Inverse atmospheric radiative transfer problems - A nonlinear minimization search method of solution
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Cerni, T. A.↗
SEARCH · Engineering Papers
Results for “NONLINEAR PROBLEMS”
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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Bounding solutions of geometrically nonlinear viscoelastic problems
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Stubstad, John M.↗
An adaptive characteristic Petrov-Galerkin finite element method for convection-dominated linear and nonlinear parabolic problems in one space variable
The present adaptive FEM technique for convection-dominated problems is based on a Petrov-Galerkin scheme for spatial approximation, whose typical time-step employs test functions chosen to yield an approximate solution coinciding with the exact solutions at the finite element grid nodes. The derivation of truly local a posteriori error estimates is made possible by this procedure, which is also shown to be a very effective solver by the numerical examples presented.
Demkowicz, L.↗
On the discretization of some second order in time differential equations - Applications to nonlinear wave problems
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Dean, E. J.↗
Solution of geometrically nonlinear statics problems by the p-version of the finite element method
This project is concerned with the possibility of using computers for the simulation of structural systems with the same degree of reliability as full scale physical experiments. Reliable numerical simulation will make it possible to reduce the costs of engineering and improve the quality of engineering decisions based on computed information. An error of idealization is an error between the actual physical quantities on which engineering decisions are based (e.g., maximum principal stress, first natural frequency, etc.) and the same data corresponding to the exact solution of the mathematical model. An error of discretization is an error between the quantities of interest corresponding to the exact and approximate solutions of a mathematical model. A high degree of reliability can be achieved in numerical simulation only if both the errors of idealization and errors of discretization can be shown to be small.
Szabo, Barna A.↗
The linearized characteristics method and its application to practical nonlinear supersonic problems
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Ferri, Antonio↗
New Algorithms for Estimating Spacecraft Position Using Scanning Techniques for Deep Space Network Antennas
As more and more nonlinear estimation techniques become available, our interest is in finding out what performance improvement, if any, they can provide for practical nonlinear problems that have been traditionally solved using linear methods. In this paper we examine the problem of estimating spacecraft position using conical scan (conscan) for NASA's Deep Space Network antennas. We show that for additive disturbances on antenna power measurement, the problem can be transformed into a linear one, and we present a general solution to this problem, with the least square solution reported in literature as a special case. We also show that for additive disturbances on antenna position, the problem is a truly nonlinear one, and we present two approximate solutions based on linearization and Unscented Transformation respectively, and one 'exact' solution based on Markov Chain Monte Carlo (MCMC) method. Simulations show that, with the amount of data collected in practice, linear methods perform almost the same as MCMC methods. It is only when we artificially reduce the amount of collected data and increase the level of noise that nonlinear methods show significantly better accuracy than that achieved by linear methods, at the expense of more computation.
Metropolis-Hastings (MH)↗
Building Blocks for Reliable Complex Nonlinear Numerical Simulations
This chapter describes some of the building blocks to ensure a higher level of confidence in the predictability and reliability (PAR) of numerical simulation of multiscale complex nonlinear problems. The focus is on relating PAR of numerical simulations with complex nonlinear phenomena of numerics. To isolate sources of numerical uncertainties, the possible discrepancy between the chosen partial differential equation (PDE) model and the real physics and/or experimental data is set aside. The discussion is restricted to how well numerical schemes can mimic the solution behavior of the underlying PDE model for finite time steps and grid spacings. The situation is complicated by the fact that the available theory for the understanding of nonlinear behavior of numerics is not at a stage to fully analyze the nonlinear Euler and Navier-Stokes equations. The discussion is based on the knowledge gained for nonlinear model problems with known analytical solutions to identify and explain the possible sources and remedies of numerical uncertainties in practical computations. Examples relevant to turbulent flow computations are included.
Yee, H. C.↗
Building Blocks for Reliable Complex Nonlinear Numerical Simulations
This talk describes some of the building blocks to ensure a higher level of confidence in the predictability and reliability (PAR) of numerical simulation of multiscale complex nonlinear problems. The focus is on relating PAR of numerical simulations with complex nonlinear phenomena of numerics. To isolate sources of numerical uncertainties, the possible discrepancy between the chosen partial differential equation (PDE) model and the real physics and/or experimental data is set aside. The discussion is restricted to how well numerical schemes can mimic the solution behavior of the underlying PDE model for finite time steps and grid spacings. The situation is complicated by the fact that the available theory for the understanding of nonlinear behavior of numerics is not at a stage to fully analyze the nonlinear Euler and Navier-Stokes equations. The discussion is based on the knowledge gained for nonlinear model problems with known analytical solutions to identify and explain the possible sources and remedies of numerical uncertainties in practical computations. Examples relevant to turbulent flow computations are included.
Yee, H. C.↗
Reliability of Complex Nonlinear Numerical Simulations
This work describes some of the procedure to ensure a higher level of confidence in the predictability and reliability (PAR) of numerical simulation of multiscale complex nonlinear problems. The focus is on relating PAR of numerical simulations with complex nonlinear phenomena of numerics. To isolate sources of numerical uncertainties, the possible discrepancy between the chosen partial differential equation (PDE) model and the real physics and/or experimental data is set aside. The discussion is restricted to how well numerical schemes can mimic the solution behavior of the underlying PDE model for finite time steps and grid spacings. The situation is complicated by the fact that the available theory for the understanding of nonlinear behavior of numerics is not at a stage to fully analyze the nonlinear Euler and Navier-Stokes equations. The discussion is based on the knowledge gained for nonlinear model problems with known analytical solutions to identify and explain the possible sources and remedies of numerical uncertainties in practical computations. Examples relevant to turbulent flow computations are included.
Yee, H. C.↗
Building Blocks for Reliable Complex Nonlinear Numerical Simulations
This chapter describes some of the building blocks to ensure a higher level of confidence in the predictability and reliability (PAR) of numerical simulation of multiscale complex nonlinear problems. The focus is on relating PAR of numerical simulations with complex nonlinear phenomena of numerics. To isolate sources of numerical uncertainties, the possible discrepancy between the chosen partial differential equation (PDE) model and the real physics and/or experimental data is set aside. The discussion is restricted to how well numerical schemes can mimic the solution behavior of the underlying PDE model for finite time steps and grid spacings. The situation is complicated by the fact that the available theory for the understanding of nonlinear behavior of numerics is not at a stage to fully analyze the nonlinear Euler and Navier-Stokes equations. The discussion is based on the knowledge gained for nonlinear model problems with known analytical solutions to identify and explain the possible sources and remedies of numerical uncertainties in practical computations.
Yee, H. C.↗
Iterative methods for solving nonlinear least squares problems
Iterative methods for solving nonlinear least squares problems
ITERATIVE SOLUTION↗
A solution of nonlinear plane strain problems in dynamic soil mechanics
Nonlinear plane strain problems in dynamic soil mechanics and solutions for spacecraft landing loads
Cox, W. R.↗
Application of symbolic and algebraic manipulation software in solving applied mechanics problems
As its name implies, symbolic and algebraic manipulation is an operational tool which not only can retain symbols throughout computations but also can express results in terms of symbols. This report starts with a history of symbolic and algebraic manipulators and a review of the literatures. With the help of selected examples, the capabilities of symbolic and algebraic manipulators are demonstrated. These applications to problems of applied mechanics are then presented. They are the application of automatic formulation to applied mechanics problems, application to a materially nonlinear problem (rigid-plastic ring compression) by finite element method (FEM) and application to plate problems by FEM. The advantages and difficulties, contributions, education, and perspectives of symbolic and algebraic manipulation are discussed. It is well known that there exist some fundamental difficulties in symbolic and algebraic manipulation, such as internal swelling and mathematical limitation. A remedy for these difficulties is proposed, and the three applications mentioned are solved successfully. For example, the closed from solution of stiffness matrix of four-node isoparametrical quadrilateral element for 2-D elasticity problem was not available before. Due to the work presented, the automatic construction of it becomes feasible. In addition, a new advantage of the application of symbolic and algebraic manipulation found is believed to be crucial in improving the efficiency of program execution in the future. This will substantially shorten the response time of a system. It is very significant for certain systems, such as missile and high speed aircraft systems, in which time plays an important role.
Tsai, Wen-Lang↗
Non-local sub-characteristic zones of influence in unsteady interactive boundary-layers
The properties of incompressible, unsteady, interactive, boundary layers are examined for a model hypersonic boundary layer and internal flow past humps or, equivalently, external flow past short-scaled humps. Using a linear high frequency analysis, it is shown that the domains of dependence within the viscous sublayer may be a strong function of position within the sublayer and may be strongly influenced by the pressure displacement interaction, or the prescribed displacement condition. Detailed calculations are presented for the hypersonic boundary layer. This effect is found to carry over directly to the fully viscous problem as well as the nonlinear problem. In the fully viscous problem, the non-local character of the domains of dependence manifests itself in the sub-characteristics. Potential implications of the domain of dependence structure on finite difference computations of unsteady boundary layers are briefly discussed.
Rothmayer, A. P.↗
The Transport of Mass, Energy, and Entropy in Cryogenic Support Struts for Engineering Design
Engineers working to understand and reduce cryogenic boil-off must solve a. variety of transport problems. An important class of nonlinear problems involves the thermal and mechanical design of cryogenic struts. These classic problems are scattered about the literature and typically require too many resources to obtain. So, to save time for practicing engineers, the author presents this essay. Herein, a variety of new, old, and revisited analytical and finite difference solutions of the thermal problem are covered in this essay, along with commentary on approach and assumptions, This includes a few thermal radiation and conduction combined mode solution with a discussion on insulation, optimum emissivity, and geometrical phenomenon. Solutions to cooling and heat interception problems are also presented, including a discussion of the entropy generation. And the literature on the combined mechanical and thermal design of cryogenic support struts is reviewed with an introduction to the associated numerical methods.
Elchert, J. P.↗
The Transport of Mass, Energy, and Entropy in Cryogenic Support Struts for Engineering Design
Engineers working to understand and reduce cryogenic boil-off must solve a variety of transport problems. An important class of nonlinear problems involves the thermal and mechanical design of cryogenic struts. These classic problems are scattered about the literature and typically require too many resources to obtain. So, to save time for practicing engineers, the author presents this essay. Herein, a variety of new, old, and revisited analytical and finite difference solutions of the thermal problem are covered in this essay, along with commentary on approach and assumptions. This includes a few thermal radiation and conduction combined mode solutions with a discussion on insulation, optimum emissivity, and geometrical phenomenon. Solutions to cooling and heat interception problems are also presented, including a discussion of the entropy generation. The literature on the combined mechanical and thermal design of cryogenic support struts is reviewed with an introduction to the associated numerical methods.
Elchert, J. P.↗
Multi-dimensional initial-boundary value problems with strong nonlinearities
Initial boundary value problems for the general scalar singularly perturbed parabolic equation in a cylindrical domain are studied. The one-dimensional reaction-diffusion equation is considered in the absence of convection. Then, the general one-dimensional and N-dimensional reaction-convection-diffusion equations are analyzed.
Howes, F. A.↗