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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 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Time-dependent SOLPS-ITER simulations of the tokamak plasma boundary for model predictive control using SINDy *

Abstract Time-dependent SOLPS-ITER simulations have been used to identify reduced models with the sparse identification of nonlinear dynamics (SINDy) method and develop model-predictive control of the boundary plasma state using main ion gas puff actuation. A series of gas actuation sequences are input into SOLPS-ITER to produce a dynamic response in upstream and divertor plasma quantities. The SINDy method is applied to identify reduced linear and nonlinear models for the electron density at the outboard midplane n e , s e p O M P and the electron temperature at the outer divertor T e , s e p d i v . Note that T e , s e p d i v is not necessarily the peak value of T e along the divertor. The identified reduced models are interpretable by construction (i.e. not black box), and have the form of coupled ordinary differential equations. Despite significant noise in T e , s e p d i v , the reduced models can be used to predict the response over a range of actuation levels to a maximum deviation of 0.5% in n e , s e p O M P and 5%–10% in T e , s e p d i v for the cases considered. Model retraining using time history data triggered by a preset error threshold is also demonstrated. A model predictive control strategy for nonlinear models is developed and used to perform feedback control of a SOLPS-ITER simulation to produce a setpoint trajectory in n e , s e p O M P using the integrated plasma simulator framework. The developed techniques are general and can be applied to time-dependent data from other boundary simulations or experimental data. Ongoing work is extending the approach to model identification and control for divertor detachment, which will present transient nonlinear behavior from impurity seeding, including realistic latency and synthetic diagnostic signals derived from the full SOLPS-ITER output.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Estimation of conditional cumulative incidence functions under generalized semiparametric regression models with missing covariates, with application to analysis of biomarker correlates in vaccine trials

Herein, this article presents generalized semiparametric regression models for conditional cumulative incidence functions with competing risks data when covariates are missing by sampling design or happenstance. A doubly robust augmented inverse probability weighted (AIPW) complete-case approach to estimation and inference is investigated. This approach modifies IPW complete-case estimating equations by exploiting the key features in the relationship between the missing covariates and the phase-one data to improve efficiency. An iterative numerical procedure is derived to solve the nonlinear estimating equations. The asymptotic properties of the proposed estimators are established. A simulation study examining the finite-sample performances of the proposed estimators shows that the AIPW estimators are more efficient than the IPW estimators. The developed method is applied to the RV144 HIV-1 vaccine efficacy trial to investigate vaccine-induced IgG binding antibodies to HIV-1 as correlates of acquisition of HIV-1 infection while taking account of whether the HIV-1 sequences are near or far from the HIV-1 sequences represented in the vaccine construct.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

A Parallel Cut-Cell Algorithm for the Free-Boundary Grad--Shafranov Problem

A parallel cut-cell algorithm is described to solve the free-boundary problem of the Grad--Shafranov equation. The algorithm reformulates the free-boundary problem in an irregular bounded domain and its important aspects include a searching algorithm for the magnetic axis and separatrix, a surface integral along the irregular boundary to determine the boundary values, an approach to optimize the coil current based on a targeting plasma shape, Picard iterations with Aitken's acceleration for the resulting nonlinear problem, and a Cartesian grid embedded boundary method to handle the complex geometry. Here the algorithm is implemented in parallel using a standard domain-decomposition approach and a good parallel scaling is observed. Numerical results verify the accuracy and efficiency of the free-boundary Grad--Shafranov solver.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Topology optimization of 3D photonic crystals with complete bandgaps

The design of photonic crystals with complete bandgaps has recently received considerable research focus for numerous reasons. This work leverages well-known nonlinear programming techniques to alleviate the non-smoothness caused by degenerate eigenvalues such that topology optimization problems can be solved with the open-source IPOPT software. A fully-vectorial plane wave expansion technique is used with an iterative eigensolver to efficiently predict dispersion properties of candidate structures. Nonlinear programming is employed to solve the inverse problem of designing three-dimensional periodic structures that exhibit complete two-dimensional (2D) and three-dimensional (3D) photonic bandgaps. Mesh refinement is performed to alleviate the large computational burden of designing and analyzing photonic crystals, and a periodic density filter is implemented to impose a minimum feature size for manufacturability considerations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Anderson acceleration stability in NDA-accelerated k-eigenvalue problems

Anderson acceleration (AA) has been used to improve the stability and convergence rate of multiphysics iterative methods for reactor analysis. Most applications studied assume a tightly converged solution for the different physics problems, and AA is usually applied to state variables like temperature, density, and heat generation rate. In this paper, we study the theoretical performance of AA in NDA-accelerated k-eigenvalue problems. The problems and algorithms studied are simplified from the coupled iteration scheme adopted by MPACT and many other high-fidelity whole-core reactor codes. Compared to previous analyses of AA for these iteration schemes, we study the case with a partially converged neutronics solution and possibly partially converged nonlinear diffusion acceleration (NDA)/coarse mesh finite difference (CMFD) solutions. We observe that the performance of the iteration scheme with AA is very sensitive to the initial guess and is affected by the partially converged CMFD solutions. When the NDA solution is fully converged, using AA cannot achieve the optimal convergence rate in large-sized problems. Conversely, if the NDA solution is partially converged, the iteration scheme with AA can diverge or converge extremely slowly. It is found that the loss of robustness for AA is due to the fact that it is applied to the iterative subspace of state variables rather than the fundamental unknowns of the governing equations. To improve the robustness, the scalar flux should also be considered in the implementation of AA. After considering the residuals of flux, we observe that the stability is regardless of the partial convergence of NDA solutions. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

On a fully-implicit VMS-stabilized FE formulation for low Mach number compressible resistive MHD with application to MCF

This study presents the development and evaluation of a fully-implicit variational multiscale (VMS) stabilized unstructured finite element (FE) formulation for compressible magnetohydrodynamics (MHD) model, at low Mach number regime. The model describes the dynamics of a compressible conducting fluid in the low Mach number limit in the presence of electromagnetic fields and can be used to study aspects of astrophysical phenomena, important science and technology applications, and basic plasma physics phenomena. The specific applications that motivate this study are macroscopic simulations of the longer time-scale stability and disruptions of magnetic confinement fusion (MCF) devices, specifically the ITER tokamak. The discussion considers the development of the VMS FE representation, the structure of the stabilizing terms that deal with significant convective flows, the stabilization of the nearly incompressible response of the fluid flow, and the stabilization of the constraint that enforces the solenoidal involution on the magnetic field. The nonlinear discretized system is solved with scalable preconditioned Newton–Krylov iterative methods, which employs a multiphysics block preconditioning method based on approximate block factorizations and Schur complements. The study presents an evaluation of the VMS method on a 2D cartesian tearing mode instability, and illustrates the scalability of the solvers on MCF relevant problems. A set of results are also presented for longer time-scale stability and disruptions for the ITER tokamak. These include a vertical displacement event (VDE), and a (1,1) internal kink mode. Here, the formulation is demonstrated to be scalable and also reasonably robust with respect to the Lundquist number scaling.

42 ENGINEERING↗
DOE OSTI2021

Modeling iterative reconstruction and displacement field in the large scale structure

The next generation of galaxy surveys like the Dark Energy Spectroscopic Instrument and Euclid will provide datasets orders of magnitude larger than anything available to date. Our ability to model nonlinear effects in late time matter perturbations will be a key to unlock the full potential of these datasets, and the area of initial condition reconstruction is attracting growing attention. Iterative reconstruction developed by Marcel Schmittfull et al. is a technique designed to reconstruct the displacement field from the observed galaxy distribution. The nonlinear displacement field and initial linear density field are highly correlated. Therefore, reconstructing the nonlinear displacement field enables us to extract the primordial cosmological information better than from the late time density field at the level of the two-point statistics. This paper will test to what extent the iterative reconstruction can recover the true displacement field and construct a perturbation theory model for the postreconstructed field. We model the iterative reconstruction process with Lagrangian perturbation theory (LPT) up to third order for dark matter in real space and compare it with N-body simulations. Here we find that the simulated iterative reconstruction does not converge to the nonlinear displacement field, and the discrepancy mainly appears in the shift term, i.e., the term correlated directly with the linear density field. On the contrary, our 3LPT model predicts that the iterative reconstruction should converge to the nonlinear displacement field. We discuss the sources of discrepancy, including numerical noise/artifacts on small scales, and present an ad hoc phenomenological model that improves the agreement.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Advanced Newton methods for geodynamical models of Stokes flow with viscoplastic rheologies

Strain localization and resulting plasticity and failure play an important role in the evolution of the lithosphere. These phenomena are commonly modeled by Stokes flows with viscoplastic rheologies. The nonlinearities of these rheologies make the numerical solution of the resulting systems challenging, and iterative methods often converge slowly or not at all. Yet accurate solutions are critical for representing the physics. Moreover, for some rheology laws, aspects of solvability are still unknown. We study a basic but representative viscoplastic rheology law. The law involves a yield stress that is independent of the dynamic pressure, referred to as von Mises yield criterion. Two commonly used variants, perfect/ideal and composite viscoplasticity, are compared. We derive both variants from energy minimization principles, and we use this perspective to argue when solutions are unique. We propose a new stress-velocity Newton solution algorithm that treats the stress as an independent variable during the Newton linearization but requires solution only of Stokes systems that are of the usual velocity-pressure form. To study different solution algorithms, we implement 2-D and 3-D finite element discretizations, and we generate Stokes problems with up to 7 orders of magnitude viscosity contrasts, in which compression or tension results in significant nonlinear localization effects. Comparing the performance of the proposed Newton method with the standard Newton method and the Picard fixed-point method, we observe a significant reduction in the number of iterations and improved stability with respect to problem nonlinearity, mesh refinement, and the polynomial order of the discretization.

Rudi, Johann↗
DOE OSTI2021

Network-Level Optimization for Unbalanced Power Distribution System: Approximation and Relaxation

The nonlinear programming (NLP) problem to solve distribution-level optimal power flow (D-OPF) poses convergence issues and does not scale well for unbalanced distribution systems. The existing scalable D-OPF algorithms either use approximations that are not valid for an unbalanced power distribution system, or apply relaxation techniques to the nonlinear power flow equations that do not guarantee a feasible power flow solution. In this paper, we propose scalable D-OPF algorithms that simultaneously achieve optimal and feasible solutions by solving multiple iterations of approximate, or relaxed, D-OPF subproblems of low complexity. The first algorithm is based on a successive linear approximation of the nonlinear power flow equations around the current operating point, where the D-OPF solution is obtained by solving multiple iterations of a linear programming (LP) problem. The second algorithm is based on the relaxation of the nonlinear power flow equations as conic constraints together with directional constraints, which achieves optimal and feasible solutions over multiple iterations of a second-order cone programming (SOCP) problem. Finally, it is demonstrated that the proposed algorithms are able to reach an optimal and feasible solution while significantly reducing the computation time as compared to an equivalent NLPD-OPF model for the same distribution system.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

Nonlinear saturation of whistler modes driven by runaway electrons

Runaway electrons exhibit kinetic instabilities with potentially beneficial consequences. The anomalous Doppler resonance between the electrons and whistler modes is a primary underlying mechanism. These instabilities require a first-principle nonlinear theoretical analysis, which would ultimately enable assessment of their impact on disruption mitigation and diagnostics, especially in ITER-relevant conditions. This paper presents recent progress in developing the required theoretical framework for isolated nonlinear resonances. By employing the generic bump-on-tail model, we predict the wave saturation levels in both near-threshold and strongly driven regimes. Remarkably, for the waves of interest, the parallel component of the wave vector dictates the parallel momentum of the resonant particles. This feature, together with the expected wave saturation level, provides a complete description of the resonance impact on the runaway electron distribution function. We show that the parametric dependence of the nonlinearly saturated mode provides a way to recover certain features of the runaway momentum distribution function.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Toward large-scale simulation of residual stress and distortion in wire and arc additive manufacturing

In this study, we aim to advance the structural analysis of wire and arc additive manufacturing (WAAM) by considering the thermomechanical features inherent in direct energy deposition. Simulation approaches including the iterative substructure method (ISM), dynamic mesh refining method (DMRM), and graphics processing unit (GPU) based explicit finite element method (FEM) were developed for accelerating additive manufacturing stress analysis that is very time consuming by conventional numerical methods. ISM and DMRM take advantage of the strong nonlinearity phenomenon near the moving heat source by reducing the global iterations and refining the local mesh, respectively. In addition to the use of GPUs, the explicit FEM is accelerated by a time scaling technique based on the inherent strain concept. The residual stress and distortion of two large builds were analyzed, showing very consistent numerical results and good agreement with experiments. Compared with the commercial software Abaqus, the novel approaches reduced the computational cost substantially without compromising accuracy. The GPU code showed the highest computational efficiency (30~70×), while DMRM and ISM had acceleration factors of 9× and 3×, respectively. Finally, such high-fidelity modeling approaches will be very useful for building up a digital twin of WAAM to reduce development time and cost.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Convergence Analysis of the Alternating Anderson–Picard Method for Nonlinear Fixed-Point Problems

Anderson acceleration (AA) has been widely used to solve nonlinear fixed-point problems due to its rapid convergence. This work focuses on a variant of AA in which multiple Picard iterations are performed between each AA step, referred to as the Alternating Anderson–Picard (AAP) method. Furthermore, despite introducing more “slow” Picard iterations, this method has been shown to be efficient and even more robust in both linear and nonlinear cases. However, there is a lack of theoretical analysis for AAP in the nonlinear case. In this paper, we address this gap by establishing the equivalence between AAP and a multisecant-GMRES method that uses GMRES to solve a multisecant linear system at each iteration. From this perspective, we show that AAP “converges” to the Newton-GMRES method. Specifically, as the residual approaches zero, the multisecant matrix, the approximate Jacobian inverse, the search direction, and the optimization gain of AAP converge to their counterparts in the Newton-GMRES method. These connections provide insights for analyzing the asymptotic convergence properties of AAP. Consequently, we show that AAP is locally 𝑞-linear convergent and provide an upper bound for the convergence factor of AAP. To validate the theoretical results, numerical examples are provided.

Anderson acceleration↗
DOE OSTI2022

Alternative formulation of weak magnetohydrodynamic turbulence theory

In a recent paper, the weak turbulence theory for incompressible magnetohydrodynamics is formulated by employing the method customarily applied in the context of kinetic weak plasma turbulence theory. Such an approach simplified certain mathematical procedures including achieving the closure relationship. The formulation in the above-cited paper starts from the equations of incompressible magnetohydrodynamic (MHD) theory expressed via Elsasser variables. The derivation of nonlinear wave kinetic equation therein is obtained via a truncated solution at the second-order of iteration following the standard practice. In the present paper, the weak MHD turbulence theory is alternatively formulated by employing the pristine form of incompressible MHD equation rather than that expressed in terms of Elsasser fields. The perturbative expansion of the nonlinear momentum equation is carried out up to the third-order iteration rather than imposing the truncation at the second order. Furthermore, it is found that while the resulting wave kinetic equation is identical to that obtained in the previous paper cited above, the third-order nonlinear correction plays an essential role for properly calculating derived quantities such as the total and residual energies.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

A Graphics Processing Unit–Based, Industrial Grade Compositional Reservoir Simulator

Summary Recently, graphics processing units (GPUs) have been demonstrated to provide a significant performance benefit for black-oil reservoir simulation, as well as flash calculations that serve an important role in compositional simulation. A comprehensive approach to compositional simulation based on GPUs has yet to emerge, and the question remains as to whether the benefits observed in black-oil simulation persist with a more complex fluid description. We present a positive answer to this question through the extension of a commercial GPU-based black-oil simulator to include a compositional description based on standard cubic equations of state (EOSs). We describe the motivations for the selected nonlinear formulation, including the choice of primary variables and iteration scheme, and support for both fully implicit methods (FIMs) and adaptive implicit methods (AIMs). We then present performance results on an example sector model and simplified synthetic case designed to allow a detailed examination of runtime and memory scaling with respect to the number of hydrocarbon components and model size, as well as the number of processors. We finally show results from two complex asset models (synthetic and real) and examine performance scaling with respect to GPU generation, demonstrating that performance correlates strongly with GPU memory bandwidth. NOTE: This paper is also published as part of the 2021 SPE Reservoir Simulation Conference Special Issue.

Engineering↗
DOE OSTI2022

Development and Analysis of Optimal Multilevel Solvers on Advanced Computers. Final Report

Constrained optimization in the context of time dependent, partial differential equations (PDE) leads to a symmetric, block-tridiagonal system of nonlinear equations that must be solved repeatedly in an iterative solution strategy. The blocks represent spatial discretization, while the connection between the blocks represents a forward and backward integration in time. The focus of this project is to apply a parallel-in-time (PiT) solution technique to the large block-triangular system.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Parallel-in-Time Solution of Hyperbolic PDE Systems via Characteristic-Variable Block Preconditioning

We consider the parallel-in-time solution of both linear and nonlinear hyperbolic partial differential equation (PDE) systems in one spatial dimension. In the nonlinear setting, the discretized equations are solved with a preconditioned residual iteration based on a global linearization. The linear(ized) equation systems are approximately solved parallel-in-time using a block preconditioner applied in the characteristic variables of the underlying linear(ized) hyperbolic PDE. This change of variables is motivated by the observation that intervariable coupling between characteristic variables is weak, at least locally where spatio-temporal variations in the eigenvectors of the associated flux Jacobian are sufficiently small, while that between the original variables is not. For an ℓ-dimensional system of PDEs, applying the preconditioner consists of solving a sequence of ℓ scalar linear(ized)-advection-like problems, each associated with a different characteristic wave-speed in the underlying linear(ized) PDE. Furthermore, we approximately solve these linear advection problems using multigrid reduction-in-time (MGRIT); however, any other suitable parallel-in-time method could be used. Numerical examples are shown for the (linear) acoustics equations in heterogeneous media and for the (nonlinear) shallow water equations and Euler equations of gas dynamics with shocks and rarefactions. For many test problems, the solver converges in just a handful of iterations and with mesh-independent convergence rates.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Accelerating the solution of the S N equations with highly anisotropic scattering using the Fokker-Planck approximation

The discrete ordinates method can model forward-peaked transport problems accurately. However, convergence of discrete ordinates solution can become arbitrarily slow upon use of standard iterative procedures like source iteration. Standard zeroth and first moment-based acceleration methods like nonlinear diffusion acceleration and diffusion synthetic acceleration are ineffective in accelerating such problems because these methods do not correct higher order Legendre-moments of angular flux. In this paper, we explore the idea of using the Fokker-Planck approximation as a preconditioner to accelerate the convergence of solution of forward-peaked transport problems. Finally, we observe that such preconditioning can successfully reduce the iteration count by up to four orders of magnitude, and solver runtime by up to three orders of magnitude when compared to diffusion synthetic acceleration.

42 ENGINEERING↗
DOE OSTI2020

PPINN: Parareal physics-informed neural network for time-dependent PDEs

Physics-informed neural networks (PINNs) encode physical conservation laws and prior physical knowledge into the neural networks, ensuring the correct physics is represented accurately while alleviating the need for supervised learning to a great degree. While effective for relatively short-term time integration, when long time integration of the time-dependent PDEs is sought, the time–space domain may become arbitrarily large and hence training of the neural network may become prohibitively expensive. To this end, we develop a parareal physics-informed neural network (PPINN), hence decomposing a long-time problem into many independent short-time problems supervised by an inexpensive/fast coarse-grained (CG) solver. In particular, the serial CG solver is designed to provide approximate predictions of the solution at discrete times, while initiate many fine PINNs simultaneously to correct the solution iteratively. There is a two-fold benefit from training PINNs with small-data sets rather than working on a large-data set directly, i.e., training of individual PINNs with small-data is much faster, while training the fine PINNs can be readily parallelized. Consequently, compared to the original PINN approach, the proposed PPINN approach may achieve a significant speed-up for long-time integration of PDEs, assuming that the CG solver is fast and can provide reasonable predictions of the solution, hence aiding the PPINN solution to converge in just a few iterations. To investigate the PPINN performance on solving time-dependent PDEs, we first apply the PPINN to solve the Burgers equation, and subsequently we apply the PPINN to solve a two-dimensional nonlinear diffusion–reaction equation. Furthermore, our results demonstrate that PPINNs converge in a few iterations with significant speed-ups proportional to the number of time-subdomains employed.

42 ENGINEERING↗