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At least 919 records · Page 51

SU-E-T-500: Initial Implementation of GPU-Based Particle Swarm Optimization for 4D IMRT Planning in Lung SBRT

Purpose 4D-IMRT planning, combined with dynamic MLC tracking delivery, utilizes the temporal dimension as an additional degree of freedom to achieve improved OAR-sparing. The computational complexity for such optimization increases exponentially with increase in dimensionality. In order to accomplish this task in a clinically-feasible time frame, we present an initial implementation of GPU-based 4D-IMRT planning based on particle swarm optimization (PSO). Methods The target and normal structures were manually contoured on ten phases of a 4DCT scan of a NSCLC patient with a 54cm3 right-lower-lobe tumor (1.5cm motion). Corresponding ten 3D-IMRT plans were created in the Eclipse treatment planning system (Ver-13.6). A vendor-provided scripting interface was used to export 3D-dose matrices corresponding to each control point (10 phases × 9 beams × 166 control points = 14,940), which served as input to PSO. The optimization task was to iteratively adjust the weights of each control point and scale the corresponding dose matrices. In order to handle the large amount of data in GPU memory, dose matrices were sparsified and placed in contiguous memory blocks with the 14,940 weight-variables. PSO was implemented on CPU (dual-Xeon, 3.1GHz) and GPU (dual-K20 Tesla, 2496 cores, 3.52Tflops, each) platforms. NiftyReg, an open-source deformable image registration package, was used to calculate the summed dose. Results The 4D-PSO plan yielded PTV coverage comparable to the clinical ITV-based plan and significantly higher OAR-sparing, as follows: lung Dmean=33%; lung V20=27%; spinal cord Dmax=26%; esophagus Dmax=42%; heart Dmax=0%; heart Dmean=47%. The GPU-PSO processing time for 14940 variables and 7 PSO-particles was 41% that of CPU-PSO (199 vs. 488 minutes). Conclusion Truly 4D-IMRT planning can yield significant OAR dose-sparing while preserving PTV coverage. The corresponding optimization problem is large-scale, non-convex and computationally rigorous. Our initial results indicate that GPU-based PSO with further software optimization can make such planning clinically feasible. This work was supported through funding from the National Institutes of Health and Varian Medical Systems.

60 APPLIED LIFE SCIENCES↗

TU-AB-BRA-04: Quantitative Radiomics: Sensitivity of PET Textural Features to Image Acquisition and Reconstruction Parameters Implies the Need for Standards

Purpose: Despite increased use of heterogeneity metrics for PET imaging, standards for metrics such as textural features have yet to be developed. We evaluated the quantitative variability caused by image acquisition and reconstruction parameters on PET textural features. Methods: PET images of the NEMA IQ phantom were simulated with realistic image acquisition noise. 35 features based on intensity histograms (IH), co-occurrence matrices (COM), neighborhood-difference matrices (NDM), and zone-size matrices (ZSM) were evaluated within lesions (13, 17, 22, 28, 33 mm diameter). Variability in metrics across 50 independent images was evaluated as percent difference from mean for three phantom girths (850, 1030, 1200 mm) and two OSEM reconstructions (2 iterations, 28 subsets, 5 mm FWHM filtration vs 6 iterations, 28 subsets, 8.6 mm FWHM filtration). Also, patient sample size to detect a clinical effect of 30% with Bonferroni-corrected α=0.001 and 95% power was estimated. Results: As a class, NDM features demonstrated greatest sensitivity in means (5–50% difference for medium girth and reconstruction comparisons and 10–100% for large girth comparisons). Some IH features (standard deviation, energy, entropy) had variability below 10% for all sensitivity studies, while others (kurtosis, skewness) had variability above 30%. COM and ZSM features had complex sensitivities; correlation, energy, entropy (COM) and zone percentage, short-zone emphasis, zone-size non-uniformity (ZSM) had variability less than 5% while other metrics had differences up to 30%. Trends were similar for sample size estimation; for example, coarseness, contrast, and strength required 12, 38, and 52 patients to detect a 30% effect for the small girth case but 38, 88, and 128 patients in the large girth case. Conclusion: The sensitivity of PET textural features to image acquisition and reconstruction parameters is large and feature-dependent. Standards are needed to ensure that prospective trials which incorporate textural features are properly designed to detect clinical endpoints. Supported by NIH grants R01 CA169072, U01 CA148131, NCI Contract (SAIC-Frederick) 24XS036-004, and a research contract from GE Healthcare.

60 APPLIED LIFE SCIENCES↗

TU-F-CAMPUS-J-04: Impact of Voxel Anisotropy On Statistic Texture Features of Oncologic PET: A Simulation Study

Purpose: Texture metrics extracted from oncologic PET have been investigated with respect to their usefulness as definitive indicants for prognosis in a variety of cancer. Metric calculation is often based on cubic voxels. Most commonly used PET scanners, however, produce rectangular voxels, which may change texture metrics. The objective of this study was to examine the variability of PET texture feature metrics resulting from voxel anisotropy. Methods: Sinograms of NEMA NU-2 phantom for 18F-FDG were simulated using the ASIM simulation tool. The obtained projection data was reconstructed (3D-OSEM) on grids of cubic and rectangular voxels, producing PET images of resolution of 2.73x2.73x3.27mm3 and 3.27x3.27x3.27mm3, respectively. An interpolated dataset obtained from resampling the rectangular voxel data for isotropic voxel dimension (3.27mm) was also considered. For each image dataset, 28 texture parameters based on grey-level co-occurrence matrices (GLCOM), intensity histograms (GLIH), neighborhood difference matrices (GLNDM), and zone size matrices (GLZSM) were evaluated within lesions of diameter of 33, 28, 22, and 17mm. Results: In reference to the isotopic image data, texture features appearing on the rectangular voxel data varied with a range of -34-10% for GLCOM based, -31-39% for GLIH based, -80 -161% for GLNDM based, and −6–45% for GLZSM based while varied with a range of -35-23% for GLCOM based, -27-35% for GLIH based, -65-86% for GLNDM based, and -22 -18% for GLZSM based for the interpolated image data. For the anisotropic data, GLNDM-cplx exhibited the largest extent of variation (161%) while GLZSM-zp showed the least (<1%). As to the interpolated data, GLNDM-busy varied the most (86%) while GLIH-engy varied the least (<1%). Conclusion: Variability of texture appearance on oncologic PET with respect to voxel representation is substantial and feature-dependent. It necessitates consideration of standardized voxel representation for inter-institution studies attempting to validate prognostic values of PET texture features in cancer treatment.

60 APPLIED LIFE SCIENCES↗

SU-F-R-36: Validating Quantitative Radiomic Texture Features for Oncologic PET: A Digital Phantom Study

Purpose: Radiomic texture features derived from the oncologic PET have recently been brought under intense investigation within the context of patient stratification and treatment outcome prediction in a variety of cancer types; however, their validity has not yet been examined. This work is aimed to validate radiomic PET texture metrics through the use of realistic simulations in the ground truth setting. Methods: Simulation of FDG-PET was conducted by applying the Zubal phantom as an attenuation map to the SimSET software package that employs Monte Carlo techniques to model the physical process of emission imaging. A total of 15 irregularly-shaped lesions featuring heterogeneous activity distribution were simulated. For each simulated lesion, 28 texture features in relation to the intensity histograms (GLIH), grey-level co-occurrence matrices (GLCOM), neighborhood difference matrices (GLNDM), and zone size matrices (GLZSM) were evaluated and compared with their respective values extracted from the ground truth activity map. Results: In reference to the values from the ground truth images, texture parameters appearing on the simulated data varied with a range of 0.73–3026.2% for GLIH-based, 0.02–100.1% for GLCOM-based, 1.11–173.8% for GLNDM-based, and 0.35–66.3% for GLZSM-based. For majority of the examined texture metrics (16/28), their values on the simulated data differed significantly from those from the ground truth images (P-value ranges from <0.0001 to 0.04). Features not exhibiting significant difference comprised of GLIH-based standard deviation, GLCO-based energy and entropy, GLND-based coarseness and contrast, and GLZS-based low gray-level zone emphasis, high gray-level zone emphasis, short zone low gray-level emphasis, long zone low gray-level emphasis, long zone high gray-level emphasis, and zone size nonuniformity. Conclusion: The extent to which PET imaging disturbs texture appearance is feature-dependent and could be substantial. It is thus advised that use of PET texture parameters for predictive and prognostic measurements in oncologic setting awaits further systematic and critical evaluation.

60 APPLIED LIFE SCIENCES↗

Quantum Time-Space Tradeoffs for Matrix Problems

We consider the time and space required for quantum computers to solve a wide variety of problems involving matrices, many of which have only been analyzed classically in prior work. Our main results show that for a range of linear algebra problems—including matrix-vector product, matrix inversion, matrix multiplication and powering—existing classical time-space tradeoffs, several of which are tight for every space bound, also apply to quantum algorithms with at most a constant factor loss. For example, for almost all fixed matrices 𝐴, including the discrete Fourier transform matrix, we prove that quantum circuits with at most 𝑇 input queries and 𝑆 qubits of memory require 𝑇 = Ω⁢(𝑛 2 /𝑆) to compute matrix-vector product 𝐴⁢𝑥 for 𝑥 ∈{0,1 𝑛 . We similarly prove that matrix multiplication for 𝑛 ×𝑛 binary matrices requires 𝑇 = Ω⁢(𝑛 3 /$\sqrt{𝑆}$). Because many of our lower bounds are matched by deterministic algorithms with the same time and space complexity, our results show that quantum computers cannot provide any asymptotic advantage for these problems with any space bound. We obtain matching lower bounds for the stronger notion of quantum cumulative memory complexity—the sum of the space per layer of a circuit. We also consider Boolean (i.e., AND-OR) matrix multiplication and matrix-vector products, improving the previous quantum time-space tradeoff lower bounds for 𝑛 × 𝑛 Boolean matrix multiplication to 𝑇 = Ω⁢(𝑛 2.5 /𝑆 1/4 ) from 𝑇 = Ω⁢(𝑛 2.5 /𝑆 1/2 ). Our improved lower bound for Boolean matrix multiplication is based on a new coloring argument that extracts more from the strong direct product theorem that was the basis for prior work. To obtain our tight lower bounds for linear algebra problems, we require much stronger bounds than strong direct product theorems. We obtain these bounds by adding a new bucketing method to the quantum recording-query technique of Zhandry that lets us apply classical arguments to upper bound the success probability of quantum circuits.

lower bounds↗

Parrallel Implementation of Fast Randomized Algorithms for Low Rank Matrix Decomposition

We analyze the parallel performance of randomized interpolative decomposition by de- composing low rank complex-valued Gaussian random matrices larger than 100 GB. We chose a Cray XMT supercomputer as it provides an almost ideal PRAM model permitting quick investigation of parallel algorithms without obfuscation from hardware idiosyncrasies. We obtain that on non-square matrices performance scales almost linearly with runtime about 100 times faster on 128 processors. We also verify that numerically discovered error bounds still hold on matrices two orders of magnitude larger than those previously tested.

Lucas, Andrew J.↗

Accelerating GNNs on GPU Sparse Tensor Cores through N:M Sparsity-Oriented Graph Reordering

Recent advancements in GPU hardware support have introduced the capability to leverage N:M sparse patterns for substantial performance gains. Graphs in Graph Neural Networks (GNNs) are typically sparse, but the sparsity is often irregular, not conforming to such sparse patterns. In this paper, we propose a novel graph reordering algorithm, the first of its kind, to reshape irregular graph data into the N:M structured sparse pattern at the tile level, allowing linear-algebra-based graph operations in GNNs to benefit from the N:M sparse hardware. The optimization is lossless, maintaining the accuracy of GNN. It can remove 98-100\% violations of the N:M sparse patterns at the vector level, and increase the proportion of conforming graphs in SuiteSparse collection from 5-9\% to 88.7-93.5\%. On A100 GPUs, the optimization accelerates Sparse Matrix Matrix (SpMM) by up to 43X (2.3X -- 7.5X on average) and speeds up the key graph operations in GNNs on real graphs by as much as 8.6X (3.5X on average).

artificial intelligence, graph neural networks↗

ButterflyPACK

ButterflyPACK is a mathematical software for rapidly solving large-scale dense linear systems that exhibit off-diagonal rank-deficiency properties. These targeted systems are either matrices arising from discretized boundary integral equations, or frontal matrices in multi-frontal solvers for differential equations. ButterflyPACK relies on low-rank and butterfly formats under Hierarchical matrix, HODLR or HSS frameworks to compress, factor/precondition and solve the linear system in quasi-linear time. ButterflyPACK is particularly useful for large-scale ill-conditioned matrices arising from high-frequency wave equations involving multiple right-hand-sides. ButterflyPACK is based on Fortran 2003, it also has interface written in C++. In addition, ButterflyPACK can be readily invoked from the software STRUMPACK. ButterflyPACK supports hybrid MPI/OpenMP programming models.

Liu, Yang↗

The Attraction Indian Buffet Distribution

We propose the attraction Indian buffet distribution (AIBD), a distribution for binary feature matrices influenced by pairwise similarity information. Binary feature matrices are used in Bayesian models to uncover latent variables (i.e., features) that explain observed data. The Indian buffet process (IBP) is a popular exchangeable prior distribution for latent feature matrices. In the presence of additional information, however, the exchangeability assumption is not reasonable or desirable. The AIBD can incorporate pairwise similarity information, yet it preserves many properties of the IBP, including the distribution of the total number of features. Thus, much of the interpretation and intuition that one has for the IBP directly carries over to the AIBD. A temperature parameter controls the degree to which the similarity information affects feature-sharing between observations. Unlike other nonexchangeable distributions for feature allocations, the probability mass function of the AIBD has a tractable normalizing constant, making posterior inference on hyperparameters straight-forward using standard MCMC methods. A novel posterior sampling algorithm is proposed for the IBP and the AIBD. We demonstrate the feasibility of the AIBD as a prior distribution in feature allocation models and compare the performance of competing methods in simulations and an application.

97 MATHEMATICS AND COMPUTING↗

Sempervirens: A Fast Reconstruction Algorithm for Noisy and Incomplete Binary Matrix Representations of Trees

Applications such as reconstructing cell lineage trees (represented as phylogenetic trees) from single-cell sequencing data require reconstructing a {0,1}-matrix that has many errors and missing entries. We introduce Sempervirens, a very fast matrix reconstruction algorithm for noisy and incomplete matrix representations of phylogenetic trees. Sempervirens uses an iterative maximum-likelihood approach to determine the topology tree represented by the corrupted data. We show that Sempervirens is at least three orders of magnitude faster than other methods on thousand by thousand matrices, with the speed gap widening with larger matrices. We also show that Sempervirens matches state-of-the-art methods in reconstruction accuracy. The speed of Sempervirens enables it to be tractably applied to reconstructing much larger matrices than those that other methods can reconstruct. In addition to experimental results, we justify the algorithm with a mathematical treatment of its subprocedures.

algorithms↗

HERO WEC V1.0 - WEC-Sim Detailed Simulation Runs and Summary Data

Data sets from simulation runs include 144 wave cases that were run based on the WEC-Sim model (https://mhkdr.openei.org/submissions/483). The 144 wave cases represent waves with the following wave height and wave period ranges: - Significant Wave Height: 0.25 - 4.0m in 0.25m increments - Wave Period: 5 - 13 sec in 1 sec increments Each run was simulated using a Pierson-Moskowitz irregular wave spectrum with a 200 second ramp time and a total simulation time of 2,200 seconds. Summary data set includes a spreadsheet and image files with matrices that are associated with data from simulation runs. All matrices cover the same significant wave height and wave periods from the sim runs, in the same increments. The following matrices are included: - Mechanical Power Input: Absorbed power calculated using linear input velocity at PTO (power take-off) multiplied by winch tension. - Mechanical Power Output: The hydraulic power calculated at the pump output prior to the pressure relief valve dump. - Feed Pressure: Average pressure at RO (reverse osmosis) input prior to pre-filters - RO Power Input: The hydraulic power calculated at the RO system inlet, accounts for flow loss due to pressure relief valve - Water Production: Average clean water flow at RO output

16 TIDAL AND WAVE POWER↗

HERO WEC V1.0 2024 - WEC-Sim Detailed Simulation Runs and Summary Data

This dataset includes results from simulations of NREL's hydraulic and electric reverse osmosis wave energy converter (HEREO WEC). Simulation runs include 135 wave cases that were based on the updated WEC-Sim model, which is linked below. The data represented in this repository is based on an updated WEC-Sim model using laboratory data to tune and refine the original WEC-Sim model for the V1.0 HERO WEC. The 135 wave cases represent waves with the following wave height and wave period ranges: - Significant Wave Height: 0.25 - 3.75m in 0.25m increments - Wave Period: 5 - 13 sec in 1 sec increments Each run was simulated using a Pierson-Moskowitz irregular wave spectrum with a 100 second ramp time, a total simulation time of 3,100 seconds, and a simulation time-step of 0.005s. A reference table has been included to map each multi condition run (MCR) case with each wave condition. Summary data set includes a spreadsheet and image files with matrices that are associated with data from simulation runs. All matrices cover the same significant wave height and wave periods from the simulation runs, in the same increments. The following matrices are included: - Power Abs: The average absorbed power from the WEC (calculated from anchor reaction force and heave velocity) - Power Hyd: The average hydraulic power output at pump (calculated from pump output flow and pressure) - Power - Hyd ROi: The average hydraulic power measured at the RO system inlet (calculated from RO system pressure and flow (pre-accumulator)) - Flow - Pump out: The average flowrate measured at the pump outlet - Flow - Perm: The average permeate (clean water) production - Flow - RO (pre): The average flowrate measured at the inlet of the RO system before the accumulators - Flow - RO (post): The average flowrate measured after the accumulator bank in the RO system - Pressure - RO: The average pressure measured at the inlet of the RO system This data set has been developed by the National Renewable Energy Laboratory, operated by the Alliance for Sustainable Energy, LLC, for the U.S. Department of Energy (DOE) under Contract No. DE-AC36-08GO28308. Funding provided by the U.S. Department of Energy Office of Energy Efficiency and Renewable Energy Water Power Technologies Office.

16 TIDAL AND WAVE POWER↗

Experimental Study of Microgel Conformance-Control Treatment for a Polymer-Flooding Reservoir Containing Superpermeable Channels

Summary Polymer flooding has been widely used to improve oil recovery. However, its effectiveness would be diminished when channels (e.g., fractures, fracture-like channels, void-space conduits) are present in a reservoir. In this study, we designed a series of particular sandwich-like channel models and tested the effectiveness and applicable conditions of micrometer-sized preformed particle gels (PPGs, or microgels) in improving the polymer-flooding efficiency. We studied the selective penetration and placement of the microgel particles, and their abilities for fluid diversion and oil-recovery improvement. The results suggest that polymer flooding alone would be inefficient to achieve a satisfactory oil recovery as the heterogeneity of the reservoir becomes more serious (e.g., permeability contrast kc/km > 50). The polymer solution would vainly flow through the channels and leave the majority of oil in the matrices behind. Additional conformance-treatment efforts are required. We tried to inject microgels in an attempt to shut off the channels. After the microgel treatment, impressive improvement of the polymer-flooding performance was observed in some of our experiments. The water cut could be reduced significantly by as high as nearly 40%, and the sweep efficiency and overall oil recovery of the polymer flood were improved. The conditions under which the microgel-treatment strategy was effective were further explored. We observed that the microgels form an external impermeable cake at the very beginning of microgel injection and prevent the gel particles from entering the matrices. Instead, the microgel particles could selectively penetrate and shut off the superpermeable channels under proper conditions. Our results suggest that the 260-µm microgel particles tested in this study are effective to attack the excessive-water-production problem and improve the oil recovery when the channel has a high permeability (>50 darcies). The gels are unlikely to be effective for channels that are less than 30 darcies because of the penetration/transport difficulties. After the gels effectively penetrate and shut off the superpermeable channel, the subsequent polymer solution is diverted to the matrices (i.e., the unswept oil zones) to displace the bypassed oil. Overall, this study provides important insights to help achieve successful polymer-flooding applications in reservoirs with superpermeable channels.

Engineering↗

Applying Quantum Tomography to Hadronic Interactions

A proper description of inclusive reactions is expressed with density matrices. Quantum tomography reconstructs density matrices from experimental observables. We review recent work that applies quantum tomography to practical experimental data analysis. Almost all field-theoretic formalism and modeling used in a traditional approach is circumvented with great efficiency. Tomographically-determined density matrices can express information about quantum systems which cannot in principle be expressed with distributions defined by classical probability. Topics such as entanglement and von Neumann entropy can be accessed using the same natural language where they are defined. A deep relation exists between separability, as defined in quantum information science, and factorization, as defined in high energy physics. Factorization acquires a non-perturbative definition when expressed in terms of a conditional form of separability. An example illustrates how to go from data for momentum 4-vectors to a density matrix while bypassing almost all the formalism of the Standard Model.

Martens, J. C.↗

Partitioning of Nanoparticles into Organic Phases and Model Cells

There is a recognized need to understand and predict the fate, transport and bioavailability of engineered nanoparticles (ENPs) in aquatic and soil ecosystems. Recent research focuses on either collection of empirical data (e.g., removal of a specific NP through water or soil matrices under variable experimental conditions) or precise NP characterization (e.g. size, degree of aggregation, morphology, zeta potential, purity, surface chemistry, and stability). However, it is almost impossible to transition from these precise measurements to models suitable to assess the NP behavior in the environment with complex and heterogeneous matrices. For decades, the USEPA has developed and applies basic partitioning parameters (e.g., octanol-water partition coefficients) and models (e.g., EPI Suite, ECOSAR) to predict the environmental fate, bioavailability, and toxicity of organic pollutants (e.g., pesticides, hydrocarbons, etc.). In this project we have investigated the hypothesis that NP partition coefficients between water and organic phases (octanol or lipid bilayer) is highly dependent on their physiochemical properties, aggregation, and presence of natural constituents in aquatic environments (salts, natural organic matter), which may impact their partitioning into biological matrices (bioaccumulation) and human exposure (bioavailability) as well as the eventual usage in modeling the fate and bioavailability of ENPs. In this report, we use the terminology "partitioning" to operationally define the fraction of ENPs distributed among different phases. The mechanisms leading to this partitioning probably involve both chemical force interactions (hydrophobic association, hydrogen bonding, ligand exchange, etc.) and physical forces that bring the ENPs in close contact with the phase interfaces (diffusion, electrostatic interactions, mixing turbulence, etc.). Our work focuses on partitioning, but also provides insight into the relative behavior of ENPs as either "more like dissolved substances" or "more like colloids" as the division between behaviors of macromolecules versus colloids remains ill-defined. Below we detail our work on two broadly defined objectives: (i) Partitioning of ENP into octanol, lipid bilayer, and water, and (ii) disruption of lipid bilayers by ENPs. We have found that the partitioning of NP reaches pseudo-equilibrium distributions between water and organic phases. The equilibrium partitioning most strongly depends on the particle surface charge, which leads us to the conclusion that electrostatic interactions are critical to understanding the fate of NP in the environment. We also show that the kinetic rate at which particle partition is a function of their size (small particles partition faster by number) as can be predicted from simple DLVO models. We have found that particle number density is the most effective dosimetry to present our results and provide quantitative comparison across experiments and experimental platforms. Cumulatively, our work shows that lipid bilayers are a more effective organic phase than octanol because of the definable surface area and ease of interpretation of the results. Our early comparison of NP partitioning between water and lipids suggest that this measurement can be predictive of bioaccumulation in aquatic organisms. We have shown that nanoparticle disrupt lipid bilayer membranes and detail how NP-bilayer interaction leads to the malfunction of lipid bilayers in regulating the fluxes of ionic charges and molecules. Our results show that the disruption of the lipid membranes is similar to that of toxin melittin, except single particles can disrupt a bilayer. We show that only a single particle is required to disrupt a 150 nm DOPC liposome. The equilibrium leakage of membranes is a function of the particle number density and particle surface charge, consistent with results from our partitioning experiments. Our disruption experiments with varying surface functionality show that positively charged particles (poly amine) are most disruptive, consistent with in in vitro toxicity panels using cell cultures. Overall, this project has resulted in 8 published or submitted archival papers and has been presented 12 times. We have trained five students and provided growth opportunities for a postdoc.

54 ENVIRONMENTAL SCIENCES↗

ANL Critical Assembly Covariance Matrix Generation - Addendum

In March 2012, a report was issued on covariance matrices for Argonne National Laboratory (ANL) critical experiments. That report detailed the theory behind the calculation of covariance matrices and the methodology used to determine the matrices for a set of 33 ANL experimental set-ups. Since that time, three new experiments have been evaluated and approved. This report essentially updates the previous report by adding in these new experiments to the preceding covariance matrix structure.

97 MATHEMATICS AND COMPUTING↗

Target Formulation and Construction in Mesh Quality Improvement

In the Target-matrix Optimization Paradigm (TMOP), it’s long been understood that one must create a set of target matrices before the mesh can be optimized. But there is still no general method to create correct, effective targets in response to a specific mesh quality improvement goal. The TMOP literature describes how certain sets of target matrices can be used to control the shape or size of mesh elements, but those examples address only a fraction of the problems that can occur in mesh quality improvement and were not derived from a general framework for target matrix construction. In this work, a general method of target construction is introduced based on an independent set of geometric parameters which are intrinsic to the Jacobian matrices upon which TMOP is based. The parameters enable a systematic approach to target definition and construction. The approach entails two parts. The first part defines correspondences between available raw data (stuff about the mesh and/or the physical solution) and intermediate data (e.g., a field of error estimates). Once the correspondences are established, the raw data is processed into intermediate field data existing on mesh sample points. The second part is to create a model that represents the values of the geometric target parameters as functions of the intermediate data. The model is then tested numerically to establish model constants and effectiveness. This systematic approach to target construction is illustrated in a set of examples to show how it can be applied to common problems in mesh optimization such as equidistribution of geometric properties, preservation of existing good quality, and adaptation of the mesh to the solution. The result is a systematic method of target construction for TMOP which can be applied to a wide variety of planar and volume mesh quality improvement tasks.

97 MATHEMATICS AND COMPUTING↗

LAW Simulant Recipes for Evaluation of Real-Time, In-Line Monitoring Instruments

Statistically designed recipes were generated for evaluation of in-line instrumentation for the Real-Time In-Line Monitoring (RTIM) program in support of the Hanford Direct-Feed Low Activity Waste (DFLAW) program. The composition matrices were prepared based on Low Activity Waste (LAW) feed vector, melter feed, and Effluent Management Facility (EMF) feed information provided by the flowsheet integration modelling for the DFLAW portion of the Waste Treatment Plant (WTP) mission. These composition matrices were converted to recipes for the LAW feed using the approaches for LAW simulant recipes developed by Savannah River National Laboratory (SRNL). Recipes for the glass forming chemicals (GFCs) were developed based on expected mineral forms to be used to for each element to be added to the recipe. The recipe matrices are shown in the Appendix.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗