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Multi-Objective Optimization Of Energy Costs And Ev Battery Health In V2g Enabled Homes, Dzifa M. Hodey Jan 2026

Multi-Objective Optimization Of Energy Costs And Ev Battery Health In V2g Enabled Homes, Dzifa M. Hodey

Theses and Dissertations--Computer Science

Electric vehicles (EVs) and rooftop solar photovoltaic (PV) systems are increasingly being integrated into residential settings, creating new opportunities for vehicle-to-grid (V2G) and vehicle-to-home (V2H) operations. In these systems, the EV battery functions as a controllable energy storage unit that can charge from the grid or PV and discharge energy to supply household load or export to the grid for a profit. By intelligently scheduling this bidirectional power exchange, households can reduce electricity costs and enhance PV utilization. Realizing these benefits requires optimization strategies that balance cost reduction with EV battery health preservation. However, existing V2G/V2H studies largely emphasize cost …


Toward Efficient And Scalable Scientific Data Management Through Quality-Oriented Data Compression, Pu Jiao Jan 2026

Toward Efficient And Scalable Scientific Data Management Through Quality-Oriented Data Compression, Pu Jiao

Theses and Dissertations--Computer Science

Scientific simulations and instruments now produce data at rates that overwhelm the storage, memory, and network subsystems of modern high-performance computing (HPC) facilities. Error-bounded lossy compression reduces data movement costs while bounding reconstruction error, yet three barriers limit its adoption in mission-critical workflows: existing compressors cannot guarantee the accuracy of domain-specific quantities of interest (QoIs) derived from compressed data; compression-induced artifacts such as posterization, blocking, and interpolation banding erode user confidence in decompressed fields; and significant compressibility in the quantization index arrays of interpolation-based pipelines remains unexploited. This dissertation addresses all three barriers through four contributions, with the artifact barrier …


A Literature Review On Ethics In Medical Diagnostic Ai & Analysis Therein, Connor J. Turetzky Jan 2026

A Literature Review On Ethics In Medical Diagnostic Ai & Analysis Therein, Connor J. Turetzky

Master's Theses

Artificial Intelligence presents a very promising future in medicine. Being able to diagnose and recommend treatments quickly is vital in ensuring positive patient outcomes. However, the new technology is not without risk. In this narrative literature review, the risks of AI in terms of bias, ethics, and environmental impact will be explored through existing research. This paper will focus on research published between 2019 and 2026, highlighting the major ethical and systematic problems currently facing diagnostic AI. Historical bias in medical data has led to AI that share those biases, and humans inherit that bias creating a potential negative feedback …


Mat 1500 Calculus I Syllabus, Tian Cai Jan 2026

Mat 1500 Calculus I Syllabus, Tian Cai

Open Educational Resources

No abstract provided.


Mat 1600 Syllabus Ii Syllabus, Tian Cai Jan 2026

Mat 1600 Syllabus Ii Syllabus, Tian Cai

Open Educational Resources

No abstract provided.


Mat 2100 Calculus Iii Syllabus, Mei Xing Jan 2026

Mat 2100 Calculus Iii Syllabus, Mei Xing

Open Educational Resources

No abstract provided.


Linking Phytoplankton Physiology And Ecology To Global Biogeochemical Cycles: A Modeling Approach, Margaret Bernish Jan 2026

Linking Phytoplankton Physiology And Ecology To Global Biogeochemical Cycles: A Modeling Approach, Margaret Bernish

Open Access Dissertations

Phytoplankton, or microscopic primary producers, contribute to carbon export through the biological transformation of carbon dioxide into organic molecules. Phytoplankton are responsible for approximately half of global net primary production, while only contributing minimally to total photosynthetic biomass. Despite their important role in the global cycling of nutrients, phytoplankton physiology and ecology are often highly simplified in global biogeochemical models. This dissertation elucidates the role of phytoplankton physiology and ecology within biogeochemical cycles, allowing for better characterization of marine microbial distribution and better representation of nutrient cycling for interpretive and predictive models. The development of formulations that link physiological responses …


Ultrafast Vibrational Dynamics In Important Wide-Bandgap Semiconductors, Dielectrics And Energetic Materials, Dinusha Madushanka Senarathna Jan 2026

Ultrafast Vibrational Dynamics In Important Wide-Bandgap Semiconductors, Dielectrics And Energetic Materials, Dinusha Madushanka Senarathna

Open Access Dissertations

This dissertation applies time-resolved coherent anti-Stokes Raman scattering (tr-CARS), to measure ultrafast vibrational dynamics in technologically important solid-state and van der Waals molecular systems. The central goal is to use time-domain Raman methods to resolve mode-specific phonon and vibrational dephasing processes with high temporal precision, high spectral selectivity, and sufficient experimental flexibility to probe materials ranging from wide-bandgap semiconductors and oxide crystals to energetic molecular crystals. Across the work, I show that carefully designed tr-CARS measurements can access vibrational lifetimes from hundreds of femtoseconds to several picoseconds, enabling direct observation of decay pathways, relaxation mechanisms, and dispersion effects that shape …


Impact Of Water Quality And Gear Type On Eastern Oyster (Crassostrea Virginica) Growth In Narragansett Bay, Ri, Jacqueline Rosa Jan 2026

Impact Of Water Quality And Gear Type On Eastern Oyster (Crassostrea Virginica) Growth In Narragansett Bay, Ri, Jacqueline Rosa

Open Access Master's Theses

Oyster aquaculture is expanding in Rhode Island, yet key farming regions in the lower West Passage of Narragansett Bay (WPNB) lack the in-situ, high-temporal resolution monitoring needed to evaluate emerging stressors and support production. At the same time, the industry is undergoing rapid technological development aimed at improving production while reducing labor and overall costs. In recent years, a low-maintenance, alternative surface gear was introduced in WPNB; however, its impact on oyster performance relative to traditional cultivation methods has not been quantified. This study established a 1.5-year continuous water quality time series in WPNB and paired these observations with …


Hydrogeochemical And Redox Controls On Nitrate And Arsenic Co-Occurrence In The Western Kansas High Plains Aquifer (Usa): A Composite Health Risk Assessment And The Case For Risk-Informed Private Well Governance, Jonathan Kuffour Owusu Jan 2026

Hydrogeochemical And Redox Controls On Nitrate And Arsenic Co-Occurrence In The Western Kansas High Plains Aquifer (Usa): A Composite Health Risk Assessment And The Case For Risk-Informed Private Well Governance, Jonathan Kuffour Owusu

Master's Theses or Doctor of Nursing Practice

Fifty-one private domestic wells across western Kansas were sampled to quantify nitrate and arsenic occurrence, identify geochemical controls, and evaluate carcinogenic and non-carcinogenic health risks for adult and child receptors in a region where groundwater serves as the primary drinking water source with no routine regulatory oversight. Samples were analyzed for major ions, nutrients, and trace elements by ICP-MS, ion chromatography, and UV-Vis spectrophotometry. Shapiro-Wilk testing confirmed non-normal distributions for both contaminants; inter-county comparisons were therefore conducted using Kruskal-Wallis tests with Dunn's post-hoc correction. Health risk was quantified via chronic daily intake (CDI), hazard quotient (HQ), HQ-based Water Quality Index …


Electronic Bills Of Lading And Blockchain Technology: A Regulatory Perspective, Hsin-Hua Tsai Jan 2026

Electronic Bills Of Lading And Blockchain Technology: A Regulatory Perspective, Hsin-Hua Tsai

Journal of Marine Science and Technology–Taiwan

Information and communications technology (ICT) systems are increasingly relevant to the maritime sector. Regarding the revolution of the bill of lading, many shipping lines and other technology startups have been looking into developing viable electronic transport documents that have the same functions as paper bills of lading to reduce supply chain risks. The limitations of the paper-based process have become increasingly visible in the COVID-19 crisis. The main purpose of the article is to analyze the application of blockchain bills of lading, which utilizes computational logic to create the digital ledger, and users can set up algorithms and rules to …


Intelligent Formation Control Using Orfbls And Adaptive Backstepping Sliding-Mode Control To Address Uncertain Tilting In Multi-Quadrotors During Wind Gusts, Ching-Chih Tsai, Chun-Fu Mao, Kumail Hussain Jan 2026

Intelligent Formation Control Using Orfbls And Adaptive Backstepping Sliding-Mode Control To Address Uncertain Tilting In Multi-Quadrotors During Wind Gusts, Ching-Chih Tsai, Chun-Fu Mao, Kumail Hussain

Journal of Marine Science and Technology–Taiwan

In terms of aerial robotics, stable and precise formation control is a significant challenge for tilting multi-quadrotors during disturbances. This paper proposes a fixed-time formation control strategy for tilting multi-quadrotors to address the effect of external wind gusts. The observer accurately predicts environmental disturbances and an adaptive backstepping sliding-mode control (ABSMC) method with an output recurrent fuzzy broad learning system (ORFBLS) addresses these disturbances within a finite time. ORFBLS dynamically adjusts its structure through a growing ORFBLS structure to allow nodes to be added as needed. The method's stability is validated using Lyapunov stability theory and ensures the convergence of …


Future Mining: Learning For Safety And Security, Md Sazedur Rahman, Mizanur Rahman Jewel, Sanjay Madria Jan 2026

Future Mining: Learning For Safety And Security, Md Sazedur Rahman, Mizanur Rahman Jewel, Sanjay Madria

Computer Science Faculty Research & Creative Works

Mining industry is rapidly transforming into an AI-driven cyber-physical ecosystem where safety and operational reliability depend on robust perception, resilient communication, trustworthy distributed intelligence and continuous monitoring of miners and equipment. Real-world mining environments impose severe constraints like poor illumination, dust, occlusion, GPS-denied conditions, irregular underground topologies, and intermittent connectivity. These factors degrade perception quality, disrupt situational awareness, impair trajectory prediction and weaken the reliability of distributed learning systems. Emerging cyber-physical threats, including backdoor triggers, sensor spoofing, label-flip attacks and poisoned model updates, further jeopardize operational safety, particularly as mines increasingly adopt autonomous vehicles, humanoid assistance, and federated learning for …


Dynamic Hub-Aware Knowledge Distillation For Efficient Traffic Flow Forecasting, Xiangjie Kong, Can Shu, Wenchao Weng, Zhenzhen Zhao, Guojiang Shen, Lei Wang, Sajal K. Das Jan 2026

Dynamic Hub-Aware Knowledge Distillation For Efficient Traffic Flow Forecasting, Xiangjie Kong, Can Shu, Wenchao Weng, Zhenzhen Zhao, Guojiang Shen, Lei Wang, Sajal K. Das

Computer Science Faculty Research & Creative Works

Real-time traffic forecasting acts as a critical enabling service for IoT-driven Intelligent Transportation Systems (ITS). While existing Spatiotemporal Graph Neural Networks (STGNNs) achieve superior forecasting accuracy, their intensive computational complexity and high latency create a deployment bottleneck for resource-constrained IoT edge devices. To address this resource-accuracy mismatch, we propose a novel framework termed Dynamic Hub-Aware Knowledge Distillation (DHKD). Unlike traditional uniform distillation paradigms, DHKD introduces a topology-aware strategy to transfer knowledge from a complex teacher to a lightweight Spatiotemporal Multi-Layer Perceptron (STMLP) student model. Specifically, we design a dynamic hub-aware gating (DHAG) mechanism that adaptively identifies time-varying pivotal sensing nodes …


Digital Twin Freshness Maximization In Edge Computing, Jing Li, Jianping Wang, Weifa Liang, Quan Chen, Sajal K. Das, Xiaohua Jia Jan 2026

Digital Twin Freshness Maximization In Edge Computing, Jing Li, Jianping Wang, Weifa Liang, Quan Chen, Sajal K. Das, Xiaohua Jia

Computer Science Faculty Research & Creative Works

Mobile Edge Computing (MEC) shifts powerful computing resource provisioning from remote powerful data centers to the edge of core networks. Meanwhile, Digital Twin (DT) has surfaced as a promising technology to provide comprehensive and dynamic descriptions of physical objects in cyberspace with bidirectional and real-time interactions. Moreover, Internet of Things (IoT) devices have contributed abundant, heterogeneous and continuous data from interconnected devices to the explosion of DTs. With technologies evolution, there is an increasing necessity to address the freshness of both DT states and DT data, through timely synchronizations between DTs and their objects in a highly dynamic IoT environment. …


Feddot: Defending Federated Learning Against Overwhelming Targeted Attacks, Priyesh Ranjan, Ashish Gupta, Federico Coro, Sajal K. Das Jan 2026

Feddot: Defending Federated Learning Against Overwhelming Targeted Attacks, Priyesh Ranjan, Ashish Gupta, Federico Coro, Sajal K. Das

Computer Science Faculty Research & Creative Works

Federated Learning (FL), which facilitates collaborative model training and protects users' privacy, has drawn great interest from the research community. With FL, participants train their models on local data and submit the corresponding updates for aggregation to a server. While concealing the identities of the participants, FL may attract adversaries in order to hamper the underlying model. In this paper, we propose an FL framework, FedDOT, to defend against adversaries performing targeted attacks. FedDOT incorporates two powerful defense algorithms, Maximum Spanning Tree based attacker detection (MSTAD) and Densest graph-based attacker detection (Density-AD), which leverage correlation between weight updates and graph …


Utility-Preserving Federated Graph Learning With Dual-Perspective Fairness, Renqiang Luo, Huafei Huang, Shuo Yu, Fengqi Yu, Feng Xia, Sajal K. Das, Chengqi Zhang Jan 2026

Utility-Preserving Federated Graph Learning With Dual-Perspective Fairness, Renqiang Luo, Huafei Huang, Shuo Yu, Fengqi Yu, Feng Xia, Sajal K. Das, Chengqi Zhang

Computer Science Faculty Research & Creative Works

Fairness-aware federated graph neural networks (FedGNNs) necessitate consideration of both the server and the clients. However, fairness-aware methods struggle to enhance dual-perspective (i.e., server and clients) fairness without sacrificing utility due to the distributed learning framework. As a consequence, the utility sacrifices of fairness-aware graph learning methods are even exacerbated in federated frameworks. In this work we propose F3GL, a dual-perspective fairness federated graph learning method that enhances both global (for the server) and local fairness (for clients) while preserving utility. Through theoretical analysis, we delineate the similarity between original sensitive features and those after convolution under different spectra. Our …


A Web-Based Wizard-Of-Oz Platform For Collaborative And Reproducible Human-Robot Interaction Research, Sean O'Connor Jan 2026

A Web-Based Wizard-Of-Oz Platform For Collaborative And Reproducible Human-Robot Interaction Research, Sean O'Connor

Honors Theses

The Wizard-of-Oz (WoZ) technique is widely used in Human-Robot Interaction (HRI) research, but two persistent problems limit its effectiveness: existing tools impose technical barriers that exclude non-engineering domain experts (the Accessibility Problem), and the fragmented landscape of robot-specific implementations makes interaction scripts difficult to port across platforms (the Reproducibility Problem- concerning execution consistency and portability, not third-party replication). Through a literature review, I identified three design principles to address both: a hierarchical specification model, an event-driven execution model, and a plugin architecture that decouples experiment logic from robot-specific implementations. I realized these principles in HRIStudio, an open-source, web-based platform providing …


Barriers To Immunity: Understanding Covid-19 Vaccine Uptake In Africa, Emilia Blechschmidt Jan 2026

Barriers To Immunity: Understanding Covid-19 Vaccine Uptake In Africa, Emilia Blechschmidt

Honors Theses

This thesis examines the factors influencing COVID-19 vaccine uptake across African countries, with a focus on structural, informational, and behavioral barriers to immunization. Drawing on cross-country data, the study analyzes how access to transportation, reliable information, and healthcare resources shape vaccination rates, alongside the effect of demographics and institutional factors in shaping individual perceptions of risk and vaccine safety.

The findings emphasize that the broader strength and preparedness of national health systems strongly influence vaccine uptake. Countries that demonstrated higher coverage of routine childhood immunizations, such as polio and hepatitis B, also tended to perform better in COVID-19 uptake efficiency …


Paleoflood Chronology For The West Branch Of The Susquehanna River Using Abandoned Chute Channel Sediments, Pennsylvania, Usa, Juliette A. Vanluven Jan 2026

Paleoflood Chronology For The West Branch Of The Susquehanna River Using Abandoned Chute Channel Sediments, Pennsylvania, Usa, Juliette A. Vanluven

Honors Theses

Anthropogenic climate change is altering the hydrologic cycle, increasing flood frequency and severity, with associated increased risks in population exposure. This is associated with increasing risks to the population of the Susquehanna River Valley, which supports over 600,000 people today. However, our understanding of the frequencies of large floods is limited by relatively short instrumental records. By studying sediments from an abandoned chute channel in the Robert Allen Natural Area near Williamsport, PA, we can extend the existing flood records using paleoflood slackwater sediments along the West Branch of the Susquehanna River.  Sylvan Dell is an abandoned chute channel that …


Anuran Occupancy Of Created Wetlands Within Reforested Legacy Surface Mines In Kentucky And West Virginia, Jillian C. Newman, Steve Price, Jacquelyn C. Guzy, Joshua Castle, John J. Cox, Jeffery L. Larkin, Christopher D. Barton Jan 2026

Anuran Occupancy Of Created Wetlands Within Reforested Legacy Surface Mines In Kentucky And West Virginia, Jillian C. Newman, Steve Price, Jacquelyn C. Guzy, Joshua Castle, John J. Cox, Jeffery L. Larkin, Christopher D. Barton

Forestry and Natural Resources Faculty Publications

Restoration of habitat is an important component of wildlife management. Surface coal mining has altered forest cover in the Central Appalachians, and most reclamation activities on previously mined lands result in non-native grasslands or shrub lands. The Forestry Reclamation Approach (FRA), which emphasizes non-native vegetation removal, soil decompaction, planting of native trees and shrubs, and, in some cases, wetland creation represents an alternative to grassland-based reclamation that may promote forest-associated wildlife on legacy surface mines. We used automated recording units to evaluate the response of anurans to created wetlands and the FRA in Kentucky and West Virginia, USA. We used …


Law Librarianship And Legal Information Science In The Age Of Genai, Paul D. Callister Jan 2026

Law Librarianship And Legal Information Science In The Age Of Genai, Paul D. Callister

Faculty Works

This article examines the relationship between law librarianship and legal information science in the age of generative AI (GenAI), arguing that closer integration between the two is essential to navigating a rapidly evolving legal information landscape. It contends that law librarianship—long grounded in stable classification systems and cognitive authority—must adopt the analytical methods of legal information science to remain effective in the digital era. Together, these fields can reinforce the rule of law by improving the organization, retrieval, and stability of legal information. The article identifies emerging subfields of legal information science that support this integration and develops several concepts …


Indigenous Land Seizure & Environmental Injustice: Impacts Of Settler Colonialism, Lydia Moorman Jan 2026

Indigenous Land Seizure & Environmental Injustice: Impacts Of Settler Colonialism, Lydia Moorman

Journal of Earth and Life Science

The fields of conservation and environmentalism prioritize ecosystem health, yet both emerged from western frameworks that displaced and criminalized Indigenous land stewardship. The idealization of “pristine wilderness” narratives served to justify the removal of Indigenous peoples from their homelands and erased millennia of sustainable land stewardship that had maintained ecological balance long before western conservation existed. These narratives not only misrepresented Indigenous relationship with land but also constructed a false dichotomy between humans and nature that positioned Indigenous presence as a threat rather than a source of ecological knowledge. Simultaneously, anthropogenic expansion; such as pipelines, mining, railroads, and other extractive …


Artificial Intelligence In Biomedical Team Science: Perceptions, Practices, And Training Needs, Emily Slade, Kelsey N. Karnik, Caitline Phan, Megan E. Hall, Yana Feygin, Kristen J. Mcquerry Jan 2026

Artificial Intelligence In Biomedical Team Science: Perceptions, Practices, And Training Needs, Emily Slade, Kelsey N. Karnik, Caitline Phan, Megan E. Hall, Yana Feygin, Kristen J. Mcquerry

Biostatistics Faculty Publications

Introduction: Artificial intelligence (AI) is increasingly used in biomedical research, yet limited empirical work has described how researchers use AI tools on collaborative research teams and how they view their role within team-based research. This study examines researchers’ experience with and attitudes toward AI use in collaborative research environments.

Methods: A cross-sectional survey was administered to 178 investigators engaged in collaborative research at the University of Kentucky. Questions assessed AI use across research and communication tasks, team-related decision-making practices, perceived benefits and concerns, and preferences for training and frameworks.

Results: Thirty-nine participants responded (22%). AI use was heterogeneous: 26% had …


Digital Technologies And Calculus: Students’ Peaks And Pits, Ricela Feliciano-Semidei, Kevin A. Palencia Infante, Alcibiades Bustillo-Zarate Jan 2026

Digital Technologies And Calculus: Students’ Peaks And Pits, Ricela Feliciano-Semidei, Kevin A. Palencia Infante, Alcibiades Bustillo-Zarate

Faculty Articles, Papers, and Other Scholarship

Understanding calculus students’ perspectives can provide valuable insights into their learning needs and help develop strategies to enhance persistence in STEM programs. Numerous studies have shown that the use of digital technologies (DT) influences student engagement, motivation, and mathematics achievement. In this project, we explored students’ perspectives on using DT in calculus. We interviewed eight calculus students from a midwestern doctorate-granting institution in the United States and used thematic analysis informed by the didactical tetrahedron, accounting for internal and external factors that may influence the teaching and learning process. Students reflected on their use of technology, identifying various benefits, including …


Holographic Sensors For The Detection Of Volatile Organic Compounds, Graceson Antony Jan 2026

Holographic Sensors For The Detection Of Volatile Organic Compounds, Graceson Antony

Doctoral

Volatile organic compound (VOC) monitoring at parts-per-million (ppm) concentration levels is essential for occupational safety, indoor air quality, and regulatory compliance. Although holographic gas sensors have been widely investigated, most operate in reflection mode as qualitative visual indicators, with limited quantitative evaluation of sensing mechanisms and scarce systematic demonstrations of repeatable multi-cycle validation for VOCs at ppm concentrations. A physics-based optimisation framework for transmission-mode holographic gas sensors which can bridge this gap has remained largely undeveloped.

This thesis presents the development and optimisation of real-time transmission-mode volume phase transmission holographic grating (VPTHG) sensors for ppm-level VOC detection. A comprehensive theoretical …


Exploring The Synergy Between Very Large Transformer And Lstm Models For Effective Medical Captioning From Videos To Text: The Impact Of Captioning In Healthcare, R. V. Aswiga, Moin Ahmed Zahir Jan 2026

Exploring The Synergy Between Very Large Transformer And Lstm Models For Effective Medical Captioning From Videos To Text: The Impact Of Captioning In Healthcare, R. V. Aswiga, Moin Ahmed Zahir

Data Science Faculty Publications

In today’s rapidly evolving digital landscape, the demand for accurate and contextually relevant subtitles for image and video content, particularly in the medical domain, is increasingly critical. Despite the proliferation of visual data across various platforms, existing captioning systems often struggle due to variations in visual settings, complex temporal relationships, and nuanced semantics. Additionally, challenges such as limited datasets, privacy issues, and specialized annotation requirements make medical image captioning particularly difficult. To tackle these challenges, we investigate cutting-edge deep learning methodologies, specifically Transfer Learning and Transformer models, through a comparative analysis. Specifically, we focus on Transfer Learning through the MedVisionCapturer …


Algorithmic Medicine And The Duty To Disclose: Informed Consent Through The Lens Of Radiology, Lee Rodriguez Jan 2026

Algorithmic Medicine And The Duty To Disclose: Informed Consent Through The Lens Of Radiology, Lee Rodriguez

Michigan Law Review

Informed consent is the law’s mechanism for protecting patient autonomy by requiring disclosure of facts that bear on the decision to accept or refuse care. Artificial intelligence now helps decide what is medically true for patients, yet informed consent law still assumes that diagnostic judgment is rendered by a human mind whose reasoning is at least in principle communicable. Radiology has become the leading setting for this tension. AI systems triage worklists, flag suspected abnormalities, and anchor first-pass impressions in ways that guide radiologists’ attention and, in practice, can coauthor diagnostic conclusions while remaining invisible to patients. When patients are …


A Fully Discrete Semi-Implicit Numerical Scheme And Its Optimal Error Estimates For Cahn-Hilliard-Mhd Model With Variable Density, Dongmei Duan, Fuzheng Gao, Xiaoming He, Yanping Lin Jan 2026

A Fully Discrete Semi-Implicit Numerical Scheme And Its Optimal Error Estimates For Cahn-Hilliard-Mhd Model With Variable Density, Dongmei Duan, Fuzheng Gao, Xiaoming He, Yanping Lin

Mathematics and Statistics Faculty Research & Creative Works

This paper proposes and analyzes a fully discrete semi-implicit unconditionally energy stable numerical scheme to solve the Cahn-Hilliard Magnetohydrodynamics (Cahn-Hilliard-MHD) model with variable density. The unconditional energy stability and optimal L2 error estimates are established for the fully discrete scheme. Major challenges in error estimation arise from the variable density, the strong nonlinearities, and the multi-physics coupling of the model. Under the mathematical induction framework, the Ritz quasi-projection and the Stokes quasi-projection, proposed in [SIAM J. Numer. Anal., 61(3):1218-1245, 2023], are utilized to avoid the gradient terms of the projection errors. The H−1 superconvergence error estimates of Ritz …


A 1d Symmetric Interior Penalty Discontinuous Galerkin Solver In Rust, William Aey Jan 2026

A 1d Symmetric Interior Penalty Discontinuous Galerkin Solver In Rust, William Aey

Williams Honors College, Honors Research Projects

This honors project will build a 1D Symmetric Interior Discontinuous Galerkin (SIPDG) solver in Rust for Stum-Liouville type problems such as the Poisson equation, with Robin, Dirichlet, and Neumann boundary conditions. The work will cover the full pipeline: starting from the strong form of the PDE, deriving the DG weak form, implementing element and interface operators, and assembling or apply the discrete operator. Rust's safety and concurrency (e.g, via Rayon) will be used to explore serial and parallel performance. A test-driven development approach will be used to maintain a strong suite of tests. The project will result in a documented …