremely time and cost intensive due to complex physical phenomena and large design space. We have previously developed a PEMFC modeling framework2 which has been a time and cost effective tool for understanding and optimizing the complex multi-physics phenomena within PEMFCs; however, several of the cell parameters used in the modeling have large spread in measured data.3 Furthermore, several transport parameters such as water adsorption kinetics have not been accurately measured and the approximations are spread over several orders of magnitude. These uncertainties cause problems in ascertaining accuracy of the modeling approach and they reduce the predictive power of the numerical models. The aim of this work is to identify the sensitivity of PEFC numerical model outputs to various input parameters. The previously in-house developed MEA modeling framework2 is used for PEMFC modeling. The sensitivity of the model outputs with respect to inputs parameters is obtained by analyzing the condition numbers for different output-input pairs at varying operating conditions. An example of the sensitivity analysis is shown in Figure 1. The condition numbers are obtained for the entire possible range of input parameters at varying operating conditions to identify the most crucial parameters of the PEMFC model. Based on our preliminary analysis, parameters related to kinetics (exchange current density and ECSA) and heat/water management in electrodes and ionomer (ionomer fraction, thermal conductivity) are most crucial. One of the major goals of this work is to identify the most crucial set of parameters towards which the model shows maximum sensitivity. This will guide future experimentalists to measure these properties with higher accuracy. Furthermore, the sensitivity analysis will also enable us to optimize the PEMFC performance by selectively targeting the most sensitive parameters and thereby making the largest impact. Acknowledgements The work is funded under the Fuel Cell Performance and Durability Consortium (FC-PAD), by the Fuel Cell Technologies Office (FCTO), Office of Energy Efficiency and Renewable Energy (EERE), of the U.S. Department of Energy under contract number DE-AC02-05CH11231. The authors would like to thank Nathan Craig at Robert Bosch LLC for his valuable input in designing the sensitivity analysis. The authors would also like to thank Giovanna Bucci and Matthias Hanauer at Robert Bosch for their valuable inputs and discussion. References P. K. Sinha, W. Gu, A. Kongkanand and E. Thompson, J. Electrochem. Soc., 158, B831 (2011). L. M. Pant, M. R. Gerhardt, N. Macauley, R. Mukundan, R. L. Borup and A. Z. Weber, Electrochim. Acta, 326, 134963 (2019). R. Vetter and J. O. Schumacher, ArXiv181110091 Phys. (2018). Figure 1

Pant, Lalit↗

DOE OSTI2023

Bayesian projection pursuit regression

In projection pursuit regression (PPR), a univariate response variable is approximated by the sum of $M$ “ridge functions,” which are flexible functions of one-dimensional projections of a multivariate input variable. Traditionally, optimization routines are used to choose the projection directions and ridge functions via a sequential algorithm, and $M$ is typically chosen via cross-validation. Here, we introduce a novel Bayesian version of PPR, which has the benefit of accurate uncertainty quantification. To infer appropriate projection directions and ridge functions, we apply novel adaptations of methods used for the single ridge function case ($M$=1), called the Bayesian Single Index Model; and use a Reversible Jump Markov chain Monte Carlo algorithm to infer the number of ridge functions $M$. We evaluate the predictive ability of our model in 20 simulated scenarios and for 23 real datasets, in a bake-off against an array of state-of-the-art regression methods. Finally, we generalize this methodology and demonstrate the ability to accurately model multivariate response variables. Its effective performance indicates that Bayesian Projection Pursuit Regression is a valuable addition to the existing regression toolbox.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Probabilistic flux limiters

The stable numerical integration of shocks in compressible flow simulations relies on the reduction or elimination of Gibbs phenomena (unstable, spurious oscillations). A popular method to virtually eliminate Gibbs oscillations caused by numerical discretization in under-resolved simulations is to use a flux limiter. A wide range of flux limiters have been studied in the literature, with recent interest in their optimization via machine learning methods trained on high-resolution datasets. The common use of flux limiters in numerical codes as plug-and-play blackbox components makes them key targets for design improvement. Even for deterministic dynamical models, numerical uncertainty is introduced via coarse-graining required by insufficient computational power to solve all scales of motion. Conventional flux limiters are deterministic and lack the capacity to address uncertainties, both aleatoric (inherent randomness) and epistemic (modeling uncertainty due to limited knowledge), which arise in coarse-grained numerical simulations. Here, we introduce a conceptually distinct type of flux limiter that is designed to handle the effects of randomness in the model and uncertainty in model parameters. Unlike traditional single-function flux limiters, these new probabilistic flux limiters incorporate multiple flux limiting functions, each applied with a learned probability drawn from high-resolution data to mitigate the effects of uncertainty in numerical simulations. This approach departs from traditional single-function limiters by explicitly modeling and incorporating uncertainty into the shock capturing process. Using the example of Burgers' equation as a testbed, we show that a machine learned, probabilistic flux limiter may be used in a shock capturing code to more accurately capture shock profiles. In particular, we show that our probabilistic flux limiter outperforms standard limiters and can be successively improved upon (up to a point) by expanding the set of probabilistically chosen flux limiting functions.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Dark Energy Survey Year 3 results: A 2.7% measurement of baryon acoustic oscillation distance scale at redshift 0.835

We present angular diameter measurements obtained by measuring the position of baryon acoustic oscillations (BAO) in an optimized sample of galaxies from the first three years of Dark Energy Survey data (DES Y3). The sample consists of 7 million galaxies distributed over a footprint of 4100 deg 2 with 0.6 < z photo < 1.1 and a typical redshift uncertainty of 0.03 ( 1 + z ) . The sample selection is the same as in the BAO measurement with the first year of DES data, but the analysis presented here uses three times the area, extends to higher redshift, and makes a number of improvements, including a fully analytical BAO template, the use of covariances from both theory and simulations, and an extensive preunblinding protocol. We used two different statistics; angular correlation function and power spectrum, and validate our pipeline with an ensemble of over 1500 realistic simulations. Both statistics yield compatible results. We combine the likelihoods derived from angular correlations and spherical harmonics to constrain the ratio of comoving angular diameter distance D M at the effective redshift of our sample to the sound horizon scale at the drag epoch. We obtain D M ( z eff = 0.835 ) / r d = 18.92 ± 0.51 , which is consistent with, but smaller than, the Planck prediction assuming flat Λ CDM , at the level of 2.3 σ . The analysis was performed blind and is robust to changes in a number of analysis choices. It represents the most precise BAO distance measurement from imaging data to date, and is competitive with the latest transverse ones from spectroscopic samples at z > 0.75 . When combined with DES 3 x 2 pt + SNIa , they lead to improvements in H 0 and Ω m constraints by ∼ 20 % .

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Bayesian, Multifidelity Operator Learning for Complex Engineering Systems–A Position Paper

Abstract Deep learning has significantly improved the state-of-the-art in computer vision and natural language processing, and holds great potential to design effective tools for predicting and simulating complex engineering systems. In particular, scientific machine learning seeks to apply the power of deep learning to scientific and engineering tasks, with operator learning (OL) emerging as a particularly effective tool. OL can approximate nonlinear operators arising in complex engineering systems, making it useful for simulating, designing, and controlling those systems. In this position paper, we provide a comprehensive overview of OL, including its potential applications to complex engineering domains. We cover three variations of OL approaches: deterministic OL for modeling nonautonomous systems, OL with uncertainty quantification (UQ) capabilities, and multifidelity OL. For each variation, we discuss drawbacks and potential applications to engineering, in addition to providing a detailed explanation. We also highlight how multifidelity OL approaches with UQ capabilities can be used to design, optimize, and control engineering systems. Finally, we outline some potential challenges for OL within the engineering domain.

Computer Science↗

DOE OSTI2023

Development of a Geothermal Module in reV: Quantifying the Geothermal Potential while Accounting for the Geospatial Intersection of the Grid Infrastructure and Land Use Characteristics

The Renewable Energy Potential (reV) model is a geospatial platform for estimating technical potential and developing renewable energy supply curves, initially developed for wind and solar technologies. The model evaluates deployment constraints, considering land use, environmental, and cultural factors, and estimates the distance to existing grid features to connect future plants (Maclaurin et al., 2021). A pressing deficiency in the reV model, however, is representation of geothermal electricity generation technologies. To address this gap, we developed a novel geothermal generation module for reV that allows for representation and analysis at the same level of detail as other renewable technologies. This paper describes our process for evaluating data sources for the modeling, and presents five preliminary reV geothermal results. More specifically, we present two sets of resource data that represent upper and lower bounds for geothermal potential. We then present several sensitivity runs using the upper bound resource data; the results are encouraging that levelized cost of electricity (LCOE) can be reduced by optimizing the location and estimated capacity of the spatially diverse geothermal resource while considering the distance to existing grid infrastructure. Our preliminary supply curves and levelized cost of electricity (LCOE) results should be considered with care due to the highly uncertainty in geothermal resource potential data. We present median LCOE values for the conterminous U.S. for five scenarios: four hydrothermal (3.5km depth) and one EGS (4.5km depth). The capital and operating costs for each respective technology are modeled. We also compare results using two different resource data sources.

exclusions↗

DOE OSTI2024

Development of a Geothermal Module in reV: Quantifying the Geothermal Potential While Accounting for the Geospatial Intersection of the Grid Infrastructure and Land Use Characteristics: Preprint

exclusions↗

DOE OSTI2020

Recent advances in computational mathematics and applications

We are honored to bring you this special issue dedicated to recent advances in computational mathematics and applications in science and engineering. The papers in this special issue were presented in ”Conference on Computational Mathematics and Applications (CCMA)” held at the University of Nevada Las Vegas (UNLV) during October 25–27, 2019. The conference has attracted about 90 attendees from six countries. The 15 papers in the special issue comprise a diverse collection of theoretical numerical analysis as well as applications in various subjects. Topics cover optimal control of PDEs, discontinuous Galerkin methods, fluid flow in porous media, turbulence flow, static and moving interface problems, complex fluids composed by the mixture of Newtonian fluid and nematic (liquid crystal) flows, modeling of ocean–atmosphere system, image segmentation algorithm, uncertainty quantification problems for turbulence model and Maxwell’s equations, iterative solver for systems resulting from mixed methods, and novel methods for solving systems of nonlinear equations. As the Guest Editors we would like to thank Dr. Leland Jameson at NSF (National Science Foundation) for kindly supporting our conference proposal which made this conference possible. We would also like to thank Darren Sugrue from Elsevier who provided partial support for our conference, and Thennarasu Gunasekaran and his production team from Elsevier who produced this nice special issue. We are grateful to many people (Dr. Zhijian Wu, Lori Ornelas, Elsa Juarez, and many Ph.D. students) at the Department of Mathematical Sciences of UNLV who provided tremendous support for the conference. Finally, we very much appreciate all authors who contributed their precious results to this special issue.

97 MATHEMATICS AND COMPUTING↗