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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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The purpose of this grant was to support research on acceleration methods for fixed-point iterations, with applications to computational frameworks and simulation problems that are of interest to DOE.
The standard LU factorization-based solution process for linear systems can be enhanced in speed or accuracy by employing mixed-precision iterative refinement. Most recent work has focused on dense systems. We investigate the potential of mixed-precision iterative refinement to enhance methods for sparse systems based on approximate sparse factorizations. In doing so, we first develop a new error analysis for LU- and GMRES-based iterative refinement under a general model of LU factorization that accounts for the approximation methods typically used by modern sparse solvers, such as low-rank approximations or relaxed pivoting strategies. We then provide a detailed performance analysis of both the execution time and memory consumption of different algorithms, based on a selected set of iterative refinement variants and approximate sparse factorizations. Our performance study uses the multifrontal solver MUMPS, which can exploit block low-rank factorization and static pivoting. We evaluate the performance of the algorithms on large, sparse problems coming from a variety of real-life and industrial applications showing that mixed-precision iterative refinement combined with approximate sparse factorization can lead to considerable reductions of both the time and memory consumption.
Newton's method for nonlinear mechanics problems replaces the governing nonlinear equations by an iterative sequence of linear equations. When the linear equations are linear differential equations, the equations are usually solved by numerical methods. The iterative sequence in Newton's method can exhibit poor convergence properties when the nonlinear problem has multiple solutions for a fixed set of parameters, unless the iterative sequences are aimed at solving for each solution separately. The theory of the linear differential operators is often a better guide for solution strategies in applying Newton's method than the theory of linear algebra associated with the numerical analogs of the differential operators. In fact, the theory for the differential operators can suggest the choice of numerical linear operators. In this paper the method of variation of parameters from the theory of linear ordinary differential equations is examined in detail in the context of Newton's method to demonstrate how it might be used as a guide for numerical solutions.
A new experimental method is proposed for reconstructing supermode profiles of a multicore fibre (MCF), small corrections to the propagation constants of its cores and coupling coefficients between the cores without phase-sensitive measurements. The method is based on intensity measurements in the cores at the output of several MCF segments differing in length, using several configurations of controlled light launch into the cores at the fibre input (in the simplest case, by sequentially exciting each core), followed by numerical treatment using an iterative algorithm. The use of the method is demonstrated experimentally for a seven-core fibre. Using numerical simulation, we assess the stability of the method and the effect of the number of measurements on the accuracy of fibre parameter reconstruction. (paper)
In this paper, preconditioned conjugate gradient (PCG) method with Strang’s circulant preconditioner is investigated to solve the Hermitian positive definite linear systems, which is result from the Crank–Nicolson (C-N) finite difference scheme with the weighted and shifted Grünwald difference (WSGD) operators to discretize the Riesz space fractional advection–dispersion equation (RSFADE). We show that the spectrum of the preconditioned matrix is clustered around 1, and the singular values of the preconditioned matrix are uniformly bounded away from zero under a certain condition, respectively; hence the PCG method, when applied to solving the preconditioned system, converges superlinearly. Moreover, the complexity in each iteration of the PCG method is O(Nlog N) via using the fast Fourier transforms, where N is the matrix size. Numerical experiments are included to demonstrate the effectiveness of our approach.
Purpose: 4D CBCT can allow evaluation of tumor motion immediately prior to radiation therapy, but suffers from heavy artifacts that limit its ability to track tumors. Various iterative and compressed sensing reconstructions have been proposed to reduce these artifacts, but are costly time-wise and can degrade the image quality of bony anatomy for alignment with regularization. We have previously proposed an iterative volume of interest (I4D VOI) method which minimizes reconstruction time and maintains image quality of bony anatomy by focusing a 4D reconstruction within a VOI. The purpose of this study is to test the tumor tracking accuracy of this method compared to existing methods. Methods: Long scan (8–10 mins) CBCT data with corresponding RPM data was collected for 12 lung cancer patients. The full data set was sorted into 8 phases and reconstructed using FDK cone beam reconstruction to serve as a gold standard. The data was reduced in way that maintains a normal breathing pattern and used to reconstruct 4D images using FDK, low and high regularization TV minimization (λ=2,10), and the proposed I4D VOI method with PTVs used for the VOI. Tumor trajectories were found using rigid registration within the VOI for each reconstruction and compared to the gold standard. Results: The root mean square error (RMSE) values were 2.70mm for FDK, 2.50mm for low regularization TV, 1.48mm for high regularization TV, and 2.34mm for I4D VOI. Streak artifacts in I4D VOI were reduced compared to FDK and images were less blurred than TV reconstructed images. Conclusion: I4D VOI performed at least as well as existing methods in tumor tracking, with the exception of high regularization TV minimization. These results along with the reconstruction time and outside VOI image quality advantages suggest I4D VOI to be an improvement over existing methods. Funding support provided by CPRIT grant RP110562-P2-01.
This paper presents a preconditioner for non-overlapping Schwarz methods applied to the Helmholtz problem. Starting from a simple analytic example, we show how such a preconditioner can be designed by approximating the inverse of the iteration operator for a layered partitioning of the domain. The preconditioner works by propagating information globally by concurrently sweeping in both directions over the subdomains, and can be interpreted as a coarse grid for the domain decomposition method. The resulting algorithm is shown to converge very fast, independently of the number of subdomains and frequency. The preconditioner has the advantage that, like the original Schwarz algorithm, it can be implemented as a matrix-free routine, with no additional preprocessing.
Purpose : A method is presented for generating simulated low-dose cone-beam CT (CBCT) preview images from which patient- and task-specific minimum-dose protocols can be confidently selected prospectively in clinical scenarios involving repeat scans. Methods : In clinical scenarios involving a series of CBCT images, the low-dose preview (LDP) method operates upon the first scan to create a projection dataset that accurately simulates the effects of dose reduction in subsequent scans by injecting noise of proper magnitude and correlation, including both quantum and electronic readout noise as important components of image noise in flat-panel detector CBCT. Experiments were conducted to validate the LDP method in both a head phantom and a cadaveric torso by performing CBCT acquisitions spanning a wide dose range (head: 0.8–13.2 mGy, body: 0.8–12.4 mGy) with a prototype mobile C-arm system. After injecting correlated noise to simulate dose reduction, the projections were reconstructed using both conventional filtered backprojection (FBP) and an iterative, model-based image reconstruction method (MBIR). The LDP images were then compared to real CBCT images in terms of noise magnitude, noise-power spectrum (NPS), spatial resolution, contrast, and artifacts. Results : For both FBP and MBIR, the LDP images exhibited accurate levels of spatial resolution and contrast that were unaffected by the correlated noise injection, as expected. Furthermore, the LDP image noise magnitude and NPS were in strong agreement with real CBCT images acquired at the corresponding, reduced dose level across the entire dose range considered. The noise magnitude agreed within 7% for both the head phantom and cadaveric torso, and the NPS showed a similar level of agreement up to the Nyquist frequency. Therefore, the LDP images were highly representative of real image quality across a broad range of dose and reconstruction methods. On the other hand, naïve injection ofuncorrelated noise resulted in strong underestimation of the true noise, which would lead to overly optimistic predictions of dose reduction. Conclusions : Correlated noise injection is essential to accurate simulation of CBCT image quality at reduced dose. With the proposed LDP method, the user can prospectively select patient-specific, minimum-dose protocols (viz., acquisition technique and reconstruction method) suitable to a particular imaging task and to the user's own observer preferences for CBCT scans following the first acquisition. The method could provide dose reduction in common clinical scenarios involving multiple CBCT scans, such as image-guided surgery and radiotherapy.
A recent application of machine learning has been to spatially-resolved angle-resolved photoemission spectroscopy (ARPES). Here we advance the state-of-the-art by applying representational learning to transform ARPES data into an embedding space of a pre-trained self-supervised learning model, thus enhancing the pipeline that improves the bandstructure classification and domain assignment/segmentation performance compared to a k-means clustering method. In the current iteration, the real-space information is entered into the domain assignment through the graph convolution method, which improves the transfer learning performance of the original self-supervised model. Lastly, an unsupervised automated tool is developed that incorporates these techniques to enable automatic domain assignment.
Bellman's dynamic programming equation for the optimal index and control law for stochastic control problems is a parabolic or elliptic partial differential equation frequently defined in an unbounded domain. Existing methods of solution require bounded domain approximations, the application of singular perturbation techniques or Monte Carlo simulation procedures. In this paper, using the fact that Poisson impulse noise tends to a Gaussian process under certain limiting conditions, a method which achieves an arbitrarily good approximate solution to the stochastic control problem is given. The method uses the two iterative techniques of successive approximation and quasi-linearization and is inherently more efficient than existing methods of solution.
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In current neutron transport calculations, particularly on continuous-energy Monte-Carlo codes, the major source of uncertainty is coming from nuclear data. In order to improve nuclear data evaluations, integral experiments are used. Feedback is then precisely obtained by re-estimating cross-section levels and correlations according to their sensitivity. k{sub eff}-sensitivity coefficients are traditionally obtained using deterministic codes since hands-on methods were not yet implemented in continuous energy Monte Carlo codes. In this paper, an Iterated-Fission-Probability-based method newly developed in the continuous energy Monte Carlo code TRIPOLI-4 will be used to calculate sensitivity coefficient breakdown on isotopes and reactions and results will be compared to those of ERANOS deterministic code. Objective is twofold: to show the reliability of the new TRIPOLI-4 method and to identify where and why profiles are slightly different. Sensitivity profiles, forward and adjoint fluxes are thus meticulously compared using a fine 1968-group energy structure. An OECD international benchmark (Uncertainty Analysis for Criticality Safety Assessment - UACSA - Phase III) is taken as working example to enforce validation and to compare to independent results (e.g. MCNP-6). This benchmark is constituted of two bare spheres filled with homogeneous mixture of uranium and polyethylene (respectively 2% and 50% U-235 enrichments) and gives an overview of issues encountered in thermal reactor cores. Several energy-group structures (1968G, 172G, 33G) are also tested in ERANOS to identify multi-group and implicit effects. Lessons learnt are that continuous Monte Carlo methods seem to be mature and compare well with deterministic codes. Only damper the U-238 elastic - and on certain conditions the U-238 capture - sensitivity coefficient for which difference can reach 30% between TRIPOLI-4 and ERANOS. Indeed concerning U-238, implicit effects are emphasized and multi-group theory remains limited by hypothesis; even a 1968-group structure is not refined enough to properly calculate U-238 elastic scattering k{sub eff}-sensitivity. This reference 3D continuous-energy sensitivity capability in TRIPOLI4-IFP will be extensively used in the uncertainty automated tool RIB of the French Criticality-Safety package CRISTAL. (authors)
A numerical method for the solution of one-dimension drift-flux model has been developed. Correlations for heat and mass transfer and kinematic constitutive equation were used to close the set of the partial differential equations. The finite volume method based on the staggered grid and fully implicit backward Euler method were applied to discretize the spatial and time differential items, respectively. The discretization equations were solved iteratively in a same manner as in SIMPLE method for a single-phase flow. The verification and validation of the numerical method and closure model for one-dimension drift-flux model have been performed by comparing the code solution with the experimental data. Furthermore, the axial distribution of void fraction and pressure also have been investigated under different heated case. (authors)
A numerical method is described which uses a rectangular grid to solve the nonlinear full potential equation about complex configurations. The grid is locally refined to resolve high velocity gradients arising from leading edge expansions or shock waves. The grid penetrates the boundary (described by networks of quadrilateral panels) and is generated automatically. Discrete operators are constructed using the finite element method. The system of nonlinear discrete equations is solved iteratively using a Krylov subspace method preconditioned by an exterior Poisson solver and a direct sparse solver. The primary emphasis is to provide design engineers with an aerodynamic analysis tool (the TRANAIR code) which is accurate, reliable, economical, and flexible to use. Computational results for many interesting configurations are presented.
In the present investigation, the basic approach is employed to view an iterative scheme as Newton's method or as a modified Newton's method. Attention is given to various modified Newton methods which can arise from differencing schemes for the Euler equations. Flux vector splitting is considered as the basic spatial differencing technique. This technique is based on the partition of a flux vector into groups which have certain properties. The Euler equations fluxes can be split into two groups, the first group having a flux Jacobian with all positive eigenvalues, and the second group having a flux Jacobian with all negative eigenvalues. Flux vector splitting based on a velocity-sound speed split is considered along with the use of numerical techniques to analyze nonlinear systems, and the steady Euler equations for quasi-one-dimensional flow in a nozzle. Results are given for steady flows with shocks.
A reverse Monte Carlo (RMC) method is developed to obtain the energy loss function (ELF) and optical constants from a measured reflection electron energy-loss spectroscopy (REELS) spectrum by an iterative Monte Carlo (MC) simulation procedure. The method combines the simulated annealing method, i.e., a Markov chain Monte Carlo (MCMC) sampling of oscillator parameters, surface and bulk excitation weighting factors, and band gap energy, with a conventional MC simulation of electron interaction with solids, which acts as a single step of MCMC sampling in this RMC method. To examine the reliability of this method, we have verified that the output data of the dielectric function are essentially independent of the initial values of the trial parameters, which is a basic property of a MCMC method. The optical constants derived for SiO{sub 2} in the energy loss range of 8-90 eV are in good agreement with other available data, and relevant bulk ELFs are checked by oscillator strength-sum and perfect-screening-sum rules. Our results show that the dielectric function can be obtained by the RMC method even with a wide range of initial trial parameters. The RMC method is thus a general and effective method for determining the optical properties of solids from REELS measurements.
We present the design methodology for arrays of neodymium iron boron (NdFeB)-based magnets for use in magnetic tweezers devices. Using finite element analysis (FEA), we optimized the geometry of the NdFeB magnet as well as the geometry of iron yokes designed to focus the magnetic fields toward the sample plane. Together, the magnets and yokes form a magnetic array which is the basis of the magnetic tweezers device. By systematically varying 15 distinct shape parameters, we determined those features that maximize the magnitude of the magnetic field gradient as well as the length scale over which the magnetic force operates. Additionally, we demonstrated that magnetic saturation of the yoke material leads to intrinsic limitations in any geometric design. Using this approach, we generated a compact and light-weight magnetic tweezers device that produces a high field gradient at the image plane in order to apply large forces to magnetic beads. We then fabricated the optimized yoke and validated the FEA by experimentally mapping the magnetic field of the device. The optimization data and iterative FEA approach outlined here will enable the streamlined design and construction of specialized instrumentation for force-sensitive microscopy.