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At least 1,513 records · Page 84
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Combining DPG in space with DPG time-marching scheme for the transient advection–reaction equation

In this article, we present a general methodology to combine the Discontinuous Petrov–Galerkin (DPG) method in space and time in the context of methods of lines for transient advection–reaction problems. We first introduce a semidiscretization in space with a DPG method redefining the ideas of optimal testing and practicality of the method in this context. Then, we apply the recently developed DPG-based time-marching scheme, which is of exponential-type, to the resulting system of Ordinary Differential Equations (ODEs). Further, we also discuss how to efficiently compute the action of the exponential of the matrix coming from the space semidiscretization without assembling the full matrix. Finally, we verify the proposed method for 1D+time advection–reaction problems showing optimal convergence rates for smooth solutions and more stable results for linear conservation laws comparing to the classical exponential integrators.

42 ENGINEERING↗
DOE OSTI2023

High-Order Mesh Morphing for Boundary and Interface Fitting to Implicit Geometries

Here, we propose a method that morphs high-order meshes such that their boundaries and interfaces coincide/align with implicitly defined geometries. Our focus is particularly on the case when the target surface is prescribed as the zero isocontour of a smooth discrete function. Common examples of this scenario include using level set functions to represent material interfaces in multimaterial configurations, and evolving geometries in shape and topology optimization. The proposed method formulates the mesh optimization problem as a variational minimization of the sum of a chosen mesh-quality metric using the Target-Matrix Optimization Paradigm (TMOP) and a penalty term that weakly forces the selected faces of the mesh to align with the target surface. The distinct features of the method are use of a source mesh to represent the level set function with sufficient accuracy, and adaptive strategies for setting the penalization weight and selecting the faces of the mesh to be fit to the target isocontour of the level set field. We demonstrate that the proposed method is robust for generating boundary- and interface-fitted meshes for curvilinear domains using different element types in 2D and 3D.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Design Space Exploration for Novel Reduced-Vortex Turbine Rotors Using Free Vortex Wake Methods

In this work, we explore the use of mid-fidelity free vortex wake (FVW) tools, namely NREL's cOnvecting LAgrangian Filaments (OLAF) tool, to design and analyze wind turbine rotor blades. The goal of the exercise is to determine whether designs exist that out-perform traditional blade designs, which are optimized using the Blade-Element Momentum (BEM) method. We find that using design of experiments to generate simple modifications of the blade tip, OLAF predicts higher performance in terms of power coefficient for redesigned blades that are non-optimal according to BEM. We then use optimization methods with OLAF in the loop to attempt to automatically find OLAF-optimal designs. We analyze the results of these optimizations, demonstrating that some roadblocks exist before OLAF and FVW tools can be used to automatically find FVW-optimal blade designs that might exceed the performance of BEM-optimal blade designs.

blade design↗
DOE OSTI2015

Principles of Bayesian Ensemble Creation: Theoretical and Empirical Observations

Bayesian methods are theoretically optimal given their underlying assumptions. Bayesian model averaging (BMA) is generally considered the standard model for creating ensembles of learners using Bayesian methods, but this technique is often out-performed by more ad hoc methods in empirical studies. It has been proposed that Bayesian model averaging struggles in practice because it accounts for uncertainty about which model is the data-generating model but still operates under the assumption that only one of them is. Thus, BMA is unable to enrich the hypothesis space as effectively as other ensemble creation methods, serving as a form of optimal model selection, not optimal model combination. This work provides empirical verification for this hypothesis using both synthetic and real-world data. We propose several different approaches for Bayesian model combination, and demonstrate that they overcome this problem with BMA. We empirically show that even the most simplistic of Bayesian model combination strategies can compete with the traditional ad hoc techniques of bagging, boosting and stacking, as well as significantly outperforming BMA over a wide variety of cases. We also explore the implications of this observation as it relates to the effectiveness of ensemble learning.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Combining DPG in space with DPG time-marching scheme for the transient advection-reaction equation

In this article, we present a general methodology to combine the Discontinuous PetrovGalerkin (DPG) method in space and time in the context of methods of lines for transient advection-reaction problems. We first introduce a semidiscretization in space with a DPG method redefining the ideas of optimal testing and practicality of the method in this context. Then, we apply the recently developed DPG-based time-marching scheme, which is of exponential-type, to the resulting system of Ordinary Differential Equations (ODEs). We also discuss how to efficiently compute the action of the exponential of the matrix coming from the space semidiscretization without assembling the full matrix. Finally, we verify the proposed method for 1D+time advection-reaction problems showing optimal convergence rates for smooth solutions and more stable results for linear conservation laws comparing to the classical exponential integrators.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Minimum feature size control in level set topology optimization via density fields

A level set topology optimization approach that uses an auxiliary density field to nucleate holes during the optimization process and achieves minimum feature size control in optimized designs is explored. The level set field determines the solid-void interface and the density field describes the distribution of a fictitious porous material using the solid isotropic material with penalization. These fields are governed by two sets of independent optimization variables which are initially coupled using a penalty for hole nucleation. The strength of the density field penalization and projection is gradually increased during the optimization process to promote a 0-1 density distribution. In addition, a second penalty regulates the evolution of the density field in the void phase. The treatment of the density field combined with the second penalty mitigate the appearance of small design features. The minimum feature size of optimized designs is controlled by the radius of the linear filter applied to the density optimization variables. The structural response is predicted by the extended finite element method, the sensitivities by the adjoint method, and the optimization variables are updated by a gradient-based optimization algorithm. Numerical examples investigate the robustness of this approach with respect to algorithmic parameters and mesh refinement. The results show the applicability of the combined density level set topology optimization approach for both optimal hole nucleation and for minimum feature size control in 2D and 3D. This comes, however, at the cost of a more complex problem formulation and additional computational cost due to an increased number of optimization variables.

42 ENGINEERING↗
DOE OSTI2021

Impact of graph structures for QAOA on MaxCut

The quantum approximate optimization algorithm (QAOA) is a promising method of solving combinatorial optimization problems using quantum computing. QAOA on the MaxCut problem has been studied extensively on graphs with specific structure; however, little is known about the general performance of the algorithm on arbitrary graphs. Here, we investigate how different graph characteristics correlate with QAOA performance at depths at most three on the MaxCut problem for all connected non-isomorphic graphs with at most eight vertices. Some good predictors of QAOA success relate to graph symmetries, odd cycles, and density. For example, on eight vertex graphs, the average probability for selecting an optimal solution for graphs that contain no odd cycles after three iterations of QAOA is 60.6% compared to 48.2% for those that do. The data generated from these studies are shared in a publicly accessible database to serve as a benchmark for QAOA calculations and experiments. Knowing the relationship between structure and performance can be used to identify classes of combinatorial problems that are likely to exhibit a quantum advantage.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Optimal field-splitting algorithm in intensity-modulated radiotherapy: Evaluations using head-and-neck and female pelvic IMRT cases

To develop an optimal field-splitting algorithm of minimal complexity and verify the algorithm using head-and-neck (H and N) and female pelvic intensity-modulated radiotherapy (IMRT) cases. An optimal field-splitting algorithm was developed in which a large intensity map (IM) was split into multiple sub-IMs (≥2). The algorithm reduced the total complexity by minimizing the monitor units (MU) delivered and segment number of each sub-IM. The algorithm was verified through comparison studies with the algorithm as used in a commercial treatment planning system. Seven IMRT, H and N, and female pelvic cancer cases (54 IMs) were analyzed by MU, segment numbers, and dose distributions. The optimal field-splitting algorithm was found to reduce both total MU and the total number of segments. We found on average a 7.9 ± 11.8% and 9.6 ± 18.2% reduction in MU and segment numbers for H and N IMRT cases with an 11.9 ± 17.4% and 11.1 ± 13.7% reduction for female pelvic cases. The overall percent (absolute) reduction in the numbers of MU and segments were found to be on average −9.7 ± 14.6% (−15 ± 25 MU) and −10.3 ± 16.3% (−3 ± 5), respectively. In addition, all dose distributions from the optimal field-splitting method showed improved dose distributions. The optimal field-splitting algorithm shows considerable improvements in both total MU and total segment number. The algorithm is expected to be beneficial for the radiotherapy treatment of large-field IMRT.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2016

Expanding Lorentz and spectrum corrections to large volumes of reciprocal space for single-crystal time-of-flight neutron diffraction

Evidence is mounting that potentially exploitable properties of technologically and chemically interesting crystalline materials are often attributable to local structure effects, which can be observed as modulated diffuse scattering (mDS) next to Bragg diffraction (BD). BD forms a regular sparse grid of intense discrete points in reciprocal space. Traditionally, the intensity of each Bragg peak is extracted by integration of each individual reflection first, followed by application of the required corrections. In contrast, mDS is weak and covers expansive volumes of reciprocal space close to, or between, Bragg reflections. For a representative measurement of the diffuse scattering, multiple sample orientations are generally required, where many points in reciprocal space are measured multiple times and the resulting data are combined. The common post-integration data reduction method is not optimal with regard to counting statistics. A general and inclusive data processing method is needed. In this contribution, a comprehensive data analysis approach is introduced to correct and merge the full volume of scattering data in a single step, while correctly accounting for the statistical weight of the individual measurements. Development of this new approach required the exploration of a data treatment and correction protocol that includes the entire collected reciprocal space volume, using neutron time-of-flight or wavelength-resolved data collected at TOPAZ at the Spallation Neutron Source at Oak Ridge National Laboratory.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2015

Deterministic absorbed dose estimation in computed tomography using a discrete ordinates method

Purpose: Organ dose estimation for a patient undergoing computed tomography (CT) scanning is very important. Although Monte Carlo methods are considered gold-standard in patient dose estimation, the computation time required is formidable for routine clinical calculations. Here, the authors instigate a deterministic method for estimating an absorbed dose more efficiently. Methods: Compared with current Monte Carlo methods, a more efficient approach to estimating the absorbed dose is to solve the linear Boltzmann equation numerically. In this study, an axial CT scan was modeled with a software package, Denovo, which solved the linear Boltzmann equation using the discrete ordinates method. The CT scanning configuration included 16 x-ray source positions, beam collimators, flat filters, and bowtie filters. The phantom was the standard 32 cm CT dose index (CTDI) phantom. Four different Denovo simulations were performed with different simulation parameters, including the number of quadrature sets and the order of Legendre polynomial expansions. A Monte Carlo simulation was also performed for benchmarking the Denovo simulations. A quantitative comparison was made of the simulation results obtained by the Denovo and the Monte Carlo methods. Results: The difference in the simulation results of the discrete ordinates method and those of the Monte Carlo methods was found to be small, with a root-mean-square difference of around 2.4%. It was found that the discrete ordinates method, with a higher order of Legendre polynomial expansions, underestimated the absorbed dose near the center of the phantom (i.e., low dose region). Simulations of the quadrature set 8 and the first order of the Legendre polynomial expansions proved to be the most efficient computation method in the authors’ study. The single-thread computation time of the deterministic simulation of the quadrature set 8 and the first order of the Legendre polynomial expansions was 21 min on a personal computer. Conclusions: The simulation results showed that the deterministic method can be effectively used to estimate the absorbed dose in a CTDI phantom. The accuracy of the discrete ordinates method was close to that of a Monte Carlo simulation, and the primary benefit of the discrete ordinates method lies in its rapid computation speed. It is expected that further optimization of this method in routine clinical CT dose estimation will improve its accuracy and speed.

07 ISOTOPE AND RADIATION SOURCES↗