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DOE OSTI2012

Is the Standard Monte Carlo Power Iteration Approach the Wrong Approach?

The power iteration method is the standard Monte Carlo approach for obtaining the eigenfunctions of a nuclear system, but the power method sometimes converges very slowly. Most discussions give a mathematical reason for the slow convergence of the Monte Carlo power method using the same concepts and terminology as when the power method is applied to a deterministic problem. This note first looks at why the convergence is slow from an intuitive Monte Carlo neutron perspective. Second, this note proposes building an eigenfunction intuitively in a cumulative (and noniterative) neutron by neutron manner that tends to better direct neutrons to where the neutrons need to be. Third, a very similar method for building the second eigenfunction is speculatively proposed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2015

ZettaBricks: A Language Compiler and Runtime System for Anyscale Computing

This grant supported the ZettaBricks and OpenTuner projects. ZettaBricks is a new implicitly parallel language and compiler where defining multiple implementations of multiple algorithms to solve a problem is the natural way of programming. ZettaBricks makes algorithmic choice a first class construct of the language. Choices are provided in a way that also allows our compiler to tune at a finer granularity. The ZettaBricks compiler autotunes programs by making both fine-grained as well as algorithmic choices. Choices also include different automatic parallelization techniques, data distributions, algorithmic parameters, transformations, and blocking. Additionally, ZettaBricks introduces novel techniques to autotune algorithms for different convergence criteria. When choosing between various direct and iterative methods, the ZettaBricks compiler is able to tune a program in such a way that delivers near-optimal efficiency for any desired level of accuracy. The compiler has the flexibility of utilizing different convergence criteria for the various components within a single algorithm, providing the user with accuracy choice alongside algorithmic choice. OpenTuner is a generalization of the experience gained in building an autotuner for ZettaBricks. OpenTuner is a new open source framework for building domain-specific multi-objective program autotuners. OpenTuner supports fully-customizable configuration representations, an extensible technique representation to allow for domain-specific techniques, and an easy to use interface for communicating with the program to be autotuned. A key capability inside OpenTuner is the use of ensembles of disparate search techniques simultaneously; techniques that perform well will dynamically be allocated a larger proportion of tests.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2017

Final report for “Extreme-scale Algorithms and Solver Resilience”

This is a joint project with principal investigators at Oak Ridge National Laboratory, Sandia National Laboratories, the University of California at Berkeley, and the University of Tennessee. Our part of the project involves developing performance models for highly scalable algorithms and the development of latency tolerant iterative methods. During this project, we extended our performance models for the Multigrid method for solving large systems of linear equations and conducted experiments with highly scalable variants of conjugate gradient methods that avoid blocking synchronization. In addition, we worked with the other members of the project on alternative techniques for resilience and reproducibility. We also presented an alternative approach for reproducible dot-products in parallel computations that performs almost as well as the conventional approach by separating the order of computation from the details of the decomposition of vectors across the processes.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

Massive Asynchronous Parallelization of Sparse Matrix Factorizations

Solving sparse problems is at the core of many DOE computational science applications. We focus on the challenge of developing sparse algorithms that can fully exploit the parallelism in extreme-scale computing systems, in particular systems with massive numbers of cores per node. Our approach is to express a sparse matrix factorization as a large number of bilinear constraint equations, and then solving these equations via an asynchronous iterative method. The unknowns in these equations are the matrix entries of the factorization that is desired.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Asymptotic Expansion of the Impedance Per Unit Length for Rectangular Conductors

An iteration method is introduced to obtain the asymptotic form of the impedance per unit length of a rectangular conductor when the half side lengths are large compared to the skin depth. The first terms of the asymptotic expansion are extracted in closed form. The manner in which the corner corrections fit into the expansion are illustrated. The asymptotic results are compared to a numerical solution in the square limit. The odd corner correction for a right angle edge is also discussed.

42 ENGINEERING↗

DOE OSTI2026

Impact of Time-Dependent Reactor and Sensor Physics on Core Power Synthesis (Rev.1)

Online synthesis of power distribution is critical in the operation and control of nuclear power reactors to ensure that the core is operating within safety margins and to provide essential knowledge associated with the burnup of the fuel. In light-water reactors, power synthesis is achieved by using some a priori knowledge of the state of the reactor core and updating based on the signals coming from in-core sensors—namely, self-powered neutron detectors (SPNDs). This report examines the effects of fuel burnup and sensor degradation on the ability to accurately synthesize the power distribution in a pressurized water reactor (PWR), considering the typical low-enriched uranium (LEU, 3%-5% enrichment) fuel cycle as well as the higher enrichment LEU+ (5%-8% enrichment) fuel cycle. Several modeling tools were used to simulate power synthesis based on the responses of SPNDs, with emitters made out of Rh or V. A representative PWR LEU core was modeled using the Polaris/Purdue Advanced Reactor Core Simulator (PARCS) approach. The Monte Carlo N-Particle Transport 6 (MCNP6) code was used as well to calculate response functions between different segments of fuel to individual SPNDs; this is a crucial parameter for power synthesis. The Oak Ridge Isotope GENeration (ORIGEN) package in the Standardized Computer Analyses for Licensing Evaluation (SCALE) code was used to model the time-dependent isotopic transmutation in the SPND emitters. All these data were fed into a custom code that enacted the point-based iterative method to simulate power synthesis. Developmental work was also performed on high-fidelity SPND models in the GEometry ANd Tracking 4 (Geant4) code, which enables higher-accuracy modeling of the current responses from SPNDs. In this work, five sets of time-dependent power synthesis test cases were conducted. In these test cases, systematic changes in the input conditions enabled an analysis of the effect of (1) slightly inaccurate a priori power distribution assumptions with respect to fuel burnup, (2) highly inaccurate a priori power distribution assumptions with respect to fuel burnup (such that burnup is not included in the a priori assumed distribution), and (3) differences between Rh and V SPNDs in terms of downstream consequences of the transmutation in the emitters and the extended nature of the LEU+ fuel cycle in comparison with LEU. The authors discovered that one may permissibly have slightly inaccurate a priori assumptions of the fuel burnup (such that the level of burnup may be slightly underapproximated or overapproximated by the accumulated burnup in approximately 9.3 full power days), but to not account for burnup at all in the a priori assumptions leads to severe levels of error, approaching 25% at maximum (for LEU). The authors also discovered that V SPNDs are extraordinarily robust in both the LEU and LEU+ fuel cycles considered in this modeling work, whereas Rh SPNDs undergo significant transmutation that can result in large errors in the synthesized power distribution.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2016

A new multi-energy neutrino radiation-hydrodynamics code in full general relativity and its application to the gravitational collapse of massive stars

We present a new multi-dimensional radiation-hydrodynamics code for massive stellar core-collapse in full general relativity (GR). Employing an M1 analytical closure scheme, we solve spectral neutrino transport of the radiation energy and momentum based on a truncated moment formalism. Regarding neutrino opacities, we take into account a baseline set in state-of-the-art simulations, in which inelastic neutrino–electron scattering, thermal neutrino production via pair annihilation, and nucleon–nucleon bremsstrahlung are included. While the Einstein field equations and the spatial advection terms in the radiation-hydrodynamics equations are evolved explicitly, the source terms due to neutrino–matter interactions and energy shift in the radiation moment equations are integrated implicitly by an iteration method. To verify our code, we first perform a series of standard radiation tests with analytical solutions that include the check of gravitational redshift and Doppler shift. A good agreement in these tests supports the reliability of the GR multi-energy neutrino transport scheme. We then conduct several test simulations of core-collapse, bounce, and shock stall of a 15M{sub ⊙} star in the Cartesian coordinates and make a detailed comparison with published results. Our code performs quite well to reproduce the results of full Boltzmann neutrino transport especially before bounce. In the postbounce phase, our code basically performs well, however, there are several differences that are most likely to come from the insufficient spatial resolution in our current 3D-GR models. For clarifying the resolution dependence and extending the code comparison in the late postbounce phase, we discuss that next-generation Exaflops class supercomputers are needed at least.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2016

POLARIZED LINE FORMATION IN NON-MONOTONIC VELOCITY FIELDS

For a correct interpretation of the observed spectro-polarimetric data from astrophysical objects such as the Sun, it is necessary to solve the polarized line transfer problems taking into account a realistic temperature structure, the dynamical state of the atmosphere, a realistic scattering mechanism (namely, the partial frequency redistribution—PRD), and the magnetic fields. In a recent paper, we studied the effects of monotonic vertical velocity fields on linearly polarized line profiles formed in isothermal atmospheres with and without magnetic fields. However, in general the velocity fields that prevail in dynamical atmospheres of astrophysical objects are non-monotonic. Stellar atmospheres with shocks, multi-component supernova atmospheres, and various kinds of wave motions in solar and stellar atmospheres are examples of non-monotonic velocity fields. Here we present studies on the effect of non-relativistic non-monotonic vertical velocity fields on the linearly polarized line profiles formed in semi-empirical atmospheres. We consider a two-level atom model and PRD scattering mechanism. We solve the polarized transfer equation in the comoving frame (CMF) of the fluid using a polarized accelerated lambda iteration method that has been appropriately modified for the problem at hand. We present numerical tests to validate the CMF method and also discuss the accuracy and numerical instabilities associated with it.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2013

Mathematical and Numerical Aspects of the Adaptive Fast Multipole Poisson-Boltzmann Solver

This paper summarizes the mathematical and numerical theories and computational elements of the adaptive fast multipole Poisson-Boltzmann (AFMPB) solver. We introduce and discuss the following components in order: the Poisson-Boltzmann model, boundary integral equation reformulation, surface mesh generation, the nodepatch discretization approach, Krylov iterative methods, the new version of fast multipole methods (FMMs), and a dynamic prioritization technique for scheduling parallel operations. For each component, we also remark on feasible approaches for further improvements in efficiency, accuracy and applicability of the AFMPB solver to large-scale long-time molecular dynamics simulations. Lastly, the potential of the solver is demonstrated with preliminary numerical results.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2014

Diverse Power Iteration Embeddings and Its Applications

Abstract—Spectral Embedding is one of the most effective dimension reduction algorithms in data mining. However, its computation complexity has to be mitigated in order to apply it for real-world large scale data analysis. Many researches have been focusing on developing approximate spectral embeddings which are more efficient, but meanwhile far less effective. This paper proposes Diverse Power Iteration Embeddings (DPIE), which not only retains the similar efficiency of power iteration methods but also produces a series of diverse and more effective embedding vectors. We test this novel method by applying it to various data mining applications (e.g. clustering, anomaly detection and feature selection) and evaluating their performance improvements. The experimental results show our proposed DPIE is more effective than popular spectral approximation methods, and obtains the similar quality of classic spectral embedding derived from eigen-decompositions. Moreover it is extremely fast on big data applications. For example in terms of clustering result, DPIE achieves as good as 95% of classic spectral clustering on the complex datasets but 4000+ times faster in limited memory environment.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2014

Physics Integration KErnels (PIKE)

Pike is a software library for coupling and solving multiphysics applications. It provides basic interfaces and utilities for performing code-to-code coupling. It provides simple "black-box" Picard iteration methods for solving the coupled system of equations including Jacobi and Gauss-Seidel solvers. Pike was developed originally to couple neutronics and thermal fluids codes to simulate a light water nuclear reactor for the Consortium for Simulation of Light-water Reactors (CASL) DOE Energy Innovation Hub. The Pike library contains no physics and just provides interfaces and utilities for coupling codes. It will be released open source under a BSD license as part of the Trilinos solver framework (trilinos.org) which is also BSD. This code provides capabilities similar to other open source multiphysics coupling libraries such as LIME, AMP, and MOOSE.

Pawlowski, Roger↗

DOE OSTI2017

Realistic Geochemical Parameter Uncertainty for Performance Assessment Modeling - 17066

Performance assessments (PAs) include uncertain geochemical parameters that affect the fate and transport of contaminants in environmental media, such as partitioning coefficients for water/rock (K{sub d}) and water/air (K{sub H}), diffusion coefficients, and aqueous solubilities. A statistical approach to realistic, as opposed to 'conservative,' stochastic distribution development for geochemical parameters is presented here. For contaminants not identified as focus elements during screening, broad generic distributions are developed. If any parameter is flagged in the subsequent model sensitivity analysis (SA), it becomes a focus element for further research during the next round of distribution development. This iterative approach is efficient and technically defensible at each stage. Data are collected in databases and may be appropriately weighted or filtered. In the relatively few cases where data exist from local or analogous rocks, those data may be prioritized. Once established, the databases can be used for future PAs or other environmental models and can be expanded as needed based on model SA results, additional screening, and as additional relevant data become available. The iterative method is demonstrated for K{sub d} and K{sub H} in a PA model for a radioactive waste disposal facility. An SA was performed based on preliminary geochemical parameter distributions that showed certain model endpoints are sensitive to K{sub d} and K{sub H} values for some contaminants. This underscores the importance of including realistic uncertainty in these geochemical parameters. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2016

Unbiased Ratio Estimator for k-Eigenvalue in Monte Carlo Criticality Calculations

In criticality calculations, the effective multiplication factor (k{sub eff}) is an important parameter for reactor analysis. It can be interpreted as the ratio of the neutron production rate to the loss rate in a reactor core. In Monte Carlo (MC) criticality calculations, k{sub eff} is obtained for each active cycle i as: k-i = P{sub i}/L{sub i} for I = 1 to I where P{sub i} and L{sub i} are the production rate and the loss rate at cycle i, respectively, and they are normalized by the nominal source size for cycle. Since all neutron particles in a cycle will be absorbed or leaks out at the end, the loss rate, L{sub i}, can be set as the source rate, which is the unity. Thus, in MCNP5, k{sub i} is simply calculated with P{sub i} by using three conventional estimators; collision, absorption, and track-length estimators. In domain decomposed MC criticality calculations based on the fission and surface source (FSS) iteration method, k{sub i} is calculated by a ratio of P{sub i} and L{sub i}, where both P{sub i} and L{sub i} are random variables, sampled by using the same particle histories. When the numerator and the denominator are correlated, the variance of the ratio can be smaller than that of the numerator. Then, the final estimate of k{sub eff} is provided as the sample mean of k{sub i}, which will be referred as 'simple' ratio estimator in this paper. In Ref., it is shown that this ratio estimator converges faster and fluctuates less than the conventional estimator. A similar ratio estimator is also used in Serpent 2, as an implicit estimate of k{sub eff}. However, this type of 'simple' ratio estimator is biased, which means that the expectation of the ratio is different from the ratio of the expectation of the numerator and that of the denominator. In this paper, an unbiased ratio estimator which was originally derived in the cytometry analysis is introduced to estimate k{sub eff} and is tested on a continuous-energy UO{sub 2} pin-cell problem. In this test problem, it is shown that the variance of the unbiased ratio estimator is smaller than those of the conventional estimators provided by MCNP5, while the simple ratio estimator can be significantly biased when the number of histories per cycle is too small. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

An iterative dynamic chemical stiffness removal method for reacting flow simulations

Abstract An iterative dynamic chemical stiffness removal method (IDCSR) based on quasi-steady-state approximation (QSSA) is proposed. The IDCSR method is built on a previously developed non-iterative method which has proved to work well for small timestep sizes. A novel iterative procedure is designed in IDCSR to enable explicit time integration of stiff chemistry at relatively large timestep sizes relevant to practical reacting flow simulations. The effectiveness of the iterative procedure is first demonstrated with a toy problem and homogeneous auto-ignition with fixed integration step sizes, showing that larger timestep sizes can be allowed for explicit time integration using IDCSR compared with the previous non-iterative method. IDCSR is then compared with existing explicit chemistry solvers for simulations of homogeneous auto-ignition and shows similar or lower computational cost but significantly higher accuracy across a wide range of timestep sizes. IDCSR is further combined with an automatic adaptive time-stepping scheme for simulations of 0-D homogeneous auto-ignition and a 2-D laminar lifted n -dodecane jet flame. For the 0-D auto-ignition simulations, IDCSR is shown to reduce both the error (by 43%–90%) and computational cost (by 6–15 times) compared with existing explicit solvers, while achieving speed-up factors of up to 400 compared with VODE for a wide range of timestep sizes and reaction mechanisms. For the 2-D jet flame simulations, speed-up factors of 15 and 31 for chemistry integration, and 5 and 9 for overall simulation, are achieved by IDCSR compared with CVODE with and without analytic Jacobian, respectively.

Xu, Chao (ORCID:0000000153074159)↗

DOE OSTI2016

Fission Matrix Convergence Diagnostic of the Iterated Fission Probability Method

Monte Carlo methods have been applied to reactor problems in order to solve for adjoint-weighted quantities. The Iterated Fission Probability (IFP) method allows adjoint-weighted tallies to be recorded during a forward Monte-Carlo simulation. A key parameter in the IFP method is the number of generations that must pass before the progeny neutrons of a progenitor neutron are tallied. A convergence diagnostic for the IFP is developed using a deterministic code. In particular, a discrete ordinates code is used as a surrogate to demonstrate the theoretical properties of the proposed Monte Carlo convergence diagnostic. The diagnostic is applied to 1-D slab problems and quantifies the error associated with tallying the neutron progeny before an asymptotic distribution is achieved. The results show that the default value of 10 for the number of generations used in MCNP is acceptable for most classes of problems. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2020

Efficient and robust phase-split computations in the internal energy, volume, and moles ( UVN ) space

Phase-split computations in an isolated system, which in general may be defined as one where the total internal energy (U), volume (V), and the number of moles (N = N 1 , N 2 ,..., N n ) of the components are fixed at some specified set of values, involves the determination of the temperature (T), pressure (P), plus the amount and composition of the various phases that constitute the system. A simpler, but analogous problem is one where T, P, and N are specified instead. In TPN space, one may first perform a stability analysis to determine whether the system is stable, meaning whether at equilibrium it will split up into multiple phases or remain in single phase. If the single-phase state is unstable, the stability analysis reliably provides a good set of initial guesses in the subsequent phase-split computations. In UVN space, however, we demonstrate that the stability analysis (which is the main subject of our earlier study [1]) may not in general provide good enough initial guesses; we offer alternative strategies for setting up good initial guesses. Furthermore, we show that a combination of successive substitution iteration (SSI) and Newton's method---two iterative methods that are prevalent in the literature in TPN space---facilitates a robust and efficient algorithm for phase-split computations in isolated systems. Finally, this combination has so far not been applied in UVN space.

02 PETROLEUM↗

DOE OSTI2014

TH-A-18C-07: Noise Suppression in Material Decomposition for Dual-Energy CT

Purpose: A general problem of dual-energy CT (DECT) is that the decomposition is sensitive to noise in the two sets of dual-energy projection data, resulting in severely degraded qualities of decomposed images. We have previously proposed an iterative denoising method for DECT. Using a linear decomposition function, the method does not gain the full benefits of DECT on beam-hardening correction. In this work, we expand the framework of our iterative method to include non-linear decomposition models for noise suppression in DECT. Methods: We first obtain decomposed projections, which are free of beam-hardening artifacts, using a lookup table pre-measured on a calibration phantom. First-pass material images with high noise are reconstructed from the decomposed projections using standard filter-backprojection reconstruction. Noise on the decomposed images is then suppressed by an iterative method, which is formulated in the form of least-square estimation with smoothness regularization. Based on the design principles of a best linear unbiased estimator, we include the inverse of the estimated variance-covariance matrix of the decomposed images as the penalty weight in the least-square term. Analytical formulae are derived to compute the variance-covariance matrix from the measured decomposition lookup table. Results: We have evaluated the proposed method via phantom studies. Using non-linear decomposition, our method effectively suppresses the streaking artifacts of beam-hardening and obtains more uniform images than our previous approach based on a linear model. The proposed method reduces the average noise standard deviation of two basis materials by one order of magnitude without sacrificing the spatial resolution. Conclusion: We propose a general framework of iterative denoising for material decomposition of DECT. Preliminary phantom studies have shown the proposed method improves the image uniformity and reduces noise level without resolution loss. In the future, we will perform more phantom studies to further validate the performance of the purposed method. This work is supported by a Varian MRA grant.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2013

Iterative Boltzmann plot method for temperature and pressure determination in a xenon high pressure discharge lamp

The Boltzmann plot method allows to calculate plasma temperatures and pressures if absolutely calibrated emission coefficients of spectral lines are available. However, xenon arcs are not very well suited to be analyzed this way, as there are only a limited number of lines with atomic data available. These lines have high excitation energies in a small interval between 9.8 and 11.5 eV. Uncertainties in the experimental method and in the atomic data further limit the accuracy of the evaluation procedure. This may result in implausible values of temperature and pressure with inadmissible uncertainty. To omit these shortcomings, an iterative scheme is proposed that is making use of additional information about the xenon fill pressure. This method is proved to be robust against noisy data and significantly reduces the uncertainties. Intentionally distorted synthetic data are used to illustrate the performance of the method, and measurements performed on a laboratory xenon high pressure discharge lamp are analyzed resulting in reasonable temperatures and pressures with significantly reduced uncertainties.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗