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At least 631 records · Page 35

Pile Driving

Machine-oriented structural engineering firm TERA, Inc. is engaged in a project to evaluate the reliability of offshore pile driving prediction methods to eventually predict the best pile driving technique for each new offshore oil platform. Phase I Pile driving records of 48 offshore platforms including such information as blow counts, soil composition and pertinent construction details were digitized. In Phase II, pile driving records were statistically compared with current methods of prediction. Result was development of modular software, the CRIPS80 Software Design Analyzer System, that companies can use to evaluate other prediction procedures or other data bases.

Source record↗

Workforce for the Future Development of Space Access Vehicles

The development of advanced vehicles that will travel between planetary surfaces with atmospheres and space requires the availability of experimental and computational capabilities that accomplish the research leading to new technologies and the development, test, and evaluation (RDT&E) of new flight systems. The United States is at risk of not having the required RDT&E workforce – qualified and in sufficient numbers – in place and ready to meet the future market’s commercial and defense needs. Systemic challenges include uncertain Federal budgets that limit and interrupt government research and development, the projectized nature of new space access systems that drive boom/bust cycles, an aging aerospace workforce (compounded by a mid-age demographic gap), limited to declining investment in sustaining and advancing experimental and computational tools infrastructure, lack of standards for sharing (and leveraging) data, dramatically changing technologies, changing social norms, and potentially large increases in commercial market needs. Flight systems have mission-based trajectories to and from space and designers must ensure risk is properly assessed across the entire trajectory. Thus, physics questions must be answered at each stage of flight, which requires a suite of experimental and computational tools. The RDT&E workforce utilizing these tools include subject matter experts from the producers, interested in acquiring data and information on the product, and from the capabilities being utilized, interested in addressing the product customer’s needs (providing robust data collection techniques, data quality, timeliness – available when needed, efficient with cost management, and teaming on data analysis). This requires a range of skills – in addition to aerospace, other engineers, and software developers, a highly trained and certified craft and technician workforce is critical to future success. This paper will present a human resources construct that addresses the system of needs for people – including, but more than just technical skills and an application of that construct in the hypersonic Test and Evaluation (T&E) community. This is part of a larger AIAA effort to document challenges and associated best practices for the aerospace RDT&E workforce.

Steven C Dunn↗

Creating Benchmark Data for Artificial Intelligence and Machine Learning Space Biology Research

To identify an appropriate AI/ML approach for a specific problem, the best practice is to measure algorithm performance through the benchmarking process. A scientific benchmark consists of an AI-ready dataset and a reference implementation on a specific scientific question. The NASA Science Mission Directorate (SMD) has started the “Benchmark Initiative for AI/ML to create scientific benchmark datasets in three applications: 1) scientific benchmarking, which finds the best algorithm for a specific problem; 2) application benchmarking, which measures algorithm performance against a set of parameters; and 3) system benchmarking, which evaluates performance of hardware and software architecture. Currently, there are no standardized datasets available to benchmark AI/ML algorithms in the domain of space biology. In this work, we constructed two AI/ML-ready biological datasets from experiments in space-flown mice: cellular imaging and RNA-seq. First, radiation-exposed immune cells harbor DNA damage foci that can be fluorescently marked to visualize the amount of damage following exposure to ionizing radiation. However, such large datasets are difficult to analyze visually, due to imaging inconsistencies and human bias, and classical image processing approaches can fail on imaging artifacts. AI/ML are therefore exciting alternative, providing the speed of machines and the accuracy of humans. We have made this dataset available at https://registry.opendata.aws/bps_microscopy/. Second, high-throughput nucleic acid sequencing (DNA-seq, RNA-seq) has become widespread in biomedical research due to the growing availability and affordability of these assays. However, most sequencing datasets suffer from high dimensionality and low sample count. In this work, we used a generative adversarial network to synthesize a standardized, AI-ready, publicly available benchmark dataset for space biology RNA-seq data with sufficient space-flown and ground control mouse liver samples from NASA GeneLab. This dataset is available at https://registry.opendata.aws/bps_rnaseq/. These datasets are now fully open the Space Biology community to test their favorite AI/ML approaches.

James Casaletto↗

Considering the Variability of Soiling in Long-Term PV Performance Forecasting: Preprint

This study presents the development of a methodology for evaluating the variability associated with soiling on long-term PV forecasting. Independent engineering firms typically build P50 forecasts for large PV plants through the use of the PVsyst software, where monthly soiling losses are one of many inputs to the P50 model. Subsequently, long-term performance distributions, or Pvalues, are constructed through a Monte Carlo analysis that includes various factors such as: satellite irradiance modeling uncertainty, uncertainty in the PVsyst model, and long-term irradiance variability. Often the PVsyst model uncertainty is increased to account for sites with significant soiling concerns but no systematic method has been presented in the literature to specifically include soiling variability within Pvalues. In this work soiling information from 16 sites in the U.S. Southwest are combined with 20 years of rainfall data to generate 20 years of energy production with soiling losses and then subsequently generate Pvalues. The results show that the spread of Pvalues (P1-P99) can increase from 0-13% when interannual soiling variability is included.

interannual variability↗

Building the Scale Model TELBOT Master Arm - 19585

For centuries, the art and science of modeling have gone hand in hand with the advancements of technology. Among the most impressive examples of the past modeling were ship models constructed for the British Royal Navy. Referred to as Admiralty models, they were principally constructed during the 18. and 19. centuries to depict proposed warship design. To this day, models are important in the field of engineering, where analytical modeling of a new design needs to be verified. In our project the old practice of building models will be fortified by the most advanced software and 3-D printing technology and used to manufacture a fully working Telbot Master Arm scaled down to 0.4-0.5 of its original size. The Telbot is a robotic arm used in different fields like the nuclear and chemical industry, often in combination with other products of our company. The main features of the Telbot's sleek construction are: 1) the high load capacity design; 2) unlimited rotation of all axes; 3) no external or internal wiring of the arm; 4) unlimited, fast and precise arm movements; 5) smooth and sealed arm bodies and joints; 6) high repeat accuracy; 7) resistance to radiation, and it can handle precise loads from 5 kg to 150 kg. Presently, to demonstrate such impressive design features and movement possibilities to its customers, HWM has to build a 3-D virtual reality simulation of the environment where Telbot is proposed to be used and then the arm simulates its movement in this environment. In addition, though HWM does have a showroom for Telbot, due to its weight and size it is not possible to take the full size Telbot on the road to show off its capabilities to customers. The challenge is to build a scaled down full working version of the Telbot robotic arm that can be moved in every direction and angle. The model will be based on the redeveloped T300 Telbot, with 3 joints and 7 free to move pivots. It will be at a 0.4 or 0.5 scale. The outer shell will be 3D printed. The sensors will forward the position and angle to HWM virtual reality software. With these features, any changes made on the model would get displayed in the software one-to-one. The result will be a Telbot Master arm model which can be easily transported; Waellischmiller would be able to present the Telbot not just virtually, but as a real product with all its functions and versatility and show it all over the world. The extensive construction of the virtual 3-D stimulation can be eliminated and the course of movement to reach specific positions could get simulated faster and easier. It can also be used internally and externally for training. This paper will address the challenges, materials used and manufacturing process of building a fully-working scaled-down version of the Telbot Master Arm. (authors)

3D PRINTING↗

A Data Processing Pipeline To Extract A Knowledge Graph From Heterogeneous Data For Socio-technical Analysis Of Critical Infrastructure Influence

The code is written in Python and consists of the following pipeline that is implemented in Apache Airflow. This pipeline intends to understand the companies that are directly or indirectly involved with a type of critical infrastructure system at some point in that system's lifecycle. The pipeline takes a configuration file that specifies a list of initial companies to consider, a geographic region of interest, and a set of SEC form types as well as other data sources (e.g. CrunchBase) from which to extract entities and relations. There are four main components to this pipeline as currently implemented: Entity Extraction, Network Construction, Analysis, and Visualization. First, Entity Extraction, is implemented as the `topear-extract_organizations` Apache Airflow workflow. Given an initial query that specifies a geographic region of interest and a time interval, the software will extract CI facilities of interest and organizations that have a direct influence relationship to those facilities (e.g. ownership). During the course of the LDRD, we focused on Electric Vehicle charging stations and this information is available via the Department of Energy (DOE) database on fueling stations maintained by NREL. Within the context of the DOE CESER project, we have focused on Battery Energy Storage Systems (BESS). Second, the Network Extraction component will iteratively construct a social network graph given the set of organizations and people extracted in the previous step. Organizations (and eventually People if desired) are then fed as a query to the `topgear-construct_social_network` Apache Airflow workflow which given a set of initial companies and data sets (e.g. SEC EDGAR form types, OpenCorporates, Crunchbase). This Airflow workflow will iteratively query such data sources to discover relationships with new organizations and people. For example, this module can iteratively query SEC EDGAR for metadata that documents the number of each type of form for the given set of companies and their location. This forms metadata represents a catalog of data sources from SEC EDGAR for the extracted social network knowledge graph. The pipeline then downloads these forms from the website and saves them in a build directory for further processing. These documents are then parsed for entities and relations. Again, we note that in additional to SEC data sources, this step can also pull in information on organizations via API services such as CrunchBase and OpenCorporates or bulk data sources. At the end of this step, the resultant social network, the Critical Infrastructure network, and the edges that encode relationships between organizations and CI facilities, form the Adversarial Socio-Technical Network (ASTN) that informs the analysis. Third, the Analysis component processes these generated ASTN. Previously, that has included the ability to compare prevalence of different vendors for a given infrastructure component type across different regions as well as identify common public and private investors across those vendors. This was demonstrated for EV Charging Stations across several different metropolitan areas within an IEEE PES GridEdge publication. More recently, we have looked at ways to identify infrastructure owners and operators of BESS with the most nameplate capacity across different states as well as other indictors of risk resulting from changes in ownership over time. Finally, the Visualization component consists of an HTML/CSS/JS framework by which users can interact geospatial, operational, and organizational relationships across a given portfolio of Critical Infrastructure facilities. The objective is to provide a library of UI/UX modules that can be repurposed for stakeholder-specific dashboards. All of the modules are related via a common event model that enables UI actions in one view to percolate across the other views.

Weaver, Gabriel [Idaho National Laboratory (INL), ↗

Technology Solutions Case Study: High-Performance Walls in Hot-Dry Climates

In this project,the Alliance for Residential Building Innovation (ARBI) team worked with builders in California to implement wall assemblies meeting a U-value lower than 0.050 Btu/h-ft2-°F. ARBI and its project team members helped builders identify preferred wall designs that met the requirements of their architects, structural engineers, and purchasing agents and that were acceptable to their subcontractors. Construction methods were observed and documented and construction costs obtained from builders were used to inform cost estimates for a range of advanced wall system types and insulation types. Wall framing types of 2 × 6 (16- and 24-in. on center [o.c.]) and double stud were modeled in Building Energy Optimization (BEopt™) software with cavity insulation levels ranging from R-19 to R-33 (double stud) and exterior rigid insulation of R-4, R-6, and R-8.

ARBI↗

Proxy Applications for Converged Workloads: DMC LDRD Initiative

Modern scientific applications are complicated and require coordination of several components. Proxy application driven software-hardware co-design plays a vital role in driving innovation among the developments of applications, software infrastructure and hardware architecture. Proxy applications are self-contained and simplified codes that are intended to model the performance-critical computations within applications. Applications executing on modern High Performance Computing (HPC) systems are susceptible to network congestion, insufficient memory bandwidth within and across compute nodes, and inadvertent loss of performance due to bugs and unoptimized programming models. Modern numerical simulations and machine learning models play a critical role in studying physical phenomenon under myriad uncertainties. Such applications often exhibit irregular computation and memory accesses at specific regions of the application code, which can contribute to various performance bottlenecks at scale. To mitigate such issues and prepare the next generation hardware for a variety of computation and data movement contingencies, a well-known practice is to consider "proxy" applications as representative motifs for various classes of scientific applications. While there is disagreement in the HPC community on the mechanisms of construction of the proxy applications, there is a strong consensus on their positive impact in co-design. Proxy Applications for Converged Workloads (PACER) is about facilitating software-hardware co-design through proxy applications with the goal of improving the performance of converged science workflows on heterogeneous systems.

97 MATHEMATICS AND COMPUTING↗

Advanced Control Architecture and Sensor Information Development for Process Automation, Optimization, and Imaging of Chemical Looping Systems

The Syngas Chemical Looping (SCL) process developed at The Ohio State University (OSU) uses an iron-based oxygen carrier to convert syngas into high-purity hydrogen while simultaneously capturing carbon dioxide that is readily sequestrable. A 25 kWth sub-pilot unit was successfully demonstrated multiple times on the OSU Clean Coal Research Facility, and a 250 kWth – 3 MWth pilot demonstration unit has been designed and constructed at the National Carbon Capture Center (NCCC) in Wilsonville, Alabama. The focus of this project is to develop multiple technologies to automate the startup and shutdown of chemical looping system. Success of this project will propel the advanced carbon capture method toward commercialization, hence be disruptive to the fossil fuel and power industries. Advanced process automation control architecture and imaging and optimization sensor software were developed for OSU chemical looping process. A high-level controller (HLC) consisting of decision-making and controller-selection logic integrated with sliding mode controllers (SMCs) were developed to perform chemical looping process startup and shutdown. Babcock & Wilcox Power Generation Group’s FocalPoint Optimization System was implemented to optimize the process operating conditions. The process automation controller and optimization information were realized and tested on OSU’s existing sub-pilot chemical looping test unit under atmospheric condition. The implemented control architecture was able to perform the complete process procedure from startup, steady-state reaction operation to shutdown with minimal operator intervention. The controller was also implemented on the pressurized syngas chemical looping (SCL) pilot test unit constructed at the National Carbon Capture Center (NCCC), demonstrating its pressure control capability with a designed transient state trajectory. An electrical capacitance volume tomography (ECVT) sensor device and its software were developed to image the packed moving bed and slugging fluidized bed of oxygen carriers in chemical looping systems at elevated temperatures. The ECVT device constructed was capable of tracking the subtle voidage variance along the moving bed axis as a feature for directly measuring the oxygen carrier particles’ linear velocity. Also, the high temperature ECVT device was used to study the fluidization characteristics of Geldart Group D particles.

08 HYDROGEN↗

Determing the Radiative Heat Transfer out of the Fireball of an Atmospheric Nuclear Detonation using Experimental Data

When Edgerton, Germeshausen and Grier, Inc. (EG&G) conducted the atmospheric nuclear tests in the 1950s, they made several continuous records of the light output over time with special "streak cameras." Once processed, these "streak films" contained long bands of varying optical density on black-and-white 35mm film. The purpose for creating them was to determine the time-dependent rate of radiative heat transfer out of the fireball. Back then, EG&G's manual examination methods were not precise enough to make complete analysis worthwhile, so the data was never fully analyzed. With the advent of new computer software, recently developed analysis techniques have reduced uncertainty in the data to where re-analysis is providing results far more reliable than anything EG&G published. Previously inaccessible information can now be accurately gathered from the original films. The method described here allows the streak films to be analyzed so a radiative power curve for an atmospheric nuclear detonation can be constructed using only experimental data. It was applied to five streak films here, though it may be applicable to other types of films as well. The data was plotted and compared to solutions generated with the Hybrid Chemistry (HYCHEM) software. The results are explained, and uncertainty values are provided. If the results from more films show consistency and the sources of uncertainty are mitigated, enough data may be discovered to create a correction factor for HYCHEM or to make more accurate yield determinations using G.I. Taylor's equations. Several other conclusions and recommendations are also posed.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

Combinatorial-Hierarchical DNA Library Design Using the TeselaGen DESIGN Module with j5.

Modern DNA assembly techniques are known for their potential to link multiple large DNA fragments together into even larger constructs in single pot reactions that are easier to automate and work more reliably than traditional cloning methods. The simplicity of the chemistry is in contrast to the increased work needed to design optimal reactions that maximize DNA fragment reuse, minimize cost, and organize thousands of potential chemical reactions. Here we examine available DNA assembly methods and describe through example, the construction of a complex but not atypical combinatorial and hierarchical library using protocols that are generated automatically with the assistance of modern synthetic biology software.

Fero, Michael J↗

Stabilized bases for high-order, interpolation semi-Lagrangian, element-based tracer transport

In a computational fluid model of the atmosphere, the advective transport of trace species, or tracers, can be computationally expensive. For efficiency, models often use semi-Lagrangian advection methods. High-order interpolation semi-Lagrangian (ISL) methods, in particular, can be extremely efficient, if the problem of property preservation specific to them can be addressed. Atmosphere models often use geometrically and logically nonuniform grids for efficiency and, as a result, element-based discretizations. Such grids and discretizations make stability a particular problem for ISL methods. Generally, high-order, element-based ISL methods that use the natural polynomial interpolant associated with a nodal finite-element discretization are unstable. Here, we derive new bases having order of accuracy up to nine, with positive nodal weights, that stabilize the element-based ISL method. We use these bases to construct the linear advection operator in the property-preserving Interpolation Semi-Lagrangian Element-based Transport (Islet) method. Then we discuss key software implementation details. Finally, we show performance results for the Energy Exascale Earth System Model's atmosphere dynamical core, comparing the original and new transport methods. These simulations used up to 27,600 Graphical Processing Units (GPU) on the Oak Ridge Leadership Computing Facility's Summit supercomputer.

97 MATHEMATICS AND COMPUTING↗

Poplar

SAND2025-00683O Poplar is a software tool that generates a phylogenetic tree from input gene and genome sequences. It integrates established tools to identify genes within genomes, group sequences, construct gene trees, and infer a species tree. Poplar processes nucleotide sequences, identifies similar sequences using Nucleotide BLAST, groups them with DBSCAN, aligns sequences with MAFFT, constructs gene trees with RAxML-NG, and infers a species tree using ASTRAL-Pro3. This pipeline provides a structured approach to phylogenetic analysis, facilitating the study of evolutionary relationships among species. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

Krishnakumar, Raga↗

Performance Characterization of LCLS-II Superconducting Radiofrequency Cryomodules

This paper will describe the LCLS (Linac Coherent Light Source)-II, Fermilab’s role in the development of LCLS-II, and my contributions as a Lee Teng intern. LCLS-II is a second generation x-ray free electron laser being constructed at SLAC National Accelerator Laboratory. Fermilab is responsible for the design, construction, and testing of several 1.3 GHz cryomodules to be used in LCLS-II. These cryomodules are currently being tested at Fermilab. Some software was written to analyze the data from the cryomodule tests. This software assesses the performance of the cryomodules by looking at data on the cavity voltage, cavity gradient, dark current, and radiation.

43 PARTICLE ACCELERATORS↗

A High-Throughput Computing Infrastructure to Generate Custom, Open Community Geothermal Datasets

The most significant challenge facing geothermal research, development, and deployment is a lack of comprehensive datasets describing the geological and economical properties of North America. Automated knowledge base construction, the process of designing algorithms to analyze text and images to programmatically build new datasets, is one possible solution to this problem. The xDD library of full-text scientific articles (https://xdd.wisc.edu) is one of the largest collections of open and controlled-access scientific documents available for knowledge base construction in the world, but it has been underutilized by experts in geothermal research. The xDD development team attributed the lack of engagement by software developers and geothermal researchers to two perceived shortcomings of the system. First, the workflow for obtaining data from xDD for local development and testing of data mining applications was unnecessarily abstruse and required significant manual intervention by xDD systems administrators. Second, although xDD already held articles from a broad cross-section of scientific literature with an emphasis on the geosciences, it did not have an explicit set of geothermal research documents that could serve as the nucleus of a geothermal data mining application. To address these issues, the Automated Data Extraction PlaTform (ADEPT) was proposed to extend the data distribution capabilities of the xDD system. The ADEPT extension added the following four key features to xDD: 1) integration of National Geothermal Data System (NGDS) documents into the xDD library to provide an explicitly geothermally-themed collection; 2) improved RESTful (i.e., https-protocol driven) web services for external partners to access xDD data for machine learning application development; 3) a web platform for end-users and xDD administrators to coordinate the development of data mining applications from the initial step of browsing available documents to the final stage of deploying a production-quality machine learning application on high-throughput computing infrastructure; and 4) the development of demonstration data mining applications to illustrate the new workflow to potential collaborators. A total of 21,674 geothermal documents from NGDS were fully ingested into the xDD library and the associated metadata is publicly available through the xDD web services; furthermore, the ADEPT web platform is now publicly accessible and fully live at https://xdd.wisc.edu/adept/.

15 GEOTHERMAL ENERGY↗

Numerical Investigation of Enhanced Dehumidification Processes By Using Dielectrophoresis Principles in Moist Airflows

Dispersed particle-laden flows are encountered in many building and industrial applications, such as flow in a fluidized bed, hydrocarbon transportation in pipelines, and the fouling of air-cooled heat exchangers (Kuruneru et al., 2016; Ray et al., 2019; Wang et al., 2019). Computational fluid dynamic (CFD) models have been developed in recent years to depict particle-fluid and particle-particle interactions in laminar or turbulent flows with increasing accuracy and stability. One particular particle-laden system of interest for moisture control is electrically-enhanced condensation in air and water droplet flows. Electrically-enhanced condensation consists of the use of highly charged water droplets injected in the moist air. The droplets become electric seeds that attract polar water vapor molecules to their surfaces and promote condensation. The nucleation and growth of the charged droplets deplete the vapor phase near a droplet, which is compensated for by the dielectrophoresis flow and diffusion. Dielectrophoresis flow involves surrounding vapor at a distance of about 10 to 100 nm for droplets charged by an electrospray compared to ~2 nm for a single electron charge in a droplet. As the vapor molecules collapse on the surface of the droplets, their initial electrical charge decreases with time due to the neutralization of the ions. While the physics of this phenomena is well known, engineering models for predicting the condensation rates are not available. This work computationally investigates dehumidification of moist airflow in a converging rectangular duct. The objective is to develop an engineering model that predicts water vapor condensation by employing dielectrophoresis principles. We construct a Computational Fluid Dynamics (CFD) model of the duct with electrically-enhanced condensation. The model is implemented in the open-source software OpenFOAM. We utilize the Multi-Phase Particle-In-Cell (MP-PIC) method coupled with a Population Balance Equation (PBE) approach to simulate the particle-laden system. This methodology is an Eulerian-Lagrangian approach used to simulate the droplets' behavior in the humid air. The MP-PIC approach (Andrews and O'Rourke, 1996) mitigates the computational cost by parceling several fundamental particles with similar properties (such as types, sizes, and temperature) into one computational particle. Thus, the billions of particles can be substituted by millions of computational particles without significant loss of information. The PBE was considered with the Lagrangian frame to combine the particle distribution function used in MP-PIC (Kim et al., 2020). This approach preserves mass and energy conservation between the phases in the Eulerian and Lagrangian structures. The PBE in this procedure was directly linked to the discrete parcels, making the simulation of the particle distribution computationally efficient and robust. The MP-PIC-PBE approach used in the present work was applied to the dehumidification of air. Water droplets were injected in the air stream and forced to grow according to experimentally derived correlation. The experiments were conducted on a converging duct with the same geometry and boundary conditions used to build the CFD model. This approach enabled us to approximate the effect of dielectrophoresis phenomena on the droplet and air interface. This presentation will discuss the details of the new CFD model built for the duct, the implementation of the model in OpenFOAM CFD programming language, and the experimental validation of the newly developed model. The results revealed a moderate yet measurable increase in droplet diameter due to water vapor condensation at the vapor-liquid interface of the electrically charged droplets' surface. The seed water droplet particles grew in size by capturing the water vapor in the surrounding air. The OpenFOAM model predicted reductions of humidity in the air from 5 to 10 percent.

Yel Mahi, Maliha↗

Man's role in space exploration and exploitation

The crew workloads on the Space Shuttle are described. The Space Shuttle is designed to minimize the activity of the crew in maintaining and operating the Shuttle in order for the crew to be involved in productive activities. The changing role of the crew due to the use of more automated systems on spacecraft is examined. The Shuttle flight system is dependent on embedded software, and the crew is to manage and support these systems. The primary functions of the Space Station are as a laboratory and for construction and assembly of systems, requiring EVA. Examples of EVA are presented. The correlation between manned and unmanned systems and the future direction of space research are discussed.

Loftus, Joseph P.↗

Experiments with conjugate gradient algorithms for homotopy curve tracking

There are algorithms for finding zeros or fixed points of nonlinear systems of equations that are globally convergent for almost all starting points, i.e., with probability one. The essence of all such algorithms is the construction of an appropriate homotopy map and then tracking some smooth curve in the zero set of this homotopy map. HOMPACK is a mathematical software package implementing globally convergent homotopy algorithms with three different techniques for tracking a homotopy zero curve, and has separate routines for dense and sparse Jacobian matrices. The HOMPACK algorithms for sparse Jacobian matrices use a preconditioned conjugate gradient algorithm for the computation of the kernel of the homotopy Jacobian matrix, a required linear algebra step for homotopy curve tracking. Here, variants of the conjugate gradient algorithm are implemented in the context of homotopy curve tracking and compared with Craig's preconditioned conjugate gradient method used in HOMPACK. The test problems used include actual large scale, sparse structural mechanics problems.

Irani, Kashmira M.↗