Search NASA⌕ Search

SEARCH · Search NASA

Results for “ITERATION”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2013

Evaluating the performance of two neutron spectrum unfolding codes based on iterative procedures and artificial neural networks

In this work the performance of two neutron spectrum unfolding codes based on iterative procedures and artificial neural networks is evaluated. The first one code based on traditional iterative procedures and called Neutron spectrometry and dosimetry from the Universidad Autonoma de Zacatecas (NSDUAZ) use the SPUNIT iterative algorithm and was designed to unfold neutron spectrum and calculate 15 dosimetric quantities and 7 IAEA survey meters. The main feature of this code is the automated selection of the initial guess spectrum trough a compendium of neutron spectrum compiled by the IAEA. The second one code known as Neutron spectrometry and dosimetry with artificial neural networks (NDSann) is a code designed using neural nets technology. The artificial intelligence approach of neural net does not solve mathematical equations. By using the knowledge stored at synaptic weights on a neural net properly trained, the code is capable to unfold neutron spectrum and to simultaneously calculate 15 dosimetric quantities, needing as entrance data, only the rate counts measured with a Bonner spheres system. Similarities of both NSDUAZ and NSDann codes are: they follow the same easy and intuitive user's philosophy and were designed in a graphical interface under the LabVIEW programming environment. Both codes unfold the neutron spectrum expressed in 60 energy bins, calculate 15 dosimetric quantities and generate a full report in HTML format. Differences of these codes are: NSDUAZ code was designed using classical iterative approaches and needs an initial guess spectrum in order to initiate the iterative procedure. In NSDUAZ, a programming routine was designed to calculate 7 IAEA instrument survey meters using the fluence-dose conversion coefficients. NSDann code use artificial neural networks for solving the ill-conditioned equation system of neutron spectrometry problem through synaptic weights of a properly trained neural network. Contrary to iterative procedures, in neural net approach it is possible to reduce the rate counts used to unfold the neutron spectrum. To evaluate these codes a computer tool called Neutron Spectrometry and dosimetry computer tool was designed. The results obtained with this package are showed. The codes here mentioned are freely available upon request to the authors.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2014

Evaluation of inter-laminar shear strength of GFRP composed of bonded glass/polyimide tapes and cyanate-ester/epoxy blended resin for ITER TF coils

The insulation system of the ITER TF coils consists of multi-layer glass/polyimide tapes impregnated a cyanate-ester/epoxy resin. The ITER TF coils are required to withstand an irradiation of 10 MGy from gamma-ray and neutrons since the ITER TF coils is exposed by fast neutron (>0.1 MeV) of 10{sup 22} n/m{sup 2} during the ITER operation. Cyanate-ester/epoxy blended resins and bonded glass/polyimide tapes are developed as insulation materials to realize the required radiation-hardness for the insulation of the ITER TF coils. To evaluate the radiation-hardness of the developed insulation materials, the inter-laminar shear strength (ILSS) of glass-fiber reinforced plastics (GFRP) fabricated using developed insulation materials is measured as one of most important mechanical properties before/after the irradiation in a fission reactor of JRR-3M. As a result, it is demonstrated that the GFRPs using the developed insulation materials have a sufficient performance to apply for the ITER TF coil insulation.

07 ISOTOPE AND RADIATION SOURCES↗
DOE OSTI2014

EC assisted start-up experiments reproduction in FTU and AUG for simulations of the ITER case

The breakdown and plasma start-up in ITER are well known issues studied in the last few years in many tokamaks with the aid of calculation based on simplified modeling. The thickness of ITER metallic wall and the voltage limits of the Central Solenoid Power Supply strongly limit the maximum toroidal electric field achievable (0.3 V/m), well below the level used in the present generation of tokamaks. In order to have a safe and robust breakdown, the use of Electron Cyclotron Power to assist plasma formation and current rump up has been foreseen. This has raised attention on plasma formation phase in presence of EC wave, especially in order to predict the required power for a robust breakdown in ITER. Few detailed theory studies have been performed up to nowadays, due to the complexity of the problems. A simplified approach, extended from that proposed in ref[1] has been developed including a impurity multispecies distribution and an EC wave propagation and absorption based on GRAY code. This integrated model (BK0D) has been benchmarked on ohmic and EC assisted experiments on FTU and AUG, finding the key aspects for a good reproduction of data. On the basis of this, the simulation has been devoted to understand the best configuration for ITER case. The dependency of impurity distribution content and neutral gas pressure limits has been considered. As results of the analysis a reasonable amount of power (1 - 2 MW) seems to be enough to extend in a significant way the breakdown and current start up capability of ITER. The work reports the FTU data reproduction and the ITER case simulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Simulation of shell pellet injection strategies for ITER-scale tokamaks

Dispersive shell pellet (DSP) injection is considered as an alternative to shattered pellet injection as a disruption mitigation system for ITER, and strategies for penetration of a shell pellet into ITER are modeled with the 3D MHD code NIMROD. Because the high plasma temperatures lead to rapid ablation of the shell, delivery of the dispersive payload to the core of ITER will be very challenging. Two strategies to increase payload delivery depth are modeled: first, multiple staggered pellets are simulated in DIII-D, to assess the ability for one DSP to "piggy-back" on another to reach deeper into the core; second, DSP injection after pre-dilution-cooling with deuterium is simulated in ITER, in order to reduce the plasma temperature before shell pellet arrival. The DIII-D simulations show that a second, slower pellet can penetrate much deeper once the release of the first payload strongly cools the mid-radius region. When the pellets are staggered, deeper penetration of the second pellet leads to higher radiation fraction and larger runaway electron loss fraction, consistent with single pellet results. However, simultaneously released pellets at mid-radius that do not trigger a large n=1 mode produce an even higher radiation fraction. The ITER simulations show that an inside-out TQ can be produced with a payload release just inside of the q=2 surface, which is achieved at a speed of 800 m/s after pre-dilution cooling. Although stochastization of the core leads to a complete thermal quench, the edge flux surfaces are surprisingly robust in the ITER simulations, regardless of payload release location. As a result, runaway electron losses would not be expected.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

First tungsten radiation studies in DIII-D’s ITER baseline demonstration discharges

Abstract ITER Baseline Scenario plasmas were studied in DIII-D using krypton and xenon gases as a proxy for the tungsten that will be present in ITER. These impurities were chosen for having the same radiative loss rate Lz as tungsten would exhibit in the hotter ITER core. Results show that the scenario with these core radiators spans the range of impurity concentration and W radiated fraction expected for ITER, and up to 50% higher values, explored at zero injected torque, as well as 1 Nm and full co-torque injection with T ∼ 3 Nm. Stationary discharges with duration >2–4 τ R are achieved with f rad ⩾ 30% leading to a reduction in confinement of ∼10%, and a comparison with real metal radiators in the same range of f rad shows that the higher Lz at the lower temperatures in these plasmas yields too pessimistic results on the survivability and performance of this scenario in ITER. Simulations of ITER power balance including W radiation show that with concentration up to three times higher than in the DIII-D plasmas the scenario can be stationary, remaining at acceptable core radiated fraction values.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2014

SU-D-12A-05: Iterative Reconstruction Techniques to Enable Intrinsic Respiratory Gated CT in Mice

Purpose: Longitudinal studies of lung function in mice need the ability to image different phases of ventilation in free-breathing mice using retrospective gating. However, retrospective gating often produces under-sampled and uneven angular samples, resulting in severe reconstruction artifacts when using traditional FDK based reconstruction algorithms. We wanted to demonstrate the utility of iterative reconstruction method to enable intrinsic respiratory gating in small-animal CT. Methods: Free-breathing mice were imaged using a Siemens Inveon PET/micro-CT system. Evenly distributed projection images were acquired at 360 angles. Retrospective respiratory gating was performed using an intrinsic marker based on the average intensity in a region covering the diaphragm. Projections were classified into 4 and 6 phases (finer temporal resolution) resulting in 138 and 67 projections respectively. Reconstruction was carried out using 3 Methods: conventional FDK, iterative penalized least-square (PWLS) with total variation (TV), and PWLS with edge-preserving penalty. The performance of the methods was compared using contrast-to-noise (CNR) in a region of interest (ROI). Line profile through a specific region was plotted to evaluate the preserving of edges. Results: In both the cases with 4 and 6 phases, inadequate and non-uniform angular sampling results in artifacts using conventional FDK. However, such artifacts are minimized using both the iterative methods. Using both 4 and 6 phases, the iterative techniques outperformed FDK in terms of CNR and maintaining sharp edges. This is further evidenced especially with increased artifacts using FDK for 6 phases. Conclusion: This work indicates fewer artifacts and better image details can be achieved with iterative reconstruction methods in non-uniform under-sampled reconstruction. Using iterative methods can enable free-breathing intrinsic respiratory gating in small-animal CT. Further studies are needed to compare the computational complexity for large datasets.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2014

SU-E-I-33: Initial Evaluation of Model-Based Iterative CT Reconstruction Using Standard Image Quality Phantoms

Purpose: The purpose of this study was to compare a new model-based iterative reconstruction with existing reconstruction methods (filtered backprojection and basic iterative reconstruction) using quantitative analysis of standard image quality phantom images. Methods: An ACR accreditation phantom (Gammex 464) and a CATPHAN600 phantom were scanned using 3 routine clinical acquisition protocols (adult axial brain, adult abdomen, and pediatric abdomen) on a Philips iCT system. Each scan was acquired using default conditions and 75%, 50% and 25% dose levels. Images were reconstructed using standard filtered backprojection (FBP), conventional iterative reconstruction (iDose4) and a prototype model-based iterative reconstruction (IMR). Phantom measurements included CT number accuracy, contrast to noise ratio (CNR), modulation transfer function (MTF), low contrast detectability (LCD), and noise power spectrum (NPS). Results: The choice of reconstruction method had no effect on CT number accuracy, or MTF (p<0.01). The CNR of a 6 HU contrast target was improved by 1–67% with iDose4 relative to FBP, while IMR improved CNR by 145–367% across all protocols and dose levels. Within each scan protocol, the CNR improvement from IMR vs FBP showed a general trend of greater improvement at lower dose levels. NPS magnitude was greatest for FBP and lowest for IMR. The NPS of the IMR reconstruction showed a pronounced decrease with increasing spatial frequency, consistent with the unusual noise texture seen in IMR images. Conclusion: Iterative Model Reconstruction reduces noise and improves contrast-to-noise ratio without sacrificing spatial resolution in CT phantom images. This offers the possibility of radiation dose reduction and improved low contrast detectability compared with filtered backprojection or conventional iterative reconstruction.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2016

Accelerated fast iterative shrinkage thresholding algorithms for sparsity-regularized cone-beam CT image reconstruction

Purpose: The development of iterative image reconstruction algorithms for cone-beam computed tomography (CBCT) remains an active and important research area. Even with hardware acceleration, the overwhelming majority of the available 3D iterative algorithms that implement nonsmooth regularizers remain computationally burdensome and have not been translated for routine use in time-sensitive applications such as image-guided radiation therapy (IGRT). In this work, two variants of the fast iterative shrinkage thresholding algorithm (FISTA) are proposed and investigated for accelerated iterative image reconstruction in CBCT. Methods: Algorithm acceleration was achieved by replacing the original gradient-descent step in the FISTAs by a subproblem that is solved by use of the ordered subset simultaneous algebraic reconstruction technique (OS-SART). Due to the preconditioning matrix adopted in the OS-SART method, two new weighted proximal problems were introduced and corresponding fast gradient projection-type algorithms were developed for solving them. We also provided efficient numerical implementations of the proposed algorithms that exploit the massive data parallelism of multiple graphics processing units. Results: The improved rates of convergence of the proposed algorithms were quantified in computer-simulation studies and by use of clinical projection data corresponding to an IGRT study. The accelerated FISTAs were shown to possess dramatically improved convergence properties as compared to the standard FISTAs. For example, the number of iterations to achieve a specified reconstruction error could be reduced by an order of magnitude. Volumetric images reconstructed from clinical data were produced in under 4 min. Conclusions: The FISTA achieves a quadratic convergence rate and can therefore potentially reduce the number of iterations required to produce an image of a specified image quality as compared to first-order methods. We have proposed and investigated accelerated FISTAs for use with two nonsmooth penalty functions that will lead to further reductions in image reconstruction times while preserving image quality. Moreover, with the help of a mixed sparsity-regularization, better preservation of soft-tissue structures can be potentially obtained. The algorithms were systematically evaluated by use of computer-simulated and clinical data sets.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2020

Stability Analysis of Inline ZFP Compression for Floating-Point Data in Iterative Methods

Currently, the dominating constraint in many high performance computing applications is data capacity and bandwidth, in both internode communications and even moreso in intranode data motion. A new approach to address this limitation is to make use of data compression in the form of a compressed data array. Storing data in a compressed data array and converting to standard IEEE-754 types as needed during a computation can reduce the pressure on bandwidth and storage. However, repeated conversions (lossy compression and decompression) introduce additional approximation errors, which need to be shown to not significantly affect the simulation results. Here, we extend recent work that analyzed the error of a single use of compression and decompression of the ZFP compressed data array representation to the case of time-stepping and iterative schemes, where an advancement operator is repeatedly applied in addition to the conversions. We show that the accumulated error for iterative methods involving fixed-point and time evolving iterations is bounded under standard constraints. An upper bound is established on the number of additional iterations required for the convergence of stationary fixed-point iterations. An additional analysis of traditional forward and backward error of stationary iterative methods using ZFP compressed arrays is also presented. The results of several 1D, 2D, and 3D test problems are provided to demonstrate the correctness of the theoretical bounds.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Preliminary Results of a New Deterministic Iterative Image Reconstruction Algorithm - Paper 117

Iterative reconstruction techniques have become the standard for Single Photon Emission Computed Tomography (SPECT). Advances in computing have allowed these techniques to incorporate more and more detail; however, computation time must be balanced against increased detail. Monte Carlo methods are generally used for modeling the physics of a SPECT study, but can have long computation times. Advances in Monte Carlo-based scatter correction have shown reasonable results, but scatter estimation by measuring narrow energy windows remains more common. An iterative reconstruction technique using a deterministic transport code has been proposed as an alternative. This paper presents preliminary results of the new technique in which the TITAN deterministic code completes the forward projection step in a maximum likelihood expectation maximization (ML-EM) reconstruction of SPECT data. The effectiveness of the deterministic algorithm is examined for a 2-dimensional phantom. This work demonstrates the feasibility of using the TITAN code in an iterative reconstruction algorithm. The appropriate deterministic parameters were chosen by comparing sinograms produced with different mesh sizes, quadrature sets, and anisotropic scattering orders. The TITAN code was then successfully used as the forward projection step in an iterative reconstruction algorithm with a 2-dimensional homogeneous phantom. The impact of deterministic parameters on reconstruction quality is being investigated, along with the incorporation of a smoothing filter. The TITAN source code is being modified to include the ML-EM algorithm and iteration steps. This will significantly improve computation time by eliminating the repeated reading and writing of files for each iteration and allowing some steps to be completed in parallel. Further testing of the new reconstruction algorithm for more realistic phantoms is also underway. (authors)

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2019

Self-consistent simulation of transport and turbulence in tokamak edge plasma by coupling SOLPS-ITER and BOUT++

The status of coupling the fluid plasma/neutral 2D transport code SOLPS-ITER and the fluid 3D turbulence code BOUT++ is reported. Both codes simulated the same region, which is from several cm inside the magnetic separatrix to the far scrape-off layer (SOL). Compared to the profile evolution time scale, the characteristic time scale of the turbulence is quite short. For the turbulence code BOUT++, the time scale is around 10 -6 s. However, for the transport code SOLPS-ITER, the time scale is around 10 -3 –10 -2 s. An iterative scheme is used that each system is evolved on its own characteristic time scale. SOLPS-ITER can provide the background profiles of density, ion, and electron temperature to BOUT++. In turn, BOUT++ can provide the corresponding radial transport coefficients to SOLPS-ITER. The coupling has involved the ion density, ion temperature, and electron temperature. After several steps of iteration, the profiles of density, ion, and electron temperature show fluctuations, and the differences of the changes between two consecutive profiles are getting smaller and smaller. Finally, the self-consistent solutions of turbulence and transport can be obtained.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Overview of the EUROfusion Tokamak Exploitation programme in support of ITER and DEMO

Within the 9th European Framework programme, since 2021 EUROfusion is operating five tokamaks under the auspices of a single Task Force called ‘Tokamak Exploitation’. The goal is to benefit from the complementary capabilities of each machine in a coordinated way and help in developing a scientific output scalable to future largre machines. The programme of this Task Force ensures that ASDEX Upgrade, MAST-U, TCV, WEST and JET (since 2022) work together to achieve the objectives of Missions 1 and 2 of the EUROfusion Roadmap: i) demonstrate plasma scenarios that increase the success margin of ITER and satisfy the requirements of DEMO and, ii) demonstrate an integrated approach that can handle the large power leaving ITER and DEMO plasmas. The Tokamak Exploitation task force has therefore organized experiments on these two missions with the goal to strengthen the physics and operational basis for the ITER baseline scenario and for exploiting the recent plasma exhaust enhancements in all four devices (PEX: Plasma EXhaust) for exploring the solution for handling heat and particle exhaust in ITER and develop the conceptual solutions for DEMO. The ITER Baseline scenario has been developed in a similar way in ASDEX Upgrade, TCV and JET. Key risks for ITER such as disruptions and run-aways have been also investigated in TCV, ASDEX Upgrade and JET. Experiments have explored successfully different divertor configurations (standard, super-X, snowflakes) in MAST-U and TCV and studied tungsten melting in WEST and ASDEX Upgrade. The input from the smaller devices to JET has also been proven successful to set-up novel control schemes on disruption avoidance and detachment.

ASDEX upgrade↗
DOE OSTI2024

Prediction of performance and turbulence in ITER burning plasmas via nonlinear gyrokinetic profile prediction

Burning plasma performance, transport, and the effect of hydrogen isotope (H, D, D-T fuel mix) on confinement has been predicted for ITER baseline scenario (IBS) conditions using nonlinear gyrokinetic profile predictions. Accelerated by surrogate modeling (Rodriguez-Fernandez et al 2022 Nucl. Fusion 62 076036), high fidelity, nonlinear gyrokinetic simulations performed with the CGYRO code (Candy et al 2016 J. Comput. Phys. 324 73), were used to predict profiles of T i , T e , and n e while including the effects of alpha heating, auxiliary power (NBI + ECH), collisional energy exchange, and radiation losses inside of $r/a$ = 0.9. Predicted profiles and resulting energy confinement are found to produce fusion power and gain that are approximately consistent with mission goals ($P_\textrm{fusion} = 500$ MW at Q = 10) for the baseline scenario and exhibit energy confinement that is within 1σ of the H-mode energy confinement scaling. The power of the surrogate modeling technique is demonstrated through the prediction of alternative ITER scenarios with reduced computational cost. These scenarios include conditions with maximized fusion gain and an investigation of potential resonant magnetic perturbation (RMP) effects on performance with a minimal number of gyrokinetic profile iterations required (3–6). These predictions highlight the stiff ITG nature of the core turbulence predicted in the ITER baseline and demonstrate that $Q \gt$ 17 conditions may be accessible by reducing auxiliary input power while operating in IBS conditions. Prediction of full kinetic profiles allowed for the projection of hydrogen isotope effects around ITER baseline conditions. The gyrokinetic fuel ion species was varied from H, D, and 50/50 D-T and kinetic profiles were predicted. Results indicate that a weak or negligible isotope effect will be observed to arise from core turbulence in IBS conditions. The resulting energy confinement, turbulence, and density peaking, and the implications for ITER operations will be discussed.

gyrokinetics↗
DOE OSTI2023

Accelerating self-consistent field iterations in Kohn-Sham density functional theory using a low-rank approximation of the dielectric matrix

We present an efficient preconditioning technique for accelerating the fixed-point iteration in real-space Kohn-Sham density functional theory (DFT) calculations. The preconditioner uses a low-rank approximation of the dielectric matrix (LRDM) based on Gâteaux derivatives of the residual of fixed-point iteration along appropriately chosen direction functions. We develop a computationally efficient method to evaluate these Gâteaux derivatives in conjunction with the Chebyshev filtered subspace iteration procedure, an approach widely used in large-scale Kohn-Sham DFT calculations. Further, we propose a variant of LRDM preconditioner based on adaptive accumulation of low-rank approximations from previous self-consistent field iterations, and also extend the LRDM preconditioner to spin-polarized Kohn-Sham DFT calculations. We demonstrate the robustness and efficiency of the LRDM preconditioner against other widely used preconditioners on a range of benchmark systems with sizes ranging from ~100 to 1100 atoms (~500–20,000 electrons). The benchmark systems include various combinations of metal-insulating-semiconducting heterogeneous material systems, nanoparticles with localized d orbitals near the Fermi energy, nanofilm with metal dopants, and magnetic systems. In all benchmark systems, the LRDM preconditioner converges robustly within 20–30 iterations. In contrast, other widely used preconditioners show slow convergence in many cases, as well as divergence of the fixed-point iteration in some cases. Lastly, we demonstrate the computational efficiency afforded by the LRDM method, with up to 3.4-fold reduction in computational cost for the total ground-state calculation compared to other preconditioners.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Iterated Gauss-Seidel GMRES

The GMRES algorithm of Saad and Schultz [SIAM J. Sci. Stat. Comput., 7 (1986), pp. 856-869] is an iterative method for approximately solving linear systems Ax = b, with initial guess x0 and residual r0 = b Ax0. The algorithm employs the Arnoldi process to generate the Krylov basis vectors (the columns of Vk ). It is well known that this process can be viewed as a QR factorization of the matrix Bk = [r0, AVk] at each iteration. Despite an O (..epsilon..)..kappa.. (Bk ) loss of orthogonality, for unit roundoff ..epsilon..and condition number ..kappa.. , the modified Gram-Schmidt formulation was shown to be backward stable in the seminal paper by Paige et al. [SIAM J. Matrix Anal.Appl., 28 (2006), pp. 264-284]. We present an iterated Gauss-Seidel formulation of the GMRES algorithm (IGS-GMRES) based on the ideas of Ruhe [Linear Algebra Appl., 52 (1983), pp. 591-601] and Swirydowicz et al. [Numer. Linear Algebra Appl., 28 (2020), pp. 1-20]. IGS-GMRES maintains orthogonality to the level O (..epsilon..)..kappa.. (Bk ) or O (..epsilon..), depending on the choice of one or two iterations; for two Gauss-Seidel iterations, the computed Krylov basis vectors remain orthogonal to working accuracy and the smallest singular value of Vk remains close to one. The resulting GMRES method is thus backward stable. We show that IGS-GMRES can be implemented with only a single synchronization point per iteration, making it relevant to large-scale parallel computing environments. We also demonstrate that, unlike MGS-GMRES, in IGS-GMRES the relative Arnoldi residual corresponding to the computed approximate solution no longer stagnates above machine precision even for highly nonnormal systems.

Arnoldi-QR↗
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 NTRS1994

Global Asymptotic Behavior of Iterative Implicit Schemes

The global asymptotic nonlinear behavior of some standard iterative procedures in solving nonlinear systems of algebraic equations arising from four implicit linear multistep methods (LMMs) in discretizing three models of 2 x 2 systems of first-order autonomous nonlinear ordinary differential equations (ODEs) is analyzed using the theory of dynamical systems. The iterative procedures include simple iteration and full and modified Newton iterations. The results are compared with standard Runge-Kutta explicit methods, a noniterative implicit procedure, and the Newton method of solving the steady part of the ODEs. Studies showed that aside from exhibiting spurious asymptotes, all of the four implicit LMMs can change the type and stability of the steady states of the differential equations (DEs). They also exhibit a drastic distortion but less shrinkage of the basin of attraction of the true solution than standard nonLMM explicit methods. The simple iteration procedure exhibits behavior which is similar to standard nonLMM explicit methods except that spurious steady-state numerical solutions cannot occur. The numerical basins of attraction of the noniterative implicit procedure mimic more closely the basins of attraction of the DEs and are more efficient than the three iterative implicit procedures for the four implicit LMMs. Contrary to popular belief, the initial data using the Newton method of solving the steady part of the DEs may not have to be close to the exact steady state for convergence. These results can be used as an explanation for possible causes and cures of slow convergence and nonconvergence of steady-state numerical solutions when using an implicit LMM time-dependent approach in computational fluid dynamics.

Yee, H. C.↗
NASA NTRS2011

Iterative Strain-Gage Balance Calibration Data Analysis for Extended Independent Variable Sets

A new method was developed that makes it possible to use an extended set of independent calibration variables for an iterative analysis of wind tunnel strain gage balance calibration data. The new method permits the application of the iterative analysis method whenever the total number of balance loads and other independent calibration variables is greater than the total number of measured strain gage outputs. Iteration equations used by the iterative analysis method have the limitation that the number of independent and dependent variables must match. The new method circumvents this limitation. It simply adds a missing dependent variable to the original data set by using an additional independent variable also as an additional dependent variable. Then, the desired solution of the regression analysis problem can be obtained that fits each gage output as a function of both the original and additional independent calibration variables. The final regression coefficients can be converted to data reduction matrix coefficients because the missing dependent variables were added to the data set without changing the regression analysis result for each gage output. Therefore, the new method still supports the application of the two load iteration equation choices that the iterative method traditionally uses for the prediction of balance loads during a wind tunnel test. An example is discussed in the paper that illustrates the application of the new method to a realistic simulation of temperature dependent calibration data set of a six component balance.

Ulbrich, Norbert Manfred↗