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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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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Global error analysis of the Chebyshev rational approximation method

The Chebyshev rational approximation method (CRAM) has become a widely adopted method for solving nuclear depletion problems. Therefore, understanding CRAM’s accuracy is important for the safe operation of nuclear power plants. This article performs a global error analysis of CRAM and finds that, as the length of the time step approaches zero, the relative error measured between the exact and CRAM solutions at a fixed end time approaches one and infinity for even and odd orders, respectively; for intermediate time step sizes, a minimum in relative error is observed. Finally, we show that the reason for CRAM’s behavior is that the method is inconsistent. Two best practices for using CRAM, derived from these results, are: (1) use CRAM order 16 or higher, (2) if necessary, increase the CRAM order when multiphysics coupling requires smaller time steps.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Practical algorithms for multivariate rational approximation

We present two approaches for computing rational approximations to multivariate functions, motivated by their effectiveness as surrogate models for high-energy physics (HEP) applications. Our first approach builds on the Stieltjes process to efficiently and robustly compute the coefficients of the rational approximation. Our second approach is based on an optimization formulation that allows us to include structural constraints on the rational approximation (in particular, constraints demanding the absence of singularities), resulting in a semi-infinite optimization problem that we solve using an outer approximation approach. We present results for synthetic and real-life HEP data, and we compare the approximation quality of our approaches with that of traditional polynomial approximations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Performance improvements of the windowed multipole formalism using a rational fraction approximation of the Faddeeva function

The windowed multipole (WMP) formalism was introduced as a way to calculate Doppler broadened cross sections on the fly during Monte Carlo simulations. While more arithmetic is needed compared to point-wise cross section look-ups, performance remained competitive from the large memory reductions and sequential data access. The single most expensive function call in a depleted fuel assembly problem using WMP comes from the evaluation of the Faddeeva function, which previously relied on a highly accurate, highly-branching algorithm. This paper explores the use of rational fraction approximations tailored to the domain interest of reactor physics applications and the development of lower accuracy approximations sufficient for our application. The rational approximations were implemented and tested in OpenMC on an infinite medium problem to stress the cross section calculation routine and a PWR assembly problem. In both cases, the rational approximation nearly eliminated the ∼ 20% penalty previously observed when comparing to point-wise libraries. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2020

A Multi-Function AAA Algorithm Applied to Frequency Dependent Line Modeling

Modeling of power distribution system components that are valid for a wide range of frequencies are crucial for highly accurate modeling of electromagnetic transient (EMT) events. This has recently become of interest due to the improvements needed for the resilient operation of distribution systems. Vector fitting (VF) is a very popular and commonly used algorithm for wide band representations of power system components in EMT simulations. In this research, we present a new multi-input rational approximation algorithm (MIAAA) and illustrate its advantages with respect to VF using examples of approximations of admittance matrices discussed in the literature. We show that MIAAA not only outperforms VF in terms of achieving better accuracy using lesser number of poles, but also has no numerical issues achieving convergence. In contrast to VF, MIAAA is not sensitive to the location of input sample points and it does not require good estimates for the location of the desired approximation poles. The novelty of this research work is the use of recent mathematical results to solve existing challenges in distribution system modeling and to develop rational approximations for power system models that intend to be optimal in terms of accuracy and performance.

41 EE - Solar Energy Technologies Office (EE-4S)↗
DOE OSTI2021

A MIMO AAA Agorithm for Frequency Dependent Line Modeling

Modeling of power distribution system components that are valid for a wide range of frequencies are crucial for highly accurate modeling of electromagnetic transient (EMT) events. This has recently become of interest due to the improvements needed for the resilient operation of distribution systems. Vector fitting (VF) is a very popular and commonly used algorithm for wide band representations of power system components in EMT simulations. In this research, we present a new multi-input rational approximation algorithm (MIAAA) and illustrate its advantages with respect to VF using examples of approximations of admittance matrices discussed in the literature. We show that MIAAA not only outperforms VF in terms of achieving better accuracy using lesser number of poles, but also has no numerical issues achieving convergence. In contrast to VF, MIAAA is not sensitive to the location of input sample points and it does not require good estimates for the location of the desired approximation poles. The novelty of this research work is the use of recent mathematical results to solve existing challenges in distribution system modeling and to develop rational approximations for power system models that intend to be optimal in terms of accuracy and performance.

AAA algorithm↗
DOE OSTI2023

Iterative Stability Enforcement in Adaptive Antoulas–Anderson Algorithms for \({\boldsymbol{\mathcal{H}_2}}\) Model Reduction

This paper presents an extension of the Adaptive-Antoulas-Anderson (AAA) algorithm for rational modelling. Specifically, our new stable multi-input multi-output AAA (smiAAA) algorithm builds rational approximations of multi-input signals with a common set of stable poles. A new methodology is presented for iteratively enforcing stability constraints on the poles. We demonstrate the strengths of this approach compared to the stability enforcement in the FastAAA algorithm. Results using the smiAAA algorithm are compared with the commonly used Vector Fitting algorithm and the more recently published RKFIT algorithm. Vector Fitting and RKFIT both require the user to input the number of poles to use in the approximations. If the final approximation is not accurate enough, the user must re-start Vector Fitting or RKFIT with a larger number of poles and/or a new starting location for the poles. In contrast, the smiAAA algorithm is designed to allow the user to simply input the desired accuracy of the approximations, and the necessary number of poles is detected automatically. This permits users to produce approximations of a desired accuracy with no knowledge about the underlying order of the system being approximated, preventing the algorithm from ever needing to be rerun. An additional feature for preventing extraneous poles from being returned by AAA is also discussed. The cause of these extraneous poles is efficiently detected and removed by our presented methodology. In conclusion, the examples presented demonstrate that smiAAA can efficiently produce approximations of similar or better accuracy than Vector Fitting and RKFIT while requiring less input from the user.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Introduction of the Adding and Doubling Method for Solving Bateman Equations for Nuclear Fuel Depletion

This paper introduces and evaluates the Adding and Doubling Method (ADM) for solving the Bateman equations for depletion systems with varying numbers of nuclides and compares it to the Chebyshev Rational Approximation Method (CRAM), both implemented in the reactor physics analysis application Griffin. ADM, when applied to the Crank-Nicolson Finite Difference method, can produce results comparable in accuracy and precision to CRAM with comparable run times for systems with 35 or 297 nuclides. For systems with more than 300 nuclides, the matrix-matrix operations required by ADM are significantly more costly than the matrix-vector operations required by CRAM, making CRAM the more efficient method for systems with large numbers of nuclides. ADM is an accurate method that maintains other advantages over CRAM in that it does not depend on pre-generated coefficients or require complex number operations. ADM also manages to outperform CRAM by a factor of more than 250 in terms of run time for depletion systems that require multiple Bateman solves while the depletion matrix and time step size remain constant over all depletion intervals.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

Adaptive Power Flow Approximations With Second-Order Sensitivity Insights

The power flow equations are fundamental to power system planning, analysis, and control. However, the inherent non-linearity and non-convexity of these equations present formidable obstacles in problem-solving processes. To mitigate these challenges, recent research has proposed adaptive power flow linearizations that aim to achieve accuracy over wide operating ranges. The accuracy of these approximations inherently depends on the curvature of the power flow equations within these ranges, which necessitates considering second-order sensitivities. In this paper, we leverage second-order sensitivities to both analyze and improve power flow approximations. We evaluate the curvature across broad operational ranges and subsequently utilize this information to inform the computation of various sample-based power flow approximation techniques. Additionally, we leverage second-order sensitivities to guide the development of rational approximations that yield linear constraints in optimization problems. In conclusion, this approach is extended to enhance accuracy beyond the limitations of linear functions across varied operational scenarios.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2020

ONIX: An open-source depletion code

Open Source software enables innovative, community-based software development. ONIX brings this concept to the field of depletion calculations. It is an open-source depletion software to be used for nuclear reactor simulations, for fissile material production analysis as well as for nuclear arms control applications. ONIX provides a module to solve the depletion equation using a Chebyshev Rational Approximation Method. For the generation of one-group cross sections, it includes a coupling interface for the open-source neutron transport code, OpenMC, as well as a module to read pre-computed values in a stand-alone mode. ONIX has special features to optimize nuclear data libraries, to update isomeric branching ratio during burnup, and to support automation of simulations for nuclear archaeology. In conclusion, ONIX has been validated against results from numerical and experimental benchmarks, and its results agree with other methods within expected error ranges.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2020

Depletion capabilities in the OpenMC Monte Carlo particle transport code

A depletion solver has been implemented in OpenMC and is described herein. The depletion solver is implemented in Python and interfaces with OpenMC’s transport solver through a C++ application programming interface, which enables an in-memory transport-depletion coupling. Multiple integration methods for advancing in time have been implemented and exhibit tradeoffs in cost, accuracy, and memory use. For all time integration methods, evaluation of the matrix exponential is performed by using the incomplete partial fraction form of the Chebyshev rational approximation method. Simulations of a pressurized water reactor (PWR) pincell and a sodium-cooled fast reactor (SFR) assembly were carried out with OpenMC and Serpent. For both problems, the use of a high-fidelity depletion chain results in predictions of k eff that agree within 20–30 pcm between OpenMC and Serpent. Predicted actinide concentrations were found to agree to a fraction of a percent, and most fission product concentrations were found to agree within 1%. Here, the few cases where larger differences were observed can be attributed either to differences in how the energy dependence of fission product yields is handled or deficiencies in the nuclear data used. OpenMC simulations of the PWR and SFR problems using a simplified 228-nuclide depletion chain demonstrate that it achieves accuracy close to that of the full, high-fidelity depletion chain with respect to the studied responses.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Non-Hermitian Quantum Mechanics Approach for Extracting and Emulating Continuum Physics Based on Bound-State-like Calculations

Here, this Letter introduces a unified emulation framework for studying continuum physics in finite quantum systems. Using a reduced basis method, we construct powerful emulators for the inhomogeneous Schrödinger equation that operate in a combined parameter space of complex energy (𝐸) and other inputs (𝜽). Within the space, the emulators simultaneously perform analytical continuation in 𝐸—extracting continuum physics from numerically simpler bound-state-like calculations—and interpolate this entire process across 𝜽. This yields a small, non-Hermitian system whose properties (e.g., resonances and scattering observables) can be rapidly predicted for any 𝜽. Crucially, the complex-𝐸 emulation provides a pathway to compute continuum observables for complex systems where advanced bound-state methods exist but direct continuum calculations are yet to be developed, while the 𝜽 emulation enables rapid parameter-space exploration and can be adapted to accelerate other existing continuum calculations. Demonstrations with two- and three-body systems highlight the method’s effectiveness and suggest its connection to (near-)optimal rational approximation. This Letter presents the key results, with further details reserved for a companion paper.

ab initio calculations↗
DOE OSTI2026

pyDecay: A CRAM-Based Isotope Decay Solver

This module (pyDecay) implements a Chebyshev Rational Approximation Method (CRAM) for solving isotope decay equations, based on the work of M. Pusa. It provides a numerically stable and efficient method for evaluating the matrix exponential involved in nuclear decay calculations. This implementation of CRAM relies on the incomplete partial factorization (IPF) algorithm published by Pusa [3], with corrections noted by Romano et al.

Skutnik, SteveEugene [Oak Ridge National Laborator↗
DOE OSTI2024

Physically interpretable approximations of many-body spectral functions

The rational function approximation provides a natural and interpretable representation of response functions such as the many-body spectral functions. We apply the vector fitting (VFIT) algorithm to fit a variety of spectral functions calculated from the Holstein model of electron-phonon interactions. We show that the resulting rational functions are highly efficient in their fitting of sharp features in the spectral functions, and could provide a means to infer physically relevant information from a spectral data set. The position of the peaks in the approximated spectral function are determined by the location of poles in the complex plane. Additionally, we developed a variant of VFIT that incorporates regularization to improve the quality of fits. With this procedure, we demonstrate it is possible to achieve accurate spectral function fits that vary smoothly as a function of physical conditions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Biexcitons are bound in CsPbBr 3 perovskite nanocrystals

Here, we study the energetics of quasiparticle excitations in CsPbBr 3 perovskite nanocrystals using path integral molecular dynamics simulations. Employing detailed molecular models, we elucidate the interplay of anharmonic lattice degrees of freedom, dielectric confinement, and electronic correlation on exciton and biexciton binding energies of a range of nanocrystal sizes. We find generally good agreement with some experimental observations of binding energies and additionally explain the observed size-dependent Stokes shift. The explicit model calculations are compared with simplified approximations to rationalize the lattice contributions to binding. We find that polaron formation significantly reduces exciton binding energies, whereas these effects are negligible for biexciton interactions. While experimentally the binding energy of biexcitons is uncertain, based on our study, we conclude that biexcitons are bound in CsPbBr 3 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗