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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 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2013

Multigrid solution of a distributed optimal control problem constrained by the Stokes equations

We construct multigrid preconditioners to accelerate the solution process of a linear-quadratic optimal control problem constrained by the Stokes system. The first order optimality conditions of the control problem form a linear system (the KKT system) connecting the state, adjoint, and control variables. Our approach is to eliminate the state and adjoint variables by essentially solving two Stokes systems, and to construct efficient multigrid preconditioners for the Schur-complement of the block associated with the state and adjoint variables. These multigrid preconditioners are shown to be of optimal order with respect to the convergence properties of the discrete methods used to solve the Stokes system. In particular, the number of conjugate gradient iterations is shown to decrease as the resolution increases, a feature shared by similar multigrid preconditioners for elliptic constrained optimal control problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2011

Interlocked optimization and fast gradient algorithm for a seismic inverse problem

Highlights: {yields} A 2D extension of the 1D nonlinear inversion of well-seismic data is given. {yields} Appropriate regularization yields a well-determined large scale inverse problem. {yields} An interlocked optimization loop acts as an efficient preconditioner. {yields} The adjoint state method is used to compute the misfit function gradient. {yields} Domain decomposition method yields an efficient parallel implementation. - Abstract: We give a nonlinear inverse method for seismic data recorded in a well from sources at several offsets from the borehole in a 2D acoustic framework. Given the velocity field, approximate values of the impedance are recovered. This is a 2D extension of the 1D inversion of vertical seismic profiles . The inverse problem generates a large scale undetermined ill-conditioned problem. Appropriate regularization terms render the problem well-determined. An interlocked optimization algorithm yields an efficient preconditioning. A gradient algorithm based on the adjoint state method and domain decomposition gives a fast parallel numerical method. For a realistic test case, convergence is attained in an acceptable time with 128 processors.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2013

Comparison Of Hybrid Methods For Global Variance Reduction In Shielding Calculations

For Monte Carlo shielding problems that calculate a mesh tally over the entire problem, the relative uncertainties computed for each voxel can vary widely. This can lead to unacceptably long run times in order to reduce the uncertainties in all areas of the problem to a reasonably low level. Hybrid methods using estimates from deterministic calculations to create importance maps for variance reduction in Monte Carlo calculations have been successfully used to optimize the calculation of specific tallies. For the global problem, several methods have been proposed that create importance maps that distribute Monte Carlo particles in such a way as to achieve a more uniform distribution of relative uncertainty across the problem. The goal is to compute a mesh tally with nearly the same relative uncertainties in the low flux/dose areas as in the high flux/dose areas. Methods based on only forward deterministic estimates and methods using both forward and adjoint deterministic methods have been implemented the SCALE/MAVRIC package and have been compared against each other by computing global mesh tallies on several representative shielding problems. Methods using both forward and adjoint estimates provide better performance for computing more uniform relative uncertainties across a global mesh tally.

FW-CADIS↗
DOE OSTI2021

A persistent adjoint method with dynamic time-scaling and an application to mass action kinetics

In this article, we consider an optimization problem where the objective function is evaluated at the fixed-point of a contraction mapping parameterized by a control variable, and optimization takes place over this control variable. Since the derivative of the fixed-point with respect to the parameter can usually not be evaluated exactly, an adjoint dynamical system can be used to estimate gradients. Using this estimation procedure, the optimization algorithm alternates between derivative estimation and an approximate gradient descent step. We analyze a variant of this approach involving dynamic time-scaling, where after each parameter update the adjoint system is iterated until a convergence threshold is passed. Here, we prove that, under certain conditions, the algorithm can find approximate stationary points of the objective function. We demonstrate the approach in the settings of an inverse problem in chemical kinetics, and learning in attractor networks.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2011

Large Scale Shape Optimization for Accelerator Cavities

We present a shape optimization method for designing accelerator cavities with large scale computations. The objective is to find the best accelerator cavity shape with the desired spectral response, such as with the specified frequencies of resonant modes, field profiles, and external Q values. The forward problem is the large scale Maxwell equation in the frequency domain. The design parameters are the CAD parameters defining the cavity shape. We develop scalable algorithms with a discrete adjoint approach and use the quasi-Newton method to solve the nonlinear optimization problem. Two realistic accelerator cavity design examples are presented.

43 PARTICLE ACCELERATORS↗
DOE OSTI2013

Comparison of hybrid methods for global variance reduction in shielding calculations

For Monte Carlo shielding problems that calculate a mesh tally over the entire problem, the statistical uncertainties computed for each voxel can vary widely. This can lead to unacceptably long run times in order to reduce the uncertainties in all areas of the problem to a reasonably low level. Hybrid methods - using estimates from deterministic calculations to create importance maps for variance reduction in Monte Carlo calculations - have been successfully used to optimize the calculation of specific tallies. For the global problem, several methods have been proposed to create importance maps that distribute Monte Carlo particles in such a way as to achieve a more uniform distribution of relative uncertainty across the problem. The goal is to compute a mesh tally with nearly the same relative uncertainties in the low flux/dose areas as in the high flux/dose areas. Methods based on only forward deterministic estimates and methods using both forward and adjoint deterministic methods have been implemented in the SCALE/MAVRIC package and have been compared against each other by computing global mesh tallies on several representative shielding problems. Methods using both forward and adjoint estimates provide better performance for computing more uniform relative uncertainties across a global mesh tally. (authors)

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Multi-scale topology optimization of multi-material structures with controllable geometric complexity — Applications to heat transfer problems

This study presents a topology optimization method to design assemblies of periodic cellular materials with controllable geometric complexity. The framework is based on a novel multi-scale and multi-material design model in which the structure, the layout of the material subdomains, and their micro-structures are optimized concurrently. To allow a tight control over its geometrical complexity, the layout at the macro-scale is described by level-set fields, parameterized by geometric primitives. The micro-scale geometry is represented through a density approach. A nonlinear programming algorithm drives the optimization process using design sensitivities computed by the discrete adjoint method. The proposed design framework is studied with heat transfer problems. Practical design problems, such as a heat sink and a thermal storage unit with phase change are discussed. The macro-scale analysis model relies on a generalized transient diffusion equation. At the micro-scale, homogenization is used to compute equivalent material properties. The numerical examples in this study show that the optimized multi-scale multi-material layouts outperform the corresponding mono-scale structures while maintaining geometric simplicity at the macro-scale level.

42 ENGINEERING↗
DOE OSTI2012

A Stochastic Maximum Principle for a Stochastic Differential Game of a Mean-Field Type

We construct a stochastic maximum principle (SMP) which provides necessary conditions for the existence of Nash equilibria in a certain form of N-agent stochastic differential game (SDG) of a mean-field type. The information structure considered for the SDG is of a possible asymmetric and partial type. To prove our SMP we take an approach based on spike-variations and adjoint representation techniques, analogous to that of S. Peng (SIAM J. Control Optim. 28(4):966-979, 1990) in the optimal stochastic control context. In our proof we apply adjoint representation procedures at three points. The first-order adjoint processes are defined as solutions to certain mean-field backward stochastic differential equations, and second-order adjoint processes of a first type are defined as solutions to certain backward stochastic differential equations. Second-order adjoint processes of a second type are defined as solutions of certain backward stochastic equations of a type that we introduce in this paper, and which we term conditional mean-field backward stochastic differential equations. From the resulting representations, we show that the terms relating to these second-order adjoint processes of the second type are of an order such that they do not appear in our final SMP equations. A comparable situation exists in an article by R. Buckdahn, B. Djehiche, and J. Li (Appl. Math. Optim. 64(2):197-216, 2011) that constructs a SMP for a mean-field type optimal stochastic control problem; however, the approach we take of using these second-order adjoint processes of a second type to deal with the type of terms that we refer to as the second form of quadratic-type terms represents an alternative to a development, to our setting, of the approach used in their article for their analogous type of term.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Uncertainty Quantification for Large-Scale Ice Sheet Modeling

This report summarizes our work to develop advanced forward and inverse solvers and uncertainty quantification capabilities for a nonlinear 3D full Stokes continental-scale ice sheet flow model. The components include: (1) forward solver: a new state-of-the-art parallel adaptive scalable high-order-accurate mass-conservative Newton-based 3D nonlinear full Stokes ice sheet flow simulator; (2) inverse solver: a new adjoint-based inexact Newton method for solution of deterministic inverse problems governed by the above 3D nonlinear full Stokes ice flow model; and (3) uncertainty quantification: a novel Hessian-based Bayesian method for quantifying uncertainties in the inverse ice sheet flow solution and propagating them forward into predictions of quantities of interest such as ice mass flux to the ocean.

58 GEOSCIENCES↗
DOE OSTI2012

MC21 analysis of the nuclear energy agency Monte Carlo performance benchmark problem

Due to the steadily decreasing cost and wider availability of large scale computing platforms, there is growing interest in the prospects for the use of Monte Carlo for reactor design calculations that are currently performed using few-group diffusion theory or other low-order methods. To facilitate the monitoring of the progress being made toward the goal of practical full-core reactor design calculations using Monte Carlo, a performance benchmark has been developed and made available through the Nuclear Energy Agency. A first analysis of this benchmark using the MC21 Monte Carlo code was reported on in 2010, and several practical difficulties were highlighted. In this paper, a newer version of MC21 that addresses some of these difficulties has been applied to the benchmark. In particular, the confidence-interval-determination method has been improved to eliminate source correlation bias, and a fission-source-weighting method has been implemented to provide a more uniform distribution of statistical uncertainties. In addition, the Forward-Weighted, Consistent-Adjoint-Driven Importance Sampling methodology has been applied to the benchmark problem. Results of several analyses using these methods are presented, as well as results from a very large calculation with statistical uncertainties that approach what is needed for design applications. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2020

Novel strategies for modal-based structural material identification

Here, we present modal-based methods for model calibration in structural dynamics, and address several key challenges in the solution of gradient-based optimization problems with eigenvalues and eigenvectors, including the solution of singular Helmholtz problems encountered in sensitivity calculations, non-differentiable objective functions caused by mode swapping during optimization, and cases with repeated eigenvalues. Unlike previous literature that relied on direct solution of the eigenvector adjoint equations, we present a parallel iterative domain decomposition strategy (Adjoint Computation via Modal Superposition with Truncation Augmentation) for the solution of the singular Helmholtz problems. For problems with repeated eigenvalues we present a novel Mode Separation via Projection algorithm, and in order to address mode swapping between inverse iterations we present a novel Injective mode ordering metric. We present the implementation of these methods in a massively parallel finite element framework with the ability to use measured modal data to extract unknown structural model parameters from large complex problems. A series of increasingly complex numerical examples are presented that demonstrate the implementation and performance of the methods in a massively parallel finite element framework [7], [5], using gradient-based optimization techniques in the Rapid Optimization Library (ROL) [21].

36 MATERIALS SCIENCE↗
DOE OSTI2015

Adjoint-based deviational Monte Carlo methods for phonon transport calculations

In the field of linear transport, adjoint formulations exploit linearity to derive powerful reciprocity relations between a variety of quantities of interest. We develop an adjoint formulation of the linearized Boltzmann transport equation for phonon transport. We use this formulation for accelerating deviational Monte Carlo simulations of complex, multiscale problems. Benefits include significant computational savings via direct variance reduction, or by enabling formulations which allow more efficient use of computational resources, such as formulations which provide high resolution in a particular phase-space dimension (e.g., spectral). We show that the proposed adjoint-based methods are particularly well suited to problems involving a wide range of length scales (e.g., nanometers to hundreds of microns) and lead to computational methods that can calculate quantities of interest with a cost that is independent of the system characteristic length scale, thus removing the traditional stiffness of kinetic descriptions. Applications to problems of current interest, such as simulation of transient thermoreflectance experiments or spectrally resolved calculation of the effective thermal conductivity of nanostructured materials, are presented and discussed in detail.

42 ENGINEERING↗
DOE OSTI2024

Performance Improvements of the Griffin Solvers in FY24

The Griffin code is a MOOSE-based reactor physics application jointly developed by Idaho National Laboratory and Argonne National Laboratory under the Department of Energy Office of Nuclear Energy Nuclear Energy Advanced Modeling and Simulation Program. This fiscal year, we have made significant efforts to improve the performance of transport solver options and cross-section generation for the efficient use of Griffin in advanced reactor applications. For the HFEM-PN solver, the residual evaluations of HFEM kernels were optimized by utilizing the pre- computed averaged cross sections for individual elements. Numerical integration involving the evaluation of basis functions at quadrature points was bypassed by facilitating precomputed element mass matrices for response matrices. Red-black iterations were improved by introducing a new generalized minimum residual based solver. The memory usage of response matrix storage was significantly reduced by applying basis function rotations on interfaces and calculating volumetric odd-parity moments on the fly. Additionally, the adjoint flux and transient calculation capabilities of the HFEM-PN solver were successfully implemented and verified using the TWIGL benchmark problem. For the DFEM-SN solver, memory footprint and computation time were significantly reduced by not treating angular flux vectors as the MOOSE nonlinear system vectors. Specifically for IQS, scalar adjoint weighting was introduced to further eliminate angular adjoint flux storage in the MOOSE auxiliary system. It was demonstrated through the three-dimensional Advanced Burner Test Reactor core problem that the memory usage for transient calculations with the IQS method was reduced by over 7.5× compared to before the optimizations. For the self-shielding application programming interface, a new double-heterogeneity treatment method, named the Bell Function-Based Analytic Two-Region Slowing Down Method, was developed to efficiently flux-volume homogenize TRISO particles with the matrix. Additionally, optimizations were made to hyper- fine group (HFG) slowing down calculations by pretabulating collision probability coefficients and grouping isotopes, significantly reducing the computational time for calculating scattering sources per HFG. Lastly, the pin power reconstruction module was extended to account for temporal behavior in a microreactor analysis problem, specifically for a control drum transient. Verification tests for each of these improvements demonstrated significant performance enhancements and memory reduction.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2018

Improved Hybrid Modeling of Spent Fuel Storage Facilities

This work developed a new computational method for improving the ability to calculate the neutron flux in deep-penetration radiation shielding problems that contain areas with strong streaming. The “gold standard” method for radiation transport is Monte Carlo (MC) as it samples the physics exactly and requires few approximations. Historically, however, MC was not useful for shielding problems because of the computational challenge of following particles through dense shields. Instead, deterministic methods, which are superior in term of computational effort for these problems types but are not as accurate, were used. Hybrid methods, which use deterministic solutions to improve MC calculations through a process called variance reduction, can make it tractable from a computational time and resource use perspective to use MC for deep-penetration shielding. Perhaps the most widespread and accessible of these methods are the Consistent Adjoint Driven Importance Sampling (CADIS) and Forward-Weighted CADIS (FW-CADIS) methods. For problems containing strong anisotropies, such as power plants with pipes through walls, spent fuel cask arrays, active interrogation, and locations with small air gaps or plates embedded in water or concrete, hybrid methods are still insufficiently accurate. In this work, a new method for generating variance reduction parameters for strongly anisotropic, deep penetration radiation shielding studies was developed. This method generates an alternate form of the adjoint scalar flux quantity, Φ Ω , which is used by both CADIS and FW-CADIS to generate variance reduction parameters for local and global response functions, respectively. The new method, called CADIS-Ω, was implemented in the Denovo/ADVANTG software. Results indicate that the flux generated by CADIS-Ω incorporates localized angular anisotropies in the flux more effectively than standard methods. CADIS-Ω outperformed CADIS in several test problems. This initial work indicates that CADIS- may be highly useful for shielding problems with strong angular anisotropies. This is a benefit to the public by increasing accuracy for lower computational effort for many problems that have energy, security, and economic importance.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2014

Automated divertor target design by adjoint shape sensitivity analysis and a one-shot method

As magnetic confinement fusion progresses towards the development of first reactor-scale devices, computational tokamak divertor design is a topic of high priority. Presently, edge plasma codes are used in a forward approach, where magnetic field and divertor geometry are manually adjusted to meet design requirements. Due to the complex edge plasma flows and large number of design variables, this method is computationally very demanding. On the other hand, efficient optimization-based design strategies have been developed in computational aerodynamics and fluid mechanics. Such an optimization approach to divertor target shape design is elaborated in the present paper. A general formulation of the design problems is given, and conditions characterizing the optimal designs are formulated. Using a continuous adjoint framework, design sensitivities can be computed at a cost of only two edge plasma simulations, independent of the number of design variables. Furthermore, by using a one-shot method the entire optimization problem can be solved at an equivalent cost of only a few forward simulations. The methodology is applied to target shape design for uniform power load, in simplified edge plasma geometry.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2011

Optimal Control of Heterogeneous Systems with Endogenous Domain of Heterogeneity

The paper deals with optimal control of heterogeneous systems, that is, families of controlled ODEs parameterized by a parameter running over a domain called domain of heterogeneity. The main novelty in the paper is that the domain of heterogeneity is endogenous: it may depend on the control and on the state of the system. This extension is crucial for several economic applications and turns out to rise interesting mathematical problems. A necessary optimality condition is derived, where one of the adjoint variables satisfies a differential inclusion (instead of equation) and the maximization of the Hamiltonian takes the form of 'min-max'. As a consequence, a Pontryagin-type maximum principle is obtained under certain regularity conditions for the optimal control. A formula for the derivative of the objective function with respect to the control from L{sub {infinity}} is presented together with a sufficient condition for its existence. A stylized economic example is investigated analytically and numerically.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Scientific Computational Imaging Code (SCICO)

Scientific Computational Imaging Code (SCICO) is a Python package for solving the inverse problems that arise in scientific imaging applications. Its primary focus is providing methods for solving ill-posed inverse problems by using an appropriate prior model of the reconstruction space. SCICO includes a growing suite of operators, cost functionals, regularizers, and optimization routines that may be combined to solve a wide range of problems, and is designed so that it is easy to add new building blocks. SCICO is built on top of JAX rather than NumPy, enabling GPU/TPU acceleration, just-in-time compilation, and automatic gradient functionality, which is used to automatically compute the adjoints of linear operators. An example of how to solve a multi-channel tomography problem with SCICO is shown in Figure 1. The SCICO source code is available from GitHub, and pre-built packages are available from PyPI. It has extensive online documentation, including API documentation and usage examples, which can be run online at Google Colab and binder.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Development of a Multiphase Adjoint Capability in OpenFOAM

Thermal hydraulic predictions of flow regimes within nuclear reactor cores require significant computational resources and accuracy to ensure that the core design does not violate the thermal limits of materials. Multiphase computational fluid dynamics (CFD) has become a valuable computational capability for predicting flow characteristics as they relate to applications such as nuclear reactor safety and mixing phenomena around spacer grids within fuel assemblies. Multiphase CFD requires closure relationships for both the effects of turbulence as well as the transfer of mass, momentum, and energy between phases. Understanding the sensitivity of the parameters used in closure relationships is important for improving accuracy, but performing rigorous sensitivity analysis is computationally expensive. Adjoint mathematics have been utilized for reactor physics and fluid dynamics applications with respect to verification, sensitivity analysis, adaptive mesh refinement, and optimization. The usage of adjoint methods to predict the sensitivities of a variety of closure relationship parameters within a given problem has been shown to return sensitivity responses with significantly fewer computations than normal 'large-scale' methods. As the complexity of multiphase CFD methods increases, the demand for accurate verification tools and improvements in computational efficiency also increases, making the development of adjoint capabilities an attractive option. Closure relationships that describe interphase momentum physics in multiphase CFD modelling rely heavily on prescribed constants determined from experimental data. Due to the computational efficiency of an adjoint approach, the time to derive these closure relationships could be dramatically reduced, and data assimilation techniques could be used to return probability density functions of closure models derived using experimental data. This work develops a multiphase adjoint capability for the Eulerian-Eulerian two field, two phase equations. Specifically, the adjoint capability has been developed for the sub-cooled nucleate boiling solver boilEulerFoam developed by Dr. Nam Dinh of NC State University within the open-source CFD library OpenFOAM.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗