Search NASA⌕ Search

SEARCH · Search NASA

Results for “adjoint problem”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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

At least 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
NASA NTRS1996

Aerodynamic Shape Optimization of Supersonic Aircraft Configurations via an Adjoint Formulation on Parallel Computers

This work describes the application of a control theory-based aerodynamic shape optimization method to the problem of supersonic aircraft design. The design process is greatly accelerated through the use of both control theory and a parallel implementation on distributed memory computers. Control theory is employed to derive the adjoint differential equations whose solution allows for the evaluation of design gradient information at a fraction of the computational cost required by previous design methods (13, 12, 44, 38). The resulting problem is then implemented on parallel distributed memory architectures using a domain decomposition approach, an optimized communication schedule, and the MPI (Message Passing Interface) Standard for portability and efficiency. The final result achieves very rapid aerodynamic design based on higher order computational fluid dynamics methods (CFD). In our earlier studies, the serial implementation of this design method (19, 20, 21, 23, 39, 25, 40, 41, 42, 43, 9) was shown to be effective for the optimization of airfoils, wings, wing-bodies, and complex aircraft configurations using both the potential equation and the Euler equations (39, 25). In our most recent paper, the Euler method was extended to treat complete aircraft configurations via a new multiblock implementation. Furthermore, during the same conference, we also presented preliminary results demonstrating that the basic methodology could be ported to distributed memory parallel computing architectures [241. In this paper, our concem will be to demonstrate that the combined power of these new technologies can be used routinely in an industrial design environment by applying it to the case study of the design of typical supersonic transport configurations. A particular difficulty of this test case is posed by the propulsion/airframe integration.

Reuther, James↗
NASA NTRS2020

Multi-Impulse to Time Optimal Finite Burn Trajectory Conversion

A novel conversion algorithm is presented that combines the fidelity of indirect optimization methods with the generality of direct methods to more easily solve time-optimal, finite-burn pseudo-rendezvous problems. An algorithm is described that converts a set of multiple-impulses, representing the entirety or a portion of a high- or low-thrust maneuver, to an exact time optimal finite-burn trajectory for a thrust limited, constant exhaust velocity spacecraft. A pseudo-rendezvous problem is one that yields a solution whose final time, position and velocity state is equal to that of the original post-impulsive trajectory. An iterative adjoint-control transformation is used to initialize the optimal control two-point boundary value problem. Examples are shown for both high and low-thrust non-coplanar Earth orbit transfers, as well as a low-thrust Hohmann-type Earth-Mars transfer.

Fogel, J.↗
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↗
NASA NTRSDate not supplied

Linearized Frequency-Domain Gust Analysis and Adjoint-Based Sensitivities

Gust analysis is added to a linearized frequency-domain method in FUN3D, a NASA computational fluid dynamics solver. The method linearizes about a nonlinear static equilibrium condition and is therefore appropriate for problems with small perturbations such as transonic stochastic gust analysis. In addition to the gust analysis, adjoint-based sensitivities of stochastic gust constraints are implemented for multidisciplinary design optimization. The linearized frequency-domain gust model and adjoint-based sensitivities are described and verified. The method is applied to an optimization for mass minimization of the AGARD 445.6 wing subject to a stochastic gust constraint limiting the displacement of the wing tip.

Aeroelasticity↗
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↗
NASA NTRS1990

Statistical analysis of static shape control in space structures

The article addresses the problem of efficient analysis of the statistics of initial and corrected shape distortions in space structures. Two approaches for improving efficiency are considered. One is an adjoint technique for calculating distortion shapes: the second is a modal expansion of distortion shapes in terms of pseudo-vibration modes. The two techniques are applied to the problem of optimizing actuator locations on a 55 m radiometer antenna. The adjoint analysis technique is used with a discrete-variable optimization method. The modal approximation technique is coupled with a standard conjugate-gradient continuous optimization method. The agreement between the two sets of results is good, validating both the approximate analysis and optimality of the results.

Burdisso, Ricardo A.↗
NASA NTRS1993

Boundary layer receptivity and control

Receptivity processes initiate natural instabilities in a boundary layer. The instabilities grow and eventually break down to turbulence. Consequently, receptivity questions are a critical element of the analysis of the transition process. Success in modeling the physics of receptivity processes thus has a direct bearing on technological issues of drag reduction. The means by which transitional flows can be controlled is also a major concern: questions of control are tied inevitably to those of receptivity. Adjoint systems provide a highly effective mathematical method for approaching many of the questions associated with both receptivity and control. The long term objective is to develop adjoint methods to handle increasingly complex receptivity questions, and to find systematic procedures for deducing effective control strategies. The most elementary receptivity problem is that in which a parallel boundary layer is forced by time-harmonic sources of various types. The characteristics of the response to such forcing form the building blocks for more complex receptivity mechanisms. The first objective of this year's research effort was to investigate how a parallel Blasius boundary layer responds to general direct forcing. Acoustic disturbances in the freestream can be scattered by flow non-uniformities to produce Tollmien-Schlichting waves. For example, scattering by surface roughness is known to provide an efficient receptivity path. The present effort is directed towards finding a solution by a simple adjoint analysis, because adjoint methods can be extended to more complex problems. In practice, flows are non-parallel and often three-dimensional. Compressibility may also be significant in some cases. Recent developments in the use of Parabolized Stability Equations (PSE) offer a promising possibility. By formulating and solving a set of adjoint parabolized equations, a method for mapping the efficiency with which external forcing excites the three-dimensional motions of a non-parallel boundary layer was developed. The method makes use of the same computationally efficient formulation that makes the PSE currently so appealing. In the area of flow control, adjoint systems offer a powerful insight into the effect of control forces. One of the simplest control strategies for boundary layers involves the application of localized mean wall suction.

Hill, D. C.↗
NASA NTRS2009

Adjoint-Based Design of Rotors using the Navier-Stokes Equations in a Noninertial Reference Frame

Optimization of rotorcraft flowfields using an adjoint method generally requires a time-dependent implementation of the equations. The current study examines an intermediate approach in which a subset of rotor flowfields are cast as steady problems in a noninertial reference frame. This technique permits the use of an existing steady-state adjoint formulation with minor modifications to perform sensitivity analyses. The formulation is valid for isolated rigid rotors in hover or where the freestream velocity is aligned with the axis of rotation. Discrete consistency of the implementation is demonstrated using comparisons with a complex-variable technique, and a number of single- and multi-point optimizations for the rotorcraft figure of merit function are shown for varying blade collective angles. Design trends are shown to remain consistent as the grid is refined.

Nielsen, Eric J.↗
NASA NTRS2010

Adjoint-Based Design of Rotors Using the Navier-Stokes Equations in a Noninertial Reference Frame

Optimization of rotorcraft flowfields using an adjoint method generally requires a time-dependent implementation of the equations. The current study examines an intermediate approach in which a subset of rotor flowfields are cast as steady problems in a noninertial reference frame. This technique permits the use of an existing steady-state adjoint formulation with minor modifications to perform sensitivity analyses. The formulation is valid for isolated rigid rotors in hover or where the freestream velocity is aligned with the axis of rotation. Discrete consistency of the implementation is demonstrated by using comparisons with a complex-variable technique, and a number of single- and multipoint optimizations for the rotorcraft figure of merit function are shown for varying blade collective angles. Design trends are shown to remain consistent as the grid is refined.

Nielsen, Eric J.↗
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↗
NASA NTRS1984

Sensitivity analysis of discrete structural systems: A survey

Methods for calculating sensitivity derivatives for discrete structural systems are surveyed, primarily covering literature published during the past two decades. Methods are described for calculating derivatives of static displacements and stresses, eigenvalues and eigenvectors, transient structural response, and derivatives of optimum structural designs with respect to problem parameters. The survey is focused on publications addressed to structural analysis, but also includes a number of methods developed in nonstructural fields such as electronics, controls, and physical chemistry which are directly applicable to structural problems. Most notable among the nonstructural-based methods are the adjoint variable technique from control theory, and the Green's function and FAST methods from physical chemistry.

Adelman, H. M.↗
NASA NTRS1986

Sensitivity analysis of discrete structural systems

Methods for calculating sensitivity derivatives for discrete structural systems are surveyed, primarily covering literature published during the past two decades. Methods are described for calculating derivatives of static displacements and stresses, eigenvalues and eigenvectors, transient structural response, and derivatives of optimum structural designs with respect to problem parameters. The survey is focused on publications developed in nonstructural fields such as electronics, controls, and physical chemistry which are directly applicable to structural problems. Most notable among the nonstructural-based methods are the adjoint variable technique from control theory, and the Green's function and FAST methods from physical chemistry.

Adelman, H. M.↗
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↗