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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Multi-Objective Adaptive Mesh Refinement Using Reinforcement Learning

Finite element methods approximate the solution to a partial differential equation (PDE) on a mesh consisting of many elements. In general, using more, smaller elements results in a lower error in the approximation. However, it is often possible to lower the error substantially by only refining, or decreasing the size of, the few elements in the mesh that have the highest error. Adaptive mesh refinement (AMR) is a process that selectively refines regions of a mesh with high error to achieve a desired accuracy in as few degrees of freedom (DOFs) as possible. AMR is favorable compared to uniform refinement, which refines all elements of the mesh equally, because it can often achieve the same accuracy without wasting extra computation time on refinement of elements that already have low error. However, it is difficult to know which elements to refine. In this report we explore ways to choose which elements to refine such that we minimize both the resulting error and the cumulative DOFs used in computation. In particular, we introduce a Pareto-front learning algorithm that trains a policy to give the optimal refinement actions to minimize the cumulative DOFs used to achieve a given target error. Such a policy is useful because it can be deployed on many different problem types where different accuracy levels are desired. Furthermore, training a single policy for a range of target errors allows us to use transfer learning to reduce the required training time.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

SU-E-T-541: Bolus Effect of Thermoplastic Masks in IMRT and VMAT Head and Neck Treatments

Purpose: To quantitatively evaluate the bolus effect of thermoplalstic mask on patient skin dose during multi-field IMRT and VMAT treatment. Methods: The clinically approved target contours for five head and neck patients were deformably registered to an anthropomorphic Rando phantom. Two plans: Multifield IMRT plan with 7-9 beams and VMAT plan with 2-4 arcs were created for each patient following same dose constraints. 3mm skin was excluded from PTVs but not constrained during optimization. The prescription dose was 200-220 cGy/fraction. A thermoplastic head and shoulder mask was customized for the Rando phantom. Each plan was delivered to the phantom twice with and without mask. During each delivery, two rectangular strips of EBT3 films (1cm x 6.8cm) were placed across the anterior upper and lower neck near PTVs to measure the surface dose. For consistency films were positioned at same locations for same patient. A total of 8 film strips were obtained for each patient. Film dose was calibrated in the range of 0-400cGy on the day of plan delivery. For dose comparison 3 regions of interests (ROIs) of 1×1 cm{sup 2} were selected at left, right and middle part of each film, resulting in 6 point doses at each plan delivery. Results: The films without mask show relatively uniform dose distribution while those with mask clearly show mesh pattern of mask, usually indicating an increase in skin dose. On average the increase in skin dose over all ROIs with mask was 31.9%(±14.8%) with a range of 11.4%- 58.4%. There is no statistically significant difference (p=0.44) between skin dose increase in VMAT (30.8%±15.3%) and IMRT delivery (33.0%±14.9%). Conclusion: Thermoplastic immobilization masks increase surface dose for HN patient by around 30%. The magnitude is comparable between multi-field IMRT and VMAT. Radiochromic EBT3 film serves as an effective tool to quantify bolus effect.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2020

GMRES with embedded ensemble propagation for the efficient solution of parametric linear systems in uncertainty quantification of computational models

In a previous work, embedded ensemble propagation was proposed to improve the efficiency of sampling-based uncertainty quantification methods of computational models on emerging computational architectures. It consists of simultaneously evaluating the model for a subset of samples together, instead of evaluating them individually. A first approach introduced to solve parametric linear systems with ensemble propagation is ensemble reduction. In Krylov methods for example, this reduction consists in coupling the samples together using an inner product that sums the sample contributions. Ensemble reduction has the advantages of being able to use optimized implementations of BLAS functions and having a stopping criterion which involves only one scalar. However, the reduction potentially decreases the rate of convergence due to the gathering of the spectra of the samples. In this paper, we investigate a second approach: ensemble propagation without ensemble reduction in the case of GMRES. This second approach solves each sample simultaneously but independently to improve the convergence compared to ensemble reduction. This raises two new issues which are solved in this paper: the fact that optimized implementations of BLAS functions cannot be used anymore and that ensemble divergence, whereby individual samples within an ensemble must follow different code execution paths, can occur. We tackle those issues by implementing a high-performing ensemble GEMV and by using masks. The proposed ensemble GEMV leads to a similar cost per GMRES iteration for both approaches, i.e. with and without reduction. For illustration, we study the performances of the new linear solver in the context of a mesh tying problem. Furthermore, this example demonstrates improved ensemble propagation speed-up without reduction.

BLAS↗
NASA NTRS1980

A Navier-Stokes fast solver for turbulence modeling applications

A computer code for the evaluation and/or optimization of the predicative potential of second order turbulent closure models in simple two dimensional flow configurations is discussed. A procedure for the numerical solution of the steady constant property Navier-Stokes equations are described together with algebraic, one dimensional and two dimensional equations of turbulence closure models. Four turbulence models are compared with several sets of experimental data. The effects of initial conditions and boundary conditions are also described. The effects of purely numerical parameters, such as mesh size, boundary locations, and convergence criteria are presented.

Murphy, J. D.↗
NASA NTRS2015

Enabling Rapid and Robust Structural Analysis During Conceptual Design

This paper describes a multi-year effort to add a structural analysis subprocess to a supersonic aircraft conceptual design process. The desired capabilities include parametric geometry, automatic finite element mesh generation, static and aeroelastic analysis, and structural sizing. The paper discusses implementation details of the new subprocess, captures lessons learned, and suggests future improvements. The subprocess quickly compares concepts and robustly handles large changes in wing or fuselage geometry. The subprocess can rank concepts with regard to their structural feasibility and can identify promising regions of the design space. The automated structural analysis subprocess is deemed robust and rapid enough to be included in multidisciplinary conceptual design and optimization studies.

Eldred, Lloyd B.↗
DOE OSTI2026

Field and Model Data Associated with the Manuscript “Drivers of Streamflow Intermittency in Humid Regions: 1. Evaluating Above- and Below-ground Controls of Flow Persistence in a Forested Catchment”

This package contains field data, modeling files, and scripts supporting the investigation of the drivers of streamflow intermittency in a forested catchment. It includes the field data collected from electrical resistivity tomography (ERT) surveys, ground penetrating radar (GPR), continuous self-potential (SP) monitoring, electromagnetic (EM) imaging, groundwater and stilling well. In addition, it contains the data and results of the coupled water- and electrical-flow model developed using the COMSOL Multiphysics and Advanced Terrestrial Simulator (ATS), as well as software files and Jupyter notebooks used to process the data and generate figures in the manuscript submitted for peer review. The data archive is organized in the following directories: 1) Climate Includes hourly precipitation and daily evapotranspiration time series (2024 – 2025) provided as CSV files, alongside a text file detailing dataset units. 2) Coupled_model Contains two subfolders: Synthetic and Field_Application subfolder. Synthetic subfolder contains the ATS XML input script (can be opened using any code editor) for the four synthetic hydrological cases tested (Connected and gaining, Connected and losing, Disconnected and losing, and dry stream). It also includes other experimental cases to test the influence of precipitation and concentration gradient. For each synthetic case, the flow model simulation is executed using the ATS XML scripts and the included Python script (generate_data_set.py) to convert ATS output to COMSOL-ready input. COMSOL Multiphysics template (.mph can be opened with the commercial software COMSOL and requires a license) is executed using the ATS output data to simulate the potential field. It also includes the Synthetic_model_plot.ipynb (can be opened using any code editor) to visualize the SP result and generate manuscript figures. The data subfolder contains mesh files to run both the ATS (.exo and .stl files can be viewed using Paraview; .h5 files can be opened using HDFView software and h5py Python package) and COMSOL models. Field_Application subfolder contains two subfolders: ES_MDA_inversion and Final_Model. ES_MDA_inversion contains the Python script (.py can be opened using any code editor) and SP observation data used to run the Ensemble Smoother with Multiple Data Assimilation (ES-MDA) inversion sequence to get the optimal model parameters. The Final_model subfolder contains the ATS XML input scripts, data files, output data for the two SP sites. The same workflow steps outlined for the Synthetic subfolder apply here. It also contains the Jupyter notebook (Plot_final_calib.ipynb) to visualize the results of the modeled SP, stream-groundwater exchange and moisture content. 3) Discharge Includes the electrical conductivity (EC) time series (provided as CSV files) from salt slug injections. It also includes the Jupyter notebook (Discharge_process.ipynyb) used to estimate discharge. All discharge measurements collated into rating_curve_processed.csv 4) EM Contains the CSV file of the EM data from the DUALEM-42, including spatial coordinates (x, y, z), apparent conductivity, and in-phase measurements at 2 m coil separations for horizontal coplanar (HCP) and perpendicular (PRP) geometries. 5) ERT Contains raw resistivity data (provided as CSV files), spatial location of each of the electrodes (provided as CSV files), and files used for the resistivity inversion (.resipy can be opened with the open-source ResIPy software). 6) GPR Includes GPR field datasets collected at 100 MHz and 250 MHz antenna frequencies, along with the processing/interpretation project file (GPR_process.gpz can be viewed using EKKO_Project 6, a commercial software by Sensors & Software that requires a license). 7) Slug_test Includes the slug test data at all the groundwater wells provided as CSV files, as well as the Jupyter notebook (Slug_test.ipynb) for calculating hydraulic conductivity. 8) SP Contains the SP data collected in field at the two SP sites (one in the perennial reach and the other in the intermittent reach), provided as DAT files. 9) Well_data Contains two subfolders: 1) Raw, which provides unprocessed pressure, electrical conductivity and temperature timeseries downloaded from the loggers in all the groundwater and stilling wells, and 2) Processed, which contains sorted, QA/QC timeseries data for each well. The data archive also contains data_process.ipynb, a Jupyter notebook used for field data analysis and generating figures (plotting well, SP, climate, and discharge data, as well as calculating head gradient at sites with nested groundwater wells). It also includes DTW.ipynb, a Jupyter notebook containing the code for the dynamic time warping (DTW) with sliding window to evaluate SP signal synchronicity.

ATS↗
DOE OSTI2021

Modeling and experimental validation of a W f /W-fabrication by chemical vapor deposition and infiltration

Tungsten (W) has a unique combination of excellent thermal properties, low sputter yield, low hydrogen retention, and acceptable activation. Therefore, W is presently the main candidate for the first wall material in future fusion devices. However, its intrinsic brittleness and its further embrittlement during operation bears the risk of a sudden and catastrophic component failure. As a countermeasure, tungsten fiber-reinforced tungsten (W f /W) with extrinsic toughening is being developed. A possible synthesis route is chemical vapor deposition (CVD) using heated W fabrics as substrate. The challenge is that the growing CVD-W can isolate domains from precursor access leading to strength-reducing pores. To deepen the process understanding and to optimize the CVD parameters, models were developed with COMSOL Multiphysics and validated experimentally. W deposition rate equations as function of the temperature and the partial pressures of the precursors H 2 and WF 6 were experimentally validated in previous work. In the present article, these equations are applied to obtain partial pressures within the CVD reactor. The results are taken as input for transient simulations in the microscale, in which W coatings, growing onto multiple adjacent W fibers, were simulated via mesh deformation and remeshing. The surface-to-surface contact of the W coatings and the corresponding potential pore formation were simulated by implementing sophisticated deposition rate stop conditions. Within the measuring uncertainties of ≃ ±1%, the models are validated successfully by experimental comparison regarding the deposition rate, pore structure, and relative densities ranging from 0.6 to 0.9.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Radsource Mr: Mixed Reality Planning Tool For Radioactive Recovery

The RadSource MR system leverages Meta Quest 3's advanced mixed reality capabilities to create a comprehensive spatial planning platform for end-of-life sealed radioactive source recovery operations. The application utilizes the Quest 3's high-resolution passthrough cameras and spatial mapping algorithms to generate accurate 3D environmental models. Core technical components include: (1) Real-time spatial measurement algorithms calculating distances, angles, slopes, and surface areas with sub-centimeter accuracy; (2) Virtual object placement system allowing users to position digital representations of recovery equipment (trailers, containment vessels, protective barriers) within the real environment; (3) Voice recording and annotation system for hands-free documentation in protective equipment; (4) 3D mesh capture and storage capabilities for post-operation analysis and regulatory documentation. (5) Procedure documentation is available for viewing in Mixed Reality, providing an innovative and convenient way to access the information during pre-visit and inspection activities. (6) Support for screen capture for the view for real world and virtual objects together to use it later for planning. The system integrates computer vision techniques for environmental understanding, spatial mathematics for precise measurements, and human-computer interaction principles optimized for hazardous environment operations. Data persistence allows teams to save and share planning sessions across multiple stakeholders while maintaining operational security requirements.

Khadka, Rajiv [Idaho National Laboratory (INL), Id↗
NASA NTRS2004

Efficient Fluid Dynamic Design Optimization Using Cartesian Grids

This report is subdivided in three parts. The first one reviews a new approach to the computation of inviscid flows using Cartesian grid methods. The crux of the method is the curvature-corrected symmetry technique (CCST) developed by the present authors for body-fitted grids. The method introduces ghost cells near the boundaries whose values are developed from an assumed flow-field model in vicinity of the wall consisting of a vortex flow, which satisfies the normal momentum equation and the non-penetration condition. The CCST boundary condition was shown to be substantially more accurate than traditional boundary condition approaches. This improved boundary condition is adapted to a Cartesian mesh formulation, which we call the Ghost Body-Cell Method (GBCM). In this approach, all cell centers exterior to the body are computed with fluxes at the four surrounding cell edges. There is no need for special treatment corresponding to cut cells which complicate other Cartesian mesh methods.

Dadone, A.↗
DOE OSTI2024

Meshfree Process Modeling and Experimental Validation of Friction Riveting of Aluminum 5052 to Aluminum 6061

Friction riveting (Fric-riveting) is an innovative, fast, and energy-efficient process for spot-joining metal-metal structures. Although fric-riveting has been studied experimentally in recent years, its process modeling is rarely found in the literature primarily because of the associated large material deformation, extreme thermomechanical conditions, and complex contact conditions. In this work, a mesh-free smoothed particle hydrodynamics (SPH) framework that can well handle the abovementioned numerical challenges is used to simulate the fric-riveting of AA5052 to AA6061. Predicted material morphology, multi-point temperatures, and plunge force are thoroughly validated by experimental observations. The material severe plastic deformation zone in the vicinity of the riveting zone is further predicted by the SPH model, which indicates the material mixing and potential grain refinement zone. Based on the validated model, process parameters can be optimized which yields better performance over the baseline case.

Friction riveting (fric-riveting), Smoothed partic↗
DOE OSTI2018

Adaptive wavelet compression of large additive manufacturing experimental and simulation datasets

New manufacturing technologies such as additive manufacturing require research and development to minimize the uncertainties in the produced parts. The research involves experimental measurements and large simulations, which result in huge quantities of data to store and analyze. We address this challenge by alleviating the data storage requirements using lossy data compression. We select wavelet bases as the mathematical tool for compression. Unlike images, additive manufacturing data is often represented on irregular geometries and unstructured meshes. Thus, we use Alpert tree-wavelets as bases for our data compression method. We first analyze different basis functions for the wavelets and find the one that results in maximal compression and miminal error in the reconstructed data. We then devise a new adaptive thresholding method that is data-agnostic and allows a priori estimation of the reconstruction error. Finally, we propose metrics to quantify the global and local errors in the reconstructed data. One of the error metrics addresses the preservation of physical constraints in reconstructed data fields, such as divergence-free stress field in structural simulations. While our compression and decompression method is general, we apply it to both experimental and computational data obtained from measurements and thermal/structural modeling of the sintering of a hollow cylinder from metal powders using a Laser Engineered Net Shape process. The results show that monomials achieve optimal compression performance when used as wavelet bases. The new thresholding method results in compression ratios that are two to seven times larger than the ones obtained with commonly used thresholds. Overall, adaptive Alpert tree-wavelets can achieve compression ratios between one and three orders of magnitude depending on the features in the data that are required to preserve. Furthermore, these results show that Alpert tree-wavelet compression is a viable and promising technique to reduce the size of large data structures found in both experiments and simulations.

42 ENGINEERING↗
DOE OSTI2018

The nonconforming virtual element method for eigenvalue problems

We analyse the nonconforming Virtual Element Method (VEM) for the approximation of elliptic eigenvalue problems. The nonconforming VEM allow to treat in the same formulation the two- and three-dimensional case.We present two possible formulations of the discrete problem, derived respectively by the nonstabilized and stabilized approximation of the L 2 -inner product, and we study the convergence properties of the corresponding discrete eigenvalue problems. The proposed schemes provide a correct approximation of the spectrum and we prove optimal-order error estimates for the eigenfunctions and the usual double order of convergence of the eigenvalues. Finally we show a large set of numerical tests supporting the theoretical results, including a comparison with the conforming Virtual Element choice.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2012

Rayleigh Quotient Iteration in 3D, Deterministic Neutron Transport

Today's "grand challenge" neutron transport problems require 3-D meshes with billions of cells, hundreds of energy groups, and accurate quadratures and scattering expansions. Leadership-class computers provide platforms on which high-fidelity fluxes can be calculated. However, appropriate methods are needed that can use these machines effectively. Such methods must be able to use hundreds of thousands of cores and have good convergence properties. Rayleigh quotient iteration (RQI) is an eigenvalue solver that has been added to the Sn code Denovo to address convergence. Rayleigh quotient iteration is an optimal shifted inverse iteration method that should converge in fewer iterations than the more common power method and other shifted inverse iteration methods for many problems of interest. Denovo's RQI uses a new multigroup Krylov solver for the fixed source solutions inside every iteration that allows parallelization in energy in addition to space and angle. This Krylov solver has been shown to scale successfully to 200,000 cores: for example one test problem scaled from 69,120 cores to 190,080 cores with 98% efficiency. This paper shows that RQI works for some small problems. However, the Krylov method upon which it relies does not always converge because RQI creates ill-conditioned systems. This result leads to the conclusion that preconditioning is needed to allow this method to be applicable to a wider variety of problems.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2014

A higher‐order unsplit 2D direct Eulerian finite volume method for two‐material compressible flows based on the MOOD paradigms

SUMMARY A higher‐order unsplit multi‐dimensional discretization of the diffuse interface model for two‐material compressible flows proposed by R. Saurel, F. Petitpas and R. A. Berry in 2009 is developed. The proposed higher‐order method is based on the concepts of the Multidimensional Optimal Order Detection (MOOD) method introduced in three recent papers for single‐material flows. The first‐order unsplit multi‐dimensional Finite Volume discretization presented by SPB serves as foundation for the development of the higher‐order unlimited schemes. Specific detection criteria along with a novel decrementing algorithm for the MOOD method are designed in order to deal with the complexity of multi‐material flows. Numerically, we compare errors and computational times on several 1D problems (stringent shock tube and cavitation problems) computed on 2D meshes with the second‐ and fourth‐order MOOD methods using a classical MUSCL method as reference. Several simulations of a 2D shocked R22 bubble in the air are also presented on Cartesian and unstructured meshes with the second‐ and fourth‐order MOOD methods, and qualitative comparisons confirm the conclusions obtained with 1D problems. These numerical results demonstrate the robustness of the MOOD approach and the interest of using more than second‐order methods even for locally singular solutions of complex physics models. Copyright © 2014 John Wiley & Sons, Ltd.

Diot, S.↗
DOE OSTI2019

The nonconforming Virtual Element Method for eigenvalue problems

In this work, we analyse the nonconforming Virtual Element Method (VEM) for the approximation of elliptic eigenvalue problems. The nonconforming VEM allows to treat in the same formulation the two- and three-dimensional case. We present two possible formulations of the discrete problem, derived respectively by the nonstabilized and stabilized approximation of the $L^2$-inner product, and we study the convergence properties of the corresponding discrete eigenvalue problem. The proposed schemes provide a correct approximation of the spectrum, in particular we prove optimal-order error estimates for the eigenfunctions and the usual double order of convergence of the eigenvalues. Finally we show a large set of numerical tests supporting the theoretical results, including a comparison with the conforming Virtual Element choice.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

SU-D-BRF-06: A Brachytherapy Simulator with Realistic Haptic Force Feedback and Real-Time Ultrasounds Image Simulation for Training and Teaching

Purpose: Surgical procedures require dexterity, expertise and repetition to reach optimal patient outcomes. However, efficient training opportunities are usually limited. This work presents a simulator system with realistic haptic force-feedback and full, real-time ultrasounds image simulation. Methods: The simulator is composed of a custom-made Linear-DELTA force-feedback robotic platform. The needle tip is mounted on a force gauge at the end effector of the robot, which responds to needle insertion by providing reaction forces. 3D geometry of the tissue is using a tetrahedral finite element mesh (FEM) mimicking tissue properties. As the needle is inserted/retracted, tissue deformation is computed using a mass-tensor nonlinear visco-elastic FEM. The real-time deformation is fed to the L-DELTA to take into account the force imparted to the needle, providing feedback to the end-user when crossing tissue boundaries or needle bending. Real-time 2D US image is also generated synchronously showing anatomy, needle insertion and tissue deformation. The simulator is running on an Intel I7 6- core CPU at 3.26 MHz. 3D tissue rendering and ultrasound display are performed on a Windows 7 computer; the FEM computation and L-DELTA control are executed on a similar PC using the Neutrino real-time OS. Both machines communicate through an Ethernet link. Results: The system runs at 500 Hz for a 8333-tetrahedron tissue mesh and a 100-node angular spring needle model. This frame rate ensures a relatively smooth displacement of the needle when pushed or retracted (±20 N in all directions at speeds of up to 2 m/s). Unlike commercially-available haptic platforms, the oblong workspace of the L-DELTA robot complies with that required for brachytherapy needle displacements of 0.1m by 0.1m by 0.25m. Conclusion: We have demonstrated a real-life, realistic brachytherapy simulator developed for prostate implants (LDR/HDR). The platform could be adapted to other sites or training for other types of needle-based procedures.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2012

RAYLEIGH QUOTIENT ITERATION IN 3D, DETERMINISTIC NEUTRON TRANSPORT

Today’s “grand challenge” neutron transport problems require 3-D meshes with billions of cells, hundreds of energy groups, and accurate quadratures and scattering expansions. Leadership-class computers provide platforms on which high-fidelity fluxes can be calculated. However, appropriate methods are needed that can use these machines effectively. Such methods must be able to to use hundreds of thousands of cores and have good convergence properties. Rayleigh quotient iteration (RQI) is an eigenvalue solver that has been added to the SN code Denovo to address convergence. Rayleigh quotient iteration is an optimal shifted inverse iteration method that should converge in fewer iterations than the more common power method and other shifted inverse iteration methods for many problems of interest. Denovo’s RQI uses a new multigroup Krylov solver for the fixed source solutions inside every iteration that allows parallelization in energy in addition to space and angle. This Krylov solver has been shown to scale successfully to 200,000 cores: for example one test problem scaled from 69,120 cores to 190,080 cores with 98% efficiency. This paper shows that RQI works for some small problems. However, the Krylov method upon which it relies does not always converge because RQI creates ill-conditioned systems. This result leads to the conclusion that preconditioning is needed to allow this method to be applicable to a wider variety of problems.

Slaybaugh, R. N.↗
NASA NTRS1997

Aerodynamic Design Optimization on Unstructured Grids with a Continuous Adjoint Formulation

A continuous adjoint approach for obtaining sensitivity derivatives on unstructured grids is developed and analyzed. The derivation of the costate equations is presented, and a second-order accurate discretization method is described. The relationship between the continuous formulation and a discrete formulation is explored for inviscid, as well as for viscous flow. Several limitations in a strict adherence to the continuous approach are uncovered, and an approach that circumvents these difficulties is presented. The issue of grid sensitivities, which do not arise naturally in the continuous formulation, is investigated and is observed to be of importance when dealing with geometric singularities. A method is described for modifying inviscid and viscous meshes during the design cycle to accommodate changes in the surface shape. The accuracy of the sensitivity derivatives is established by comparing with finite-difference gradients and several design examples are presented.

Anderson, W. Kyle↗