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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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1996

Some Experiences with Nonoverlapping Schur Complement Parallel Preconditioning for CFD Calculations

In this work we consider solving matrices which arise from the discretization of advection-diffusion field equations on arbitrary triangulated domains using stabilized numerical methods. The talk will discuss several candidate matrix preconditioning algorithms based on the 2 x 2 block factorization induced by an apriori partitioning of the triangulated domain. Application of the 2 x 2 block preconditioner requires the formation and inversion of the Schur complement submatrix. We consider several strategies for simplifying this task: incomplete Schur complement factorizations, drop tolerance element filling, Schur complement probing, and localized Schur complement inversion. Numerical results will be shown comparing performance and efficiency of these approximations. The matrix preconditioner has also been embedded into a Newton algorithm for solving the nonlinear Euler and Navier-Stokes equations governing compressible flow. The remainder of the talk will show numerous examples in CFD to demonstrate the efficiency and robustness of the techniques.

Barth, Timothy J.↗
NASA NTRS1979

Optimization of multiple flyby trajectories

A procedure has been developed which minimizes total delta-V (instantaneous velocity change) for a multiple flyby trajectory with constraints on flyby altitude and orientation. The solution is found by varying the locations of maneuver points between each flyby to minimize the delta-Vs at the maneuver points. Each trajectory segment connecting consecutive maneuver points is found by solving an N-body analog to Lambert's problem. Multiconic techniques are used for trajectory propagation and for computation of the state transition matrix. The constrained parameter optimization problem is converted to an unconstrained problem by means of penalty functions and then solved with a quasi-Newton algorithm utilizing analytic first derivatives. This procedure has been successfully applied to Galileo satellite tour trajectories.

Damario, L. A.↗
NASA NTRS1980

A new method for optimizing multiple flyby trajectories

A new procedure has been developed which minimizes total impulsive Delta V for multiple flyby trajectories with constraints on flyby parameters and maneuver times. The method involves solving a bounds-constrained parameter optimization problem with a Newton algorithm utilizing analytic first and second derivatives. Each trajectory segment connecting consecutive maneuver points is found by first targeting from the preceding maneuver point to the parameters of the upcoming flyby and then propagating the resulting trajectory to the next maneuver point. Multi-conic techniques are used for trajectory propagation and for computation of the state transition matrix. This procedure has successfully optimized Galileo satellite tours containing up to 11 flybys.

Damario, L. A.↗
NASA NTRS1982

Comparison of starting values for iterative solutions to a universal Kepler's equation

General starting values for the iterative numerical solution of a universal Kepler's equation for position in a conic orbit at a specified time are investigated. Three starting values based on recent refinements of previously obtained bounds on the solution are derived and tested numerically. Of these, a simple starting value based on a cubic approximation to Kepler's equation provides the most rapid convergence using both first and second order Newton algorithms. The performance of the starting values are compared with similar studies which used the restricted case of elliptical orbits with the initial epoch at periapse.

Bergam, M. J.↗
NASA NTRS1983

Finite-element methods for steady solidification problems

Four Galerkin finite-element methods are tested for solving the free-boundary problem that describes steady solidification. The formulations differ in the solution method used to account for the unknown shape of the melt/solid interface, in the interphase condition (either balance of heat flux or equilibrium of temperature) distinguished for locating the interface, and in the technique used for solving the systems of algebraic equations that result from the finite-element approximations. Methods that use the melting point isotherm to locate the melt/solid interface are found more accurate and efficient than formulations based on the interfacial energy balance. Solution by a Galerkin-Newton algorithm of the free-boundary problem transformed to a fixed domain is most efficient when the field problem in each phase is made nonlinear by including radiation from the melt and solid to the surroundings.

Ettouney, H. M.↗
NASA NTRS1983

Finite element calculation of buoyancy-driven convection near a melt/solid phase boundary

Two iterative schemes based on the mixed finite element method are developed for analyzing steady natural convection in a melt adjacent to its solid phase. The simplest method decouples the calculation of the field variables and the shape of the melt/solid interface into two interlocked iterations that are performed successively. The second method uses Newton's iteration to solve simultaneously for both types of unknowns and has a quadratic convergence rate. Results for a model problem of melt and solid in a cylindrical ampoule show the Newton algorithm to be a factor of three more efficient.

Chang, C. J.↗
NASA NTRS1987

A parallelized elliptic solver for reacting flows

A modified Newton algorithm for the solution of nonlinear elliptic boundary value problems via finite discretization methods is presented. A serial implementation of this algorithm which has recently been applied successfully to the computation of an axisymmetric over-ventilated subsonic laminar methane-air jet diffusion flame is described. Parallel implementation issues and a complexity theory are presented. Included as well are actual performance data for model systems obtained on the Intel Hypercube and a discussion of its implications for modeling realistic systems.

Keyes, David E.↗
NASA NTRS1990

Maximum likelihood tuning of a vehicle motion filter

This paper describes the use of maximum likelihood parameter estimation unknown parameters appearing in a nonlinear vehicle motion filter. The filter uses the kinematic equations of motion of a rigid body in motion over a spherical earth. The nine states of the filter represent vehicle velocity, attitude, and position. The inputs to the filter are three components of translational acceleration and three components of angular rate. Measurements used to update states include air data, altitude, position, and attitude. Expressions are derived for the elements of filter matrices needed to use air data in a body-fixed frame with filter states expressed in a geographic frame. An expression for the likelihood functions of the data is given, along with accurate approximations for the function's gradient and Hessian with respect to unknown parameters. These are used by a numerical quasi-Newton algorithm for maximizing the likelihood function of the data in order to estimate the unknown parameters. The parameter estimation algorithm is useful for processing data from aircraft flight tests or for tuning inertial navigation systems.

Trankle, Thomas L.↗
NASA NTRS2003

CAD-Based Aerodynamic Design of Complex Configurations using a Cartesian Method

A modular framework for aerodynamic optimization of complex geometries is developed. By working directly with a parametric CAD system, complex-geometry models are modified nnd tessellated in an automatic fashion. The use of a component-based Cartesian method significantly reduces the demands on the CAD system, and also provides for robust and efficient flowfield analysis. The optimization is controlled using either a genetic or quasi-Newton algorithm. Parallel efficiency of the framework is maintained even when subject to limited CAD resources by dynamically re-allocating the processors of the flow solver. Overall, the resulting framework can explore designs incorporating large shape modifications and changes in topology.

Nemec, Marian↗
NASA NTRS1998

Globalized Newton-Krylov-Schwarz Algorithms and Software for Parallel Implicit CFD

Implicit solution methods are important in applications modeled by PDEs with disparate temporal and spatial scales. Because such applications require high resolution with reasonable turnaround, "routine" parallelization is essential. The pseudo-transient matrix-free Newton-Krylov-Schwarz (Psi-NKS) algorithmic framework is presented as an answer. We show that, for the classical problem of three-dimensional transonic Euler flow about an M6 wing, Psi-NKS can simultaneously deliver: globalized, asymptotically rapid convergence through adaptive pseudo- transient continuation and Newton's method-, reasonable parallelizability for an implicit method through deferred synchronization and favorable communication-to-computation scaling in the Krylov linear solver; and high per- processor performance through attention to distributed memory and cache locality, especially through the Schwarz preconditioner. Two discouraging features of Psi-NKS methods are their sensitivity to the coding of the underlying PDE discretization and the large number of parameters that must be selected to govern convergence. We therefore distill several recommendations from our experience and from our reading of the literature on various algorithmic components of Psi-NKS, and we describe a freely available, MPI-based portable parallel software implementation of the solver employed here.

Gropp, W. D.↗
NASA NTRS1986

Locally bound constrained Newton-Raphson solution algorithms

This paper develops strategies which enable the automatic adjustment of the constraint surfaces recently used to extend the range and numerical stability/efficiency of nonlinear finite-element equation solvers. In addition to handling kinematic and material induced nonlinearity, both pre- and postbuckling behavior can be treated. The scheme developed employs localized bounds on various hierarchical partitions of the field variables. These are used to resize, shape, and orient the global constraint surface, thereby enabling essentially automatic load/deflection incrementation. Due to the generality of the approach taken, it can be implemented in conjunction with constraints of arbitrary functional type. To benchmark the method, several numerical experiments are presented. These include problems involving kinematic and material nonlinearity, as well as, pre- and postbuckling characteristics.

Padovan, J.↗
NASA NTRS1991

Self adaptive solution strategies: Locally bound constrained Newton Raphson solution algorithms

A summary is given of strategies which enable the automatic adjustment of the constraint surfaces recently used to extend the range and numerical stability/efficiency of nonlinear finite element equation solvers. In addition to handling kinematic and material induced nonlinearity, both pre-and postbuckling behavior can be treated. The scheme employs localized bounds on various hierarchical partitions of the field variables. These are used to resize, shape, and orient the global constraint surface, thereby enabling essentially automatic load/deflection incrementation. Due to the generality of the approach taken, it can be implemented in conjunction with the constraints of an arbitrary functional type. To benchmark the method, several numerical experiments are presented. These include problems involving kinematic and material nonlinearity, as well as pre- and postbuckling characteristics. Also included is a list of papers published in the course of the work.

Padovan, Joe↗
NASA NTRS1993

Modeling Spectralon's Bidirectional Reflectance for In-Flight Calibration of Earth-Orbiting Sensors

This paper describes the results of a model inversion which was conducted using measured Spectralon BRDF data at several illumination angles. We can describe the bidirectional reflectance of the Spectralon and in paticular its slight anisotrophy with a physically-based model. The root mean square difference between the model and the observations is currently of the order of the noise in the data (+/-1%). It is expected that meaningful corrections to account for the anisotrophy of the Spectralon panels will be achieved in the next few years and will improve the calibration of the MISR instrument.

EOS↗
NASA NTRS1985

Finite element simulation of temperature dependent free surface flows

The method of Engelman and Sani (1984) for a finite-element simulation of incompressible surface flows with a free and/or moving fluid interface, such as encountered in crystal growth and coating and polymer technology, is extended to temperature-dependent flows, including the effect of temperature-dependent surface tension. The basic algorithm of Saito and Scriven (1981) and Ruschak (1980) has been generalized and implemented in a robust and versatile finite-element code that can be employed with relative ease for the simulation of free-surface problems in complex geometries. As a result, the costly dependence on the Newton-Raphson algorithm has been eliminated by replacing it with a quasi-Newton iterative method, which nearly retains the superior convergence properties of the Newton-Raphson method.

Engelman, M. S.↗
NASA NTRS1989

Iterative procedures for space shuttle main engine performance models

Performance models of the Space Shuttle Main Engine (SSME) contain iterative strategies for determining approximate solutions to nonlinear equations reflecting fundamental mass, energy, and pressure balances within engine flow systems. Both univariate and multivariate Newton-Raphson algorithms are employed in the current version of the engine Test Information Program (TIP). Computational efficiency and reliability of these procedures is examined. A modified trust region form of the multivariate Newton-Raphson method is implemented and shown to be superior for off nominal engine performance predictions. A heuristic form of Broyden's Rank One method is also tested and favorable results based on this algorithm are presented.

Santi, L. Michael↗
NASA NTRS1990

A superlinear interior points algorithm for engineering design optimization

We present a quasi-Newton interior points algorithm for nonlinear constrained optimization. It is based on a general approach consisting of the iterative solution in the primal and dual spaces of the equalities in Karush-Kuhn-Tucker optimality conditions. This is done in such a way to have primal and dual feasibility at each iteration, which ensures satisfaction of those optimality conditions at the limit points. This approach is very strong and efficient, since at each iteration it only requires the solution of two linear systems with the same matrix, instead of quadratic programming subproblems. It is also particularly appropriate for engineering design optimization inasmuch at each iteration a feasible design is obtained. The present algorithm uses a quasi-Newton approximation of the second derivative of the Lagrangian function in order to have superlinear asymptotic convergence. We discuss theoretical aspects of the algorithm and its computer implementation.

Herskovits, J.↗
NASA NTRS1975

A two-level trajectory decomposition algorithm featuring optimal intermediate target selection

A decomposition algorithm is presented that optimizes complex missions by partitioning the trajectory into natural segments such as ascent or entry. Each segment defines a full-rank targeting subproblem. These are solved sequentially using the Newton-Raphson algorithm. The master problem, representing the complete mission, is to determine subproblem targets and master-problem controls that optimize the mission objective subject to intersegment constraints. The gradient projection algorithm solves this problem using derivatives obtained analytically from finite-difference subproblem sensitivities. Thus, the mission is optimized by coordinating the solution of tractible subproblems. Computational results for a synchronous equatorial mission are included.

Petersen, F. M.↗