NASA Scientific and Technical Aerospace Reports

heat transfer problems, the initial condition may have to be approximated. Also, if the parabolic problem is proposed on a
multi-dimensional region, the parameter alpha, for most cases, would be difficult to compute exactly even in the case that the
initial condition is known exactly. The second objective of this proposed research is to establish a method to estimate this
parameter. This will be done by computing two discontinuous Galerkin approximate solutions at two different time steps
starting from the initial time and use them to derive alpha. (3) The third objective is to consider the heat transfer problem over
a two dimensional thin plate. The technique developed by Vogelius and Babuska will be used to establish a discontinuous
Galerkin method in which the p-element will be used for through thickness approximation. This h-p finite element approach,
that results in a dimensional reduction method, was used for elliptic problems, but the application appears new for the
parabolic problem. The dimension reduction method will be discussed together with the time discretization method.
Author (revised)
Error Analysis; Galerkin Method; Parabolic Differential Equations
20040073529 California Inst. of Tech., Pasadena, CA, USA
Dynamical Chaos in the Wisdom-Holman Integrator: Origins and Solutions
Rauch, Kevin P.; Holman, Matthew; The Astronomical Journal; 1999; Volume 117, pp. 1087-1102; In English
Contract(s)/Grant(s): NAG5-10365; Copyright; Avail: Other Sources; Abstract Only
We examine the nonlinear stability of the Wisdom-Holman (WH) symplectic mapping applied to the integration of
perturbed, highly eccentric (e-0.9) two-body orbits. We find that the method is unstable and introduces artificial chaos into the
computed trajectories for this class of problems, unless the step size chosen 1s small enough that PeriaPse is always resolved,
in which case the method is generically stable. This ‘radial orbit instability’ persists even for weakly perturbed systems. Using
the Stark problem as a fiducial test case, we investigate the dynamical origin of this instability and argue that the numerical
chaos results from the overlap of step-size resonances; interestingly, for the Stark-problem many of these resonances appear
to be absolutely stable. We similarly examine the robustness of several alternative integration methods: a time-regularized
version of the WH mapping suggested by Mikkola; the potential-splitting (PS) method of Duncan, Levison, Lee; and two
original methods incorporating approximations based on Stark motion instead of Keplerian motion. The two fixed point
problem and a related, more general problem are used to conduct a comparative test of the various methods for several types
of motion. Among the algorithms tested, the time-transformed WH mapping is clearly the most efficient and stable method
of integrating eccentric, nearly Keplerian orbits in the absence of close encounters. For test particles subject to both high
eccentricities and very close encounters, we find an enhanced version of the PS method-incorporating time regularization,
force-center switching, and an improved kernel function-to be both economical and highly versatile. We conclude that
Stark-based methods are of marginal utility in N-body type integrations. Additional implications for the symplectic integration
of N-body systems are discussed.
Author
Eccentric Orbits; Chaos; Robustness (Mathematics); Many Body Problem; Kernel Functions
20040073569 Naval Postgraduate School, Monterey, CA
Sensitivity Analysis for an Assignment Incentive Pay in the U.S. Navy Enlisted Personnel Assignment Process in a
Simulation Environment
Logemann, Karsten; Mar. 2004; 90 pp.; In English; Original contains color illustrations
Report No.(s): AD-A422386; No Copyright; Avail: CASI; A05, Hardcopy
The enlisted personnel assignment process is a major part in the USA Navy’s Personnel Distribution system. It ensures
warfighters and supporting activities receive the right sailor with the right training to the right billet at the right time (R4) and
is a critical element in meeting the challenges of Seapower 21 and Global CONOPS. In order to attain these optimal goals
the ways-to-do-it need to be customer-centered and should optimize both, the Navy’s needs and the sailor’s interests. Recent
studies and a detailing pilot in 2002 used a web-based marketplace with two- sided matching mechanisms to accomplish this
vision. This research examines the introduction of an Assignment Incentive Pay (AlP) as part of the U,S, Navy’s enlisted
personnel assignment process in a simulation environment. It uses a previously developed simulation tool, including the
Deferred Acceptance (DA) and the Linear Programming (LP) matching algorithm to simulate the assignment process. The
results of the sensitivity analysis suggested that the Navy should mainly emphasize sailor quality rather than saving AIP funds
in order to maximize utility and the possible matches When adopting such an introduction policy also the percentage of
unstable matches under the LP as the matching algorithm was reduced.
DTIC
Algorithms; Billets; Incentives; Navy; Personnel; Sensitivity Analysis; Simulation
218