A general method for selection and optimization of trajectories.
Space mission trajectory optimization by iterative minimizing of residual vector, using linear correction
SPACECRAFT TRAJECTORY↗
SEARCH · Engineering Papers
Results for “Iteration method”
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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Uniform convergence of multigrid V-cycle iterations for indefinite and nonsymmetric problems
In this paper, we present an analysis of a multigrid method for nonsymmetric and/or indefinite elliptic problems. In this multigrid method various types of smoothers may be used. One type of smoother which we consider is defined in terms of an associated symmetric problem and includes point and line, Jacobi, and Gauss-Seidel iterations. We also study smoothers based entirely on the original operator. One is based on the normal form, that is, the product of the operator and its transpose. Other smoothers studied include point and line, Jacobi, and Gauss-Seidel. We show that the uniform estimates for symmetric positive definite problems carry over to these algorithms. More precisely, the multigrid iteration for the nonsymmetric and/or indefinite problem is shown to converge at a uniform rate provided that the coarsest grid in the multilevel iteration is sufficiently fine (but not depending on the number of multigrid levels).
Bramble, James H.↗
The calculation of steady non-linear transonic flow over finite wings with linear theory aerodynamics
The feasibility of calculating steady mean flow solutions for nonlinear transonic flow over finite wings with a linear theory aerodynamic computer program is studied. The methodology is based on independent solutions for upper and lower surface pressures that are coupled through the external flow fields. Two approaches for coupling the solutions are investigated which include the diaphragm and the edge singularity method. The final method is a combination of both where a line source along the wing leading edge is used to account for blunt nose airfoil effects; and the upper and lower surface flow fields are coupled through a diaphragm in the plane of the wing. An iterative solution is used to arrive at the nonuniform flow solution for both nonlifting and lifting cases. Final results for a swept tapered wing in subcritical flow show that the method converges in three iterations and gives excellent agreement with experiment at alpha = 0 deg and 2 deg. Recommendations are made for development of a procedure for routine application.
Cunningham, A. M., Jr.↗
A DG-IMEX Method for Two-moment Neutrino Transport: Nonlinear Solvers for Neutrino–Matter Coupling
Neutrino-matter interactions play an important role in core-collapse supernova (CCSN) explosions as they contribute to both lepton number and/or four-momentum exchange between neutrinos and matter, and thus act as the agent for neutrino-driven explosions. Due to the multiscale nature of neutrino transport in CCSN simulations, an implicit treatment of neutrino-matter interactions is desired, which requires solutions of coupled nonlinear systems in each step of the time integration scheme. In this paper we design and compare nonlinear iterative solvers for implicit systems with energy coupling neutrino-matter interactions commonly used in CCSN simulations. Specifically, we consider electron neutrinos and antineutrinos, which interact with static matter configurations through the Bruenn 85 opacity set. The implicit systems arise from the discretization of a nonrelativistic two-moment model for neutrino transport, which employs the discontinuous Galerkin (DG) method for phase-space discretization and an implicit-explicit (IMEX) time integration scheme. In the context of this DG-IMEX scheme, we propose two approaches to formulate the nonlinear systems — a coupled approach and a nested approach. For each approach, the resulting systems are solved with Anderson-accelerated fixedpoint iteration and Newton’s method. The performance of these four iterative solvers has been compared on relaxation problems with various degree of collisionality, as well as proto-neutron star deleptonization problems with several matter profiles adopted from spherically symmetric CCSN simulations. Here, numerical results suggest that the nested Anderson-accelerated fixed-point solver is more efficient than other tested solvers for solving implicit nonlinear systems with energy coupling neutrino-matter interactions.
79 ASTRONOMY AND ASTROPHYSICS↗
New Parallel Algorithms for Structural Analysis and Design of Aerospace Structures
Subspace and Lanczos iterations have been developed, well documented, and widely accepted as efficient methods for obtaining p-lowest eigen-pair solutions of large-scale, practical engineering problems. The focus of this paper is to incorporate recent developments in vectorized sparse technologies in conjunction with Subspace and Lanczos iterative algorithms for computational enhancements. Numerical performance, in terms of accuracy and efficiency of the proposed sparse strategies for Subspace and Lanczos algorithm, is demonstrated by solving for the lowest frequencies and mode shapes of structural problems on the IBM-R6000/590 and SunSparc 20 workstations.
Nguyen, Duc T.↗
Efficient computation of optimal low thrust gravity perturbed orbit transfers
We have developed a new method for solving low-thrust fuel-optimal orbit transfer problems in the vicinity of a large body (planet or asteroid), considering a high-fidelity spherical harmonic gravity model. The algorithm is formulated via the indirect optimization method, leading to a two-point boundary value problem (TPBVP). We make use of a hyperbolic tangent smoothing law for performing continuation on the thrust magnitude to reduce the sharpness of the control switches in early iterations and thus promote convergence. The TPBVP is solved using the method of particular solutions (MPS) shooting method and Picard-Chebyshev numerical integration. Application of Picard-Chebyshev integration affords an avenue for increased efficiency that is not available with step-by-step integrators. We demonstrate that computing the particular solutions with only a low-fidelity force model greatly increases the efficiency of the algorithm while ultimately achieving near machine precision accuracy. A salient feature of the MPS is that it is parallelizable, and thus further speedups are available. It is also shown that, for near Earth orbits and over a small number of en-route revolutions around the Earth, only the zonal perturbation terms are required in the costate equations to obtain a solution that is accurate to machine precision and optimal to engineering precision. The proposed framework can be used for trajectory design around small asteroids and also for orbit debris rendezvous and removal tasks.
Junkins, John L.↗
Cas3-Mediated Genome Reduction: Demonstration in Cupriavidus Necator H16 Improves Growth on Heterotrophic and Autotrophic Carbon Sources
Genome reduction is widely used to improve microbial bioprocessing hosts by reducing the burden of inessential physiology. Rationally identifying genomic regions that are dispensable or even detrimental to bioprocessing is challenged by our inability to map genome sequence to function across complex regulation and physiology. Thus, there is a need for tools that rapidly generate reduced genome strains with improved performance in process-relevant conditions. Here, we report a Cascade-Cas3-enabled method called TRIM3 that generates large deletions by targeting a randomly integrated transposon, enabling facile generation of a genome-reduced mutant library. Mutants with improved performance were isolated following growth-coupled selection and analyzed by long-read DNA sequencing to identify deletions in their genomes. We deploy this system iteratively in the industrial host Cupriavidus necator H16 on fructose and on formate. After two rounds of TRIM3, we isolate a strain containing a total reduction of 1.4 Mb (18.4% of the genome) that grows 25% faster in a bioreactor on fructose and a strain with a total reduction of 0.5 Mb (7.3% of the genome) that grows 14% faster on formate. This work demonstrates a method for random, iterative, growth-selectable genome reduction that represents a new avenue for large-scale genome modifications and the development of improved bioprocessing hosts.
09 BIOMASS FUELS↗
A three-dimensional solution of flows over wings with leading-edge vortex separation
The application of a new, general, potential flow computational technique to the solution of the subsonic, three-dimensional flow over wings with leading-edge vortex separation is presented. The present method is capable of predicting forces, moments, and detailed surface pressures on thin, sharp-edged wings of rather arbitrary planform. The wing geometry is arbitrary in the sense that leading and trailing edges may be curved or kinked and the wing may have arbitrary camber and twist. The method employs an inviscid flow model in which the wing, the rolled-up vortex sheets, and the wake are represented by piecewise continuous quadratic doublet sheet distributions. The Kutta condition is imposed along all wing edges. Strengths of the doublet distributions as well as shape and position of the free fortex sheet spirals are computed in iterative fashion starting with an assumed initial sheet geometry. The method is verified by numerous computed results.
Weber, J. A.↗
Automated design of controlled diffusion blades
A numerical automation procedure was developed to be used in conjunction with an inverse hodograph method for the design of controlled diffusion blades. With this procedure a cascade of airfoils with a prescribed solidity, inlet Mach No., inlet air flow angle and air flow turning can be produced automatically. The trailing edge thickness of the airfoil, an important quantity in inverse methods, is also prescribed. The automation procedure consists of a multi-dimensional Newton iteration in which the objective design conditions are achieved by acting on the hodograph input parameters of the underlying inverse code. The method, although more general in scope, is applied to the design of axial flow turbomachinery blade sections, both compressors and turbines. A collaborative effort with U.S. Engine Companies to identify designs of interest to the industry will be described.
Sanz, Jose M.↗
Exploring the Connection Between Sampling Problems in Bayesian Inference and Statistical Mechanics
The Bayesian and statistical mechanical communities often share the same objective in their work - estimating and integrating probability distribution functions (pdfs) describing stochastic systems, models or processes. Frequently, these pdfs are complex functions of random variables exhibiting multiple, well separated local minima. Conventional strategies for sampling such pdfs are inefficient, sometimes leading to an apparent non-ergodic behavior. Several recently developed techniques for handling this problem have been successfully applied in statistical mechanics. In the multicanonical and Wang-Landau Monte Carlo (MC) methods, the correct pdfs are recovered from uniform sampling of the parameter space by iteratively establishing proper weighting factors connecting these distributions. Trivial generalizations allow for sampling from any chosen pdf. The closely related transition matrix method relies on estimating transition probabilities between different states. All these methods proved to generate estimates of pdfs with high statistical accuracy. In another MC technique, parallel tempering, several random walks, each corresponding to a different value of a parameter (e.g. "temperature"), are generated and occasionally exchanged using the Metropolis criterion. This method can be considered as a statistically correct version of simulated annealing. An alternative approach is to represent the set of independent variables as a Hamiltonian system. Considerab!e progress has been made in understanding how to ensure that the system obeys the equipartition theorem or, equivalently, that coupling between the variables is correctly described. Then a host of techniques developed for dynamical systems can be used. Among them, probably the most powerful is the Adaptive Biasing Force method, in which thermodynamic integration and biased sampling are combined to yield very efficient estimates of pdfs. The third class of methods deals with transitions between states described by rate constants. These problems are isomorphic with chemical kinetics problems. Recently, several efficient techniques for this purpose have been developed based on the approach originally proposed by Gillespie. Although the utility of the techniques mentioned above for Bayesian problems has not been determined, further research along these lines is warranted
Pohorille, Andrew↗
Tungsten control in long pulse operation: feedback from WEST to ITER
The full W environment that is now foreseen for ITER puts strong emphasis on experimental results obtained in present devices in similar conditions. In this context, the WEST tokamak is well equipped to bring key contributions to the preparation of ITER operation, thanks to its capability to perform long pulses in dominant electron heating, torque-free scheme based on RF systems, and its ITER-grade actively cooled divertor. Recent results of interest cover the understanding of tungsten contamination and the evaluation of conditioning methods, the feedback on the current ramp-up phase, and the ageing of the ITER divertor components in L-mode attached condition. Further, new directions are being explored, in particular low divertor temperature operation that should be the normal operating regime of ITER. We also report on tungsten peaking physics, and the role of light impurity content.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
A comparative study of an ABC and an artificial absorber for truncating finite element meshes
The type of mesh termination used in the context of finite element formulations plays a major role on the efficiency and accuracy of the field solution. The performance of an absorbing boundary condition (ABC) and an artificial absorber (a new concept) for terminating the finite element mesh was evaluated. This analysis is done in connection with the problem of scattering by a finite slot array in a thick ground plane. The two approximate mesh truncation schemes are compared with the exact finite element-boundary integral (FEM-BI) method in terms of accuracy and efficiency. It is demonstrated that both approximate truncation schemes yield reasonably accurate results even when the mesh is extended only 0.3 wavelengths away from the array aperture. However, the artificial absorber termination method leads to a substantially more efficient solution. Moreover, it is shown that the FEM-BI method remains quite competitive with the FEM-artificial absorber method when the FFT is used for computing the matrix-vector products in the iterative solution algorithm. These conclusions are indeed surprising and of major importance in electromagnetic simulations based on the finite element method.
Oezdemir, T.↗
Computing Contact Stresses In Gear Teeth
Improved method of computing contact stresses in gear teeth accounts for complicating effects like those of static and sliding friction. Provides iterative procedure for determination of contact region and nodal contact forces along with contact stresses. Method based on equations and computational procedure incorporating these effects routinely.
Oswald, Fred B.↗
Energy Exascale Computational Fluid Dynamics Simulations With the Spectral Element Method
Development and application of the open-source GPU-based fluid-thermal simulation code, NekRS, are described. Time advancement is based on an efficient kth-order accurate timesplit formulation coupled with scalable iterative solvers. Spatial discretization is based on the high-order spectral element method (SEM), which affords the use of fast, low-memory, matrix-free operator evaluation. Further, recent developments include support for nonconforming meshes using overset grids and for GPU-based Lagrangian particle tracking. Results of large-eddy simulations of atmospheric boundary layers for wind-energy applications as well as extensive nuclear energy applications are presented.
42 ENGINEERING↗
Domain Decomposition Algorithms for First-Order System Least Squares Methods
Least squares methods based on first-order systems have been recently proposed and analyzed for second-order elliptic equations and systems. They produce symmetric and positive definite discrete systems by using standard finite element spaces, which are not required to satisfy the inf-sup condition. In this paper, several domain decomposition algorithms for these first-order least squares methods are studied. Some representative overlapping and substructuring algorithms are considered in their additive and multiplicative variants. The theoretical and numerical results obtained show that the classical convergence bounds (on the iteration operator) for standard Galerkin discretizations are also valid for least squares methods.
Pavarino, Luca F.↗
Contact stresses in gear teeth: A new method of analysis
A new, innovative procedure called point load superposition for determining the contact stresses in mating gear teeth. It is believed that this procedure will greatly extend both the range of applicability and the accuracy of gear contact stress analysis. Point load superposition is based upon fundamental solutions from the theory of elasticity. It is an iterative numerical procedure which has distinct advantages over the classical Hertz method, the finite element method, and over existing applications with the boundary element method. Specifically, friction and sliding effects, which are either excluded from or difficult to study with the classical methods, are routinely handled with the new procedure. Presented here are the basic theory and the algorithms. Several examples are given. Results are consistent with those of the classical theories. Applications to spur gears are discussed.
Somprakit, Paisan↗
Tracing structural optima as a function of available resources by a homotopy method
Optimization problems are typically solved by starting with an initial estimate and proceeding iteratively to improve it until the optimum is found. The design points along the path from the initial estimate to the optimum are usually of no value. The present work proposes a strategy for tracing a path of optimum solutions parameterized by the amount of available resources. The paper specifically treats the optimum design of a structure to maximize its buckling load. Equations for the optimum path are obtained using Lagrange multipliers, and solved by a homotopy method. The solution path has several transitions from unimodal to bimodal solutions. The Lagrange multipliers and second-order optimality conditions are used to detect branching points and to switch to the optimum solution path. The procedure is applied to the design of a foundation which supports a column for maximum buckling load. Using the total available foundation stiffness as a homotopy parameter, a set of optimum foundation designs is obtained.
Haftka, Raphael T.↗
Contact stresses in gear teeth - A new method of analysis
A new, innovative procedure called point load superposition for determining the contact stresses in mating gear teeth is presented. It is believed that this procedure will greatly extend both the range of applicability and the accuracy of gear contact stress analysis. Point load superposition is based upon fundamental solutions from the theory of elasticity. It is an iterative numerical procedure which has distinct advantages over the classical Hertz method, the finite element method, and over existing applications with the boundary element method. Specifically, friction and sliding effects, which are either excluded from or difficult to study with the classical methods, are routinely handled with the new procedure. Presented here are the basic theory and the algorithms. Several examples are given. Results are consistent with those of the classical theories. Applications to spur gears are discussed.
Somprakit, Paisan↗