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DOE OSTI2023

Data reduction considerations for the burning velocity of spherical constant volume flames of R32 (CH 2 F 2 ) with air

Here, the present work explores data reduction techniques for the measurement of the laminar burning velocities of R32(CH 2 F 2 )-air mixtures using a constant volume combustion device, in which the pressure-time history is the only measured parameter. To allow clear assessment of the accuracy of the data reduction methods, the pressure-time histories used for analysis are synthetically generated via a detailed numerical simulation employing full kinetics and with and without an optically-thin radiation model. Various data reduction models are employed, including a two-zone model and two multi-zone models, and these are compared with the results from the burning velocity obtained from the output of the numerical simulation. The data reduction schemes are shown to be accurate if the same radiation model is employed in the data reduction as was used in the flame simulation to generate the pressure trace used for post-processing. If the incorrect radiation model is employed, however, the errors can be quite large. The effects of stretch, radiation, and different data post-processing methodologies are explored and the errors quantified. Stretch is shown to be important for the early stages and the selected data range that is used for extrapolation has a significant effect on the extrapolated burning velocity. However, with an appropriate choice of data considered for extrapolation, the prediction of the unstretched burning velocity can be quite accurate.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS2002

Reducing the Requirements and Cost of Astronomical Telescopes

Limits on astronomical telescope apertures are being rapidly approached. These limits result from logistics, increasing complexity, and finally budgetary constraints. In an historical perspective, great strides have been made in the area of aperture, adaptive optics, wavefront sensors, detectors, stellar interferometers and image reconstruction. What will be the next advances? Emerging data analysis techniques based on communication theory holds the promise of yielding more information from observational data based on significant computer post-processing. This paper explores some of the current telescope limitations and ponders the possibilities increasing the yield of scientific data based on the migration computer post-processing techniques to higher dimensions. Some of these processes hold the promise of reducing the requirements on the basic telescope hardware making the next generation of instruments more affordable.

Smith, W. Scott↗

DOE OSTI2014

Scanning ARM Cloud Radars. Part II: Data Quality Control and Processing

The Scanning ARM Cloud Radars (SACR’s) are the primary instruments for documenting the four-dimensional structure and evolution of clouds within a 20-30 km radius from the ARM fixed and mobile sites. Here, the post-processing of the calibrated SACR measurements is discussed. First, a feature mask algorithm that objectively determines the presence of significant radar returns is described. The feature mask algorithm is based on the statistical properties of radar receiver noise. It accounts for atmospheric emission and is applicable even for SACR profiles with few or no signal-free range gates. Using the nearest-in-time atmospheric sounding, the SACR radar reflectivities are corrected for gaseous attenuation (water vapor and oxygen) using a line-by-line absorption model. Despite having a high pulse repetition frequency, the SACR has a narrow Nyquist velocity limit and thus Doppler velocity folding is commonly observed. An unfolding algorithm that makes use of a first guess for the true Doppler velocity using horizontal wind measurements from the nearest sounding is described. The retrieval of the horizontal wind profile from the HS-RHI SACR scan observations and/or nearest sounding is described. The retrieved horizontal wind profile can be used to adaptively configure SACR scan strategies that depend on wind direction. Several remaining challenges are discussed, including the removal of insect and second-trip echoes. The described algorithms significantly enhance SACR data quality and constitute an important step towards the utilization of SACR measurements for cloud research.

climate↗

DOE OSTI2016

Organic Scintillator Detector Response Simulations with DRiFT

Here, this work presents the organic scintillation simulation capabilities of DRiFT, a post-processing Detector Response Function Toolkit for MCNPR output. DRiFT is used to create realistic scintillation detector response functions to incident neutron and gamma mixed- field radiation. As a post-processing tool, DRiFT leverages the extensively validated radiation transport capabilities of MCNPR ® 6, which also provides the ability to simulate complex sources and geometries. DRiFT is designed to be flexible, it allows the user to specify scintillator material, PMT type, applied PMT voltage, and quenching data used in simulations. The toolkit's capabilities, which include the generation of pulse shape discrimination plots and full-energy detector spectra, are demonstrated in a comparison of measured and simulated neutron contributions from 252 Cf and PuBe, and photon spectra from 22 Na and 228 Th sources. DRiFT reproduced energy resolution effects observed in EJ-301 measurements through the inclusion of scintillation yield variances, photon transport noise, and PMT photocathode and multiplication noise.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2020

An Adaptive Reference Scheme to Extend the Functional Range of Optical Backscatter Reflectometry in Extreme Environments

Optical frequency domain reflectometry (OFDR) measurements are performed by recording the interference pattern of light backscattered by density fluctuations or Bragg gratings along the length of an optical fiber. Changes in local temperature or strain in the fiber cause shifts in the backscattered light spectrum, which can be calibrated to the applied temperature or strain. Comparing the backscattered optical spectra from each reflection site with a reference (unstrained) spectrum allows for quantification of local spectral shifts. While mature OFDR-based technologies can provide high-precision spatially distributed measurements over kilometer lengths, the post-processing approaches used to recover spectral shifts from raw optical intensity data can limit the use of OFDR in harsh environments. This paper presents a novel approach to post-processing OFDR data which extends the usability of optical fibers exposed to harsh environments. This approach is the first to use the spectral shift quality, calculated for two OFDR measurements, to identify an appropriate reference scan from which the spectral shift can be determined. Here, three experimental data sets are used to test the algorithm: (1) an optical fiber heated to >950°C, (2) an aluminum-embedded optical fiber under strain from differential thermal expansion, and (3) an optical fiber exposed to a total neutron flux of 2×10 13 n/cm 2 /s over 40 hours in a nuclear test reactor. Results show that using a metric of quality to select an appropriate reference measurement extends the functional range of OFDR strain and temperature sensors. Furthermore, this algorithm can be applied to existing OFDR data.

47 OTHER INSTRUMENTATION↗

NASA NTRS1982

Evaluation of automated decisionmaking methodologies and development of an integrated robotic system simulation, volume 2, part 1. Appendix A: Software documentation

Documentation of the preliminary software developed as a framework for a generalized integrated robotic system simulation is presented. The program structure is composed of three major functions controlled by a program executive. The three major functions are: system definition, analysis tools, and post processing. The system definition function handles user input of system parameters and definition of the manipulator configuration. The analysis tools function handles the computational requirements of the program. The post processing function allows for more detailed study of the results of analysis tool function executions. Also documented is the manipulator joint model software to be used as the basis of the manipulator simulation which will be part of the analysis tools capability.

Lowrie, J. W.↗

DOE OSTI2026

Data From: "Warming and snow loss increase reliance on old groundwater in a Colorado River headwater"

This repository contains the data and code associated with the paper titled "Warming and snow loss increase reliance on old groundwater in a Colorado River headwater," published in Nature Geoscience, 2026. This study seeks to answer how various ages of groundwater interact with mountainous streamflow in mountainous headwaters such as the East River. It includes various model-data processing scripts, primarily for ParFlow-CLM analysis of simulated water years 2015-2021, and two numerical warming experiments (+2.5 and +4.0 degrees C), including run scripts, forcing scripts, and post-processing, as well as comparison to observation datasets, detailed below. This data requires the use of R (.r, .rmd), Python (.py), Jupyter Notebook or Jupyter Lab (.ipynb), ParFLOW-CLM, EcoSLIM. Further information on the use of all file formats mentioned below (e.g. .tff. .nc) are provided within the associated scripts and directory where the files are located. Contents & Usage ASO/: Contains the bash and python scripts used to convert airborne snow observatory (ASO) data (ASO, 2023) in various data formats (georeferenced tiff file, NetCDF, UTM, and to latitude/longitude) then regrided to the ParFlow equivalent grid. Output data are in regrid_regll_data.zip and subsequently visualized and analyzed in plot_and_compare.py for Supplementary Figures A14 and A15. The wksht_ASO_comparison.xlsx spreadsheet is used to calculate the data for Supplementary Figure A16. EcoSLIM/: Contains the scripts and input files to run the EcoSLIM particle tracking simulations (/run_scripts) and the post-processing python script (/plot_scripts/eco_agedist_plots.ipynb). Jasechko et al./: Contains the jupyter notebook (Extract_Elevation.ipynb) to determine the outlet elevations of the 260 watersheds used in Jasechko et al. (2016), and the corresponding table, Table_S1_Watersheds_alt.csv. Used to create Supplementary Information Figure A2. PLM_Wells/: Contains the QA/QC-ed groundwater level time series of the PLM-1 and PLM-6 Monitoring Wells from Faybishenko et al. (2023), reformatted to water years used for Supplementary Figures A19 and and A20. ParFlow/: Contains the input files and run scripts to run ParFlow-CLM (/run_scripts), the python and tool command language (Tcl) scripts to create and distribute the ParFlow forcing simulation files (/forcing), and various scripts and intermediary files to analyze the model outputs (/post_process). SQUIRE/: Contains the processing scripts and intermediary files for the Surface QUantitatIve pRecipitation Estimation (SQUIRE) data (Grover, 2023) used to generate Supplementary Figure A18. USGS_Streamflow/: Contains the raw and gap-filled United States Geological Survey streamflow data (U.S. Geological Survey, 2026) used at the Almont station (site number 09112500). Gap-filling is performed in the R script with data from the Taylor station (site number 09110000). (/USGS_09112500_EAST_RIVER_AT_ALMONT_GAP_FILLED/code_almont_streamflow_gap_fill.Rmd). discharge/: Contains the gap-filled discharge data at the Watershed Function SFA East River pumphouse site (Newcomer et al., 2022) used to generate Supplementary Figure A13 and to compute hourly Nash-Sutcliffe model efficiency coefficients (NSE) in Table A4. snotel_and_flux_tower/: Contains the snow telemetry data (U.S. Department of Agriculture, 2024) from the Butte (site ID 380) and Schofield (site ID 737) stations, reformatted by water year, accessed with the snotelr R package. Used to create Supplementary Figure A17. Also contains the flux tower observational data (FluxTower_Pumphouse_ESS-DIVE.ET_only.h.txt) from Ryken et al. (2022) and sap flux transpiration data (MaxB_Transpiration_5Sites.daily_sums.h.txt) from Ryken (2021), used to create Supplementary Figures A22 and A23, respectively. Raw EcoSLIM model outputs are in excess of 24TB, and are stored on National Energy Research Scientific Computing Center (NERSC) and publicly available via the external link provided in the paper.

atmospheric warming↗

NASA NTRS2022

Europa Clipper Payload Verification and Validation: Avionics-Instrument Interface Test Campaign

NASA's Europa Clipper mission will investigate Jupiter's icy moon Europa using a payload suite consisting of nine instruments to address a range of scientific objectives concerning Europa's habitability. As the project proceeds past its Critical Design Review, confidence is being built in the system's ability to achieve mission objectives through the implementation of a rigorous payload verification and validation (V&V) program. As part of this payload V&V program, instrument box-level testing was performed by the payload team to verify select instrument-avionics interface requirements. This testing was performed at JPL using the avionics testbed's Bulk Data Storage Emulator (BDSEM) with visiting instrument Test Models. This paper summarizes the Data Link test campaign involving roughly four days of functional testing per instrument, including planning, testing methods, types of issues found, and the requirement closure process. Detail is also provided on the development, deployment, and validation of a standardized analysis tool used in data reviews. This testing verified requirements related to commanding rates, loss of link, packet format, clock counters, loopback test capability, and SpaceWire jitter and skew margins. Additional risk reduction testing of basic commanding, counter behavior, science data collection and transfer, and interface swapping was also performed. Because the BDSEM venue was not originally designed to be a run for record venue, the process of characterizing venue fidelity and establishing suitability for requirement closure using data collected in this venue will also be addressed.In order to close requirements, an extensible tool was developed to post-process instrument command and telemetry data from their original binary to a human-readable format and give visibility to errors detected within the data, such as packets with Cyclic Redundancy Check errors. This tool, called payload-packet-parser, is a Python 3.9 command line tool built using a variety of open-source Python libraries. Payload-packet-parser was designed to support parsing command and telemetry packets for all Europa Clipper instruments and additional analysis tools were developed for verification of specific information interface requirements. This test campaign, including post-processing using a single parsing and verification toolset, allowed for early interface testing, alleviating testing burdens on instrument teams and buying down risk on the instrument-avionics interface by finding hardware and software issues and idiosyncrasies prior to integration with system test venues. Over twenty issues were discovered across the payload, resulting in software updates and instrument rework well in advance of any system impacts. This paper concludes with an assessment of benefits and costs of this type of testing and lessons learned.

Montanez, Leticia↗

DOE OSTI2020

Leaf-scale carbon assimilation simulated by the multi-assumption architecture & testbed for process sensitivity analysis

Raw and processed output from the Multi-Assumption Architecture & Testbed (MAAT, https://github.com/walkeranthonyp/MAAT, tag: v1.2.1_walker2020; Walker et al., 2018). The dataset contains leaf-scale carbon assimilation data from three MAAT simulations and their post-processing and plotting scripts. Simulation 1, labelled "FvC_4proc_proc," is a four-process, process sensitivity analysis (Dai et al., 2017) of carbon assimilation based on the Farquhar et al. (1980) photosynthesis model, and its variant proposed by Collatz et al. (1991). Simulation 2, labelled "FvC_4proc_salt," is a 14 parameter sensitivity analysis (Saltelli et al., 2010) of carbon assimilation based on the Farquhar and Collatz photosynthesis models. Simulation 3, labelled "FvC," is a factorial combination of the alternative process representations and parameter values presented in those original papers across a factorial combination of incident photosynthetically active radiation (50-2000 µmol m-2 s-1, in increments of 50) and atmospheric CO2 concentration (50-1500 µmol m-2 s-1, in increments of 50). Additional scripts/functions for post-processing and plotting are part of the MAAT repository. These data were generated to evaluate and compare the Farquhar and Collatz models of leaf-scale photosynthesis across a range of CO2 and incident light conditions. Analysis of results can be found in Walker et al. (2020). This dataset is comprised of R scripts to process data and produce figures; .RDS files, a binary format specific to R and read with the 'readRDS' function, to store raw MAAT output; R and bash scripts (.bs) that help to run a MAAT simulation, .XML files that are output from MAAT describing a run, and .csv files which contain the calculated sensitivity indexes published in Walker et al. (2020).

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

DESPERATE: A Python Library for Processing and Denoising NMR Spectra

NMR spectroscopy is an inherently insensitive technique with respect to the amount of observable signal. A common element in all NMR spectra is random thermal noise that is often characterized by a signal-to-noise ratio (SNR). SNR can be generically improved experimentally with repetitive signal averaging or during post-processing with apodization; the former of which often results in long experimental times and the latter results in the loss of spectral resolution. Denoising techniques can instead be used during post-processing to enhance SNR without compromising resolution. The most common approach relies on the singular-value decomposition (SVD) to discard noisy components of NMR data. SVD-based approaches work well, such as Cadzow and PCA, but are computationally expensive when used for large datasets that are often encountered in NMR (e.g., Carr-Purcell/Meiboom-Gill and nD datasets). Herein, we describe the implementation of a new wavelet transform (WT) routine for the fast and robust denoising of 1D and 2D NMR spectra. Several simulated and experimental datasets are denoised with both SVD-based Cadzow or PCA and WT’s, and the resulting SNR enhancements and spectral uniformity are compared. WT denoising offers similar and improved denoising compared with SVD and operates faster by several orders-of-magnitude in some cases. Further, all denoising and processing routines used in this work are included in a free and open-source Python library called DESPERATE.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Year-long buoy-based observations of the air–sea transition zone off the US west coast

Abstract. Two buoys equipped with Doppler lidars owned by the US Department of Energy (DOE) were deployed off the coast of California in autumn of 2020 by Pacific Northwest National Laboratory. The buoys collected data for an entire annual cycle at two offshore locations proposed for offshore wind development by the Bureau of Ocean Energy Management. One of the buoys was deployed approximately 50 km off the coast near Morro Bay in central California in 1100 m of water. The second buoy was deployed approximately 40 km off Humboldt County in northern California in 625 m of water. The buoys provided the first-ever continuous measurements of the air–sea transition zone off the coast of California. The atmospheric and oceanographic characteristics of the area and estimates of annual energy production at both the Morro Bay and Humboldt wind energy areas show that both locations have a high wind energy yield and are prime locations for future floating offshore wind turbines. This article provides a description and comprehensive analysis of the data collected by the buoys, and a final post-processed dataset is uploaded to a data archive maintained by the DOE. Additional analysis was conducted to show the value of the data collected by the DOE buoys. All post-processed data from this study are available on the Wind Data Hub website: https://a2e.energy.gov/data# (last access: 14 September 2023). Near-surface, wave, current, and cloud datasets for Humboldt and Morro Bay are provided at https://doi.org/10.21947/1783807 (Krishnamurthy and Sheridan, 2023b) and https://doi.org/10.21947/1959715 (Krishnamurthy and Sheridan, 2023a), respectively. Lidar datasets for Humboldt and Morro Bay are provided at https://doi.org/10.21947/1783809 (Krishnamurthy and Sheridan, 2023d) and https://doi.org/10.21947/1959721 (Krishnamurthy and Sheridan, 2023c), respectively.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS2015

Space Telescope Design to Directly Image the Habitable Zone of Alpha Centauri

The scientific interest in directly imaging and identifying Earth-like planets within the Habitable Zone (HZ) around nearby stars is driving the design of specialized direct imaging missions such as ACESAT, EXO-C, EXO-S and AFTA-C. The inner edge of Alpha Cen A&B Habitable Zone is found at exceptionally large angular separations of 0.7" and 0.4" respectively. This enables direct imaging of the system with a 0.3m class telescope. Contrast ratios on the order of 10(exp 10) are needed to image Earth-brightness planets. Low-resolution (5-band) spectra of all planets may allow establishing the presence and amount of an atmosphere. This star system configuration is optimal for a specialized small, and stable space telescope that can achieve high-contrast but has limited resolution. This paper describes an innovative instrument design and a mission concept based on a full Silicon Carbide off-axis telescope, which has a Phase Induced Amplitude Apodization coronagraph embedded in the telescope. This architecture maximizes stability and throughput. A Multi-Star Wave Front algorithm is implemented to drive a deformable mirror controlling simultaneously diffracted light from the on-axis and binary companion star. The instrument has a Focal Plane Occulter to reject starlight into a high precision pointing control camera. Finally we utilize a Orbital Differential Imaging (ODI) post-processing method that takes advantage of a highly stable environment (Earth-trailing orbit) and a continuous sequence of images spanning 2 years, to reduce the final noise floor in post processing to approximately 2e-11 levels, enabling high confidence and at least 90% completeness detections of Earth-like planets.

Low-resolution (5-band) spectra↗

DOE OSTI2020

Programmable Quantum Networked Microgrids

Quantum key distribution (QKD) provides a potent solution to securely distribute keys for two parties. However, QKD itself is vulnerable to denial of service (DoS) attacks. A flexible and resilient QKD-enabled networked microgrids (NMs) architecture is needed but does not yet exist. In this article, we present a programmable quantum NMs (PQNMs) architecture. It is a novel framework that integrates both QKD and software-defined networking (SDN) techniques capable of enabling scalable, programmable, quantum-engineered, and ultra-resilient NMs. Equipped with a software-defined adaptive post-processing approach, a two-level key pool sharing strategy and an SDN-enabled event-triggered communication scheme, these PQNMs mitigate the impact of DoS attacks through programmable post-processing and secure key sharing among QKD links, a capability unattainable using existing technologies. Through comprehensive evaluations, we validate the benefits of PQNMs and demonstrate the efficacy of the presented strategies under various circumstances. Extensive results provide insightful resources for building QKD-enabled NMs in practice.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2015

Fabrication of Conductive Paths on a Fused Deposition Modeling Substrate using Inkjet Deposition

Inkjet deposition is one of the most attractive fabrication techniques for producing cost efficient and lightweight electronic devices on various substrates with low environmental impact. Fused Deposition Modeling (FDM) is one of the most used and reliable additive manufacturing processes by extrusion of wire-shaped thermoplastic materials, which provides an opportunity for embedding printed electronics into mechanical structures during the building process and enables the design of compact smart structures that can sense and adapt to their own state and the environment. This paper represents one of the first explorations of integrating inkjet deposition of silver nanoparticle inks with the FDM process for making compact electro-mechanical structures. Three challenges have been identified and investigated, including the discontinuity of the printed lines resulting from the irregular surface of the FDM substrate, the non-conductivity of the printed lines due to the particle segregation during the droplet drying process, and the slow drying process caused by the skinning effect . Two different techniques are developed in this paper to address the issue of continuity of the printed lines, including surface ironing and a novel thermal plow technique that plows a channel in the FDM substrate to seal off the pores in the substrate and contain the deposited inks. Two solutions are also found for obtaining conductivity from the continuous printed lines, including porous surface coating and using a more viscous ink with larger nanoparticle size. Then the effects of the printing and post-processing parameters on the conductivity are examined. It is found that post-processing is a dominant factor in determining the conductivity of the printed lines.

42 ENGINEERING↗

DOE OSTI2025

Leveraging FPGA Advantages for Quicker Data Processing for LBNF

The Long Baseline Neutrino Facility (LBNF) will deliver a 2.4 MW muon neutrino beam from Fermilab to the Deep Underground Neutrino Experiment (DUNE), requiring unprecedented precision in beamline alignment to achieve DUNE's neutrino oscillation measurement goals. Vertical misalignments of beamline components as small as 0.5 mm can contribute 6-7\% uncertainty in predicted neutrino flux, necessitating sub-0.1 mm alignment monitoring capabilities. The Horn Location Sensor (HLS) system employs frequency sweep interferometry (FSI) in a distributed hydrostatic leveling network to achieve the required precision under harsh radiation conditions up to 5000 kRad/year. Traditional FSI implementations suffer from laser sweep nonlinearities that degrade resolution and require computationally intensive post-processing corrections using gas reference cells. This work presents a real-time FPGA-based implementation of the HLS data acquisition and processing system using a sweep tracker interferometer for dynamic sweep linearization. The system utilizes a PYNQ-Z2 FPGA with programmable logic implementing parallel 16k-point FFT processing across four channels, synchronized by the sweep tracker signal to eliminate post-processing requirements. Spectral performance testing demonstrates significant improvements in peak sharpness compared to traditional fixed-frequency digitization. The FPGA implementation enables real-time displacement monitoring with processing speeds orders of magnitude faster than software-based approaches, essential for the operational requirements of LBNF's eventual distributed sensor network. This advancement in real-time FSI processing directly supports DUNE's precision neutrino physics program by providing the rapid feedback necessary for maintaining stringent beamline alignment tolerances during high-power beam operations.

Rossel, Jacob↗

NASA NTRS2009

Synthetic Foveal Imaging Technology

Synthetic Foveal imaging Technology (SyFT) is an emerging discipline of image capture and image-data processing that offers the prospect of greatly increased capabilities for real-time processing of large, high-resolution images (including mosaic images) for such purposes as automated recognition and tracking of moving objects of interest. SyFT offers a solution to the image-data processing problem arising from the proposed development of gigapixel mosaic focal-plane image-detector assemblies for very wide field-of-view imaging with high resolution for detecting and tracking sparse objects or events within narrow subfields of view. In order to identify and track the objects or events without the means of dynamic adaptation to be afforded by SyFT, it would be necessary to post-process data from an image-data space consisting of terabytes of data. Such post-processing would be time-consuming and, as a consequence, could result in missing significant events that could not be observed at all due to the time evolution of such events or could not be observed at required levels of fidelity without such real-time adaptations as adjusting focal-plane operating conditions or aiming of the focal plane in different directions to track such events. The basic concept of foveal imaging is straightforward: In imitation of a natural eye, a foveal-vision image sensor is designed to offer higher resolution in a small region of interest (ROI) within its field of view. Foveal vision reduces the amount of unwanted information that must be transferred from the image sensor to external image-data-processing circuitry. The aforementioned basic concept is not new in itself: indeed, image sensors based on these concepts have been described in several previous NASA Tech Briefs articles. Active-pixel integrated-circuit image sensors that can be programmed in real time to effect foveal artificial vision on demand are one such example. What is new in SyFT is a synergistic combination of recent advances in foveal imaging, computing, and related fields, along with a generalization of the basic foveal-vision concept to admit a synthetic fovea that is not restricted to one contiguous region of an image.

Hoenk, Michael↗

DOE OSTI2023

Preserving Superconvergence of Spectral Elements for Curved Domains via $h$ and $p$-Geometric Refinement

Spectral element methods (SEM), extensions of finite element methods (FEM), have emerged as significant techniques for solving partial differential equations in physics and engineering. SEM can potentially deliver superior accuracy due to the potential superconvergence in nodal solutions for well-shaped tensor-product elements. However, the accuracy of SEM often degrades in complex geometries due to geometric inaccuracies near curved boundaries and the loss of superconvergence with simplicial or non-tensor-product elements. To overcome the first issue, we propose using h- and p-geometric refinement, which refines the mesh near high-curvature regions and increases the degree of geometric basis functions, respectively. We show that when using mixed-element meshes with tensor-product elements in the interior of the domain, curvature-based geometric refinement near boundaries can improve the accuracy of the interior elements by reducing pollution errors and preserving the superconvergence in nodal solutions. To address the second issue, we introduce a post-processing technique using the adaptive extended stencil finite element method (AES-FEM) to recover the accuracy near the curved boundaries. The combination of curvature-based geometric refinement and accurate post-processing offers an effective and easier-to-implement alternative to methods reliant on exact geometries. We demonstrate our techniques by solving the convection-diffusion equation in 2D and show up to two orders of magnitude of improvement in the solution accuracy, even when the elements are poorly shaped near boundaries.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Preserving Superconvergence of Spectral Elements for Curved Domains

Spectral element methods (SEM), extensions of finite element methods (FEM), have emerged as significant techniques for solving partial differential equations in physics and engineering. SEM can potentially deliver superior accuracy due to the potential superconvergence in nodal solutions for well-shaped tensor-product elements. However, the accuracy of SEM often degrades in complex geometries due to geometric inaccuracies near curved boundaries and the loss of superconvergence with simplicial or non-tensor-product elements. To overcome the first issue, we propose using geometric refinement, which both refines the mesh near high-curvature regions and increases the degree of geometric basis functions. We show that when using mixed-element meshes with tensor-product elements in the interior of the domain, curvature-based geometric refinement near boundaries can improve the accuracy of the interior elements by reducing pollution errors and preserving the superconvergence in nodal solutions. To address the second issue, we introduce ApSEM, a post-processing technique using the adaptive extended stencil finite element method (AES-FEM) to recover the accuracy near the curved boundaries. The combination of curvature-based geometric refinement and accurate post-processing offers an effective and easier-to-implement alternative to methods reliant on exact geometries. We demonstrate our techniques by solving the convection-diffusion equation in 2D and 3D and show up to two orders of magnitude of improvement in the solution accuracy, even when the elements are poorly shaped near boundaries. We also show the efficiency of ApSEM as it can recover superconvergence in nodal solutions without drastically increasing the computational cost.

97 MATHEMATICS AND COMPUTING↗