NASA Scientific and Technical Aerospace Reports - The University ...

20100017897 Center for Mathematics and Computer Science, Amsterdam, Netherlands
Iterated Radau Method for Time-Dependent PDE’s
Perez-Rodriguez, S.; Gonzalez-Pinto, S.; Sommeijer, B. P.; November 2008; ISSN 1386-3703; 32 pp.; In English
Contract(s)/Grant(s): MTM2007-67530-C02-02
Report No.(s): PB2010-107583; MAS-E0805; Copyright; Avail.: National Technical Information Service (NTIS)
This paper is concerned with the time integration of semi-discretized, multi-dimensional PDE’s of advection-diffusionreaction
type. To cope with the stiffness of these ODE’s, an implicit method has been selected, for example, the two-stage,
third-order Radau IIA method. The main topic of this paper is the efficient solution of the resulting implicit relations. First a
modified Newton process has been transformed into an iteration process in which the 2 stages are decoupled and, moreover,
can exploit the same LU-factorization of the iteration matrix. Next, we apply a socalled Approximate Matrix Factorization
(AMF) technique to solve the linear systems in each Newton iteration. This AMF approach is very efficient since it reduces
the ‘multi-dimensional’ system to a series of ‘one-dimensional’ systems. The total amount of linear algebra work involved is
reduced enormously by this approach. The idea of applying AMF to two-dimensional problems is quite old and goes back to
Peaceman and Rachford in the early fifties. The situation in three space dimensions is less favourable and will be analyzed
here in more detail, both theoretically and experimentally. Furthermore, we analyze a variant in which the AMF-technique has
been used to really solve (’until convergence’) the underlying Radau IIA method so that we can rely on its excellent stability
and accuracy characteristics. Finally, the method has been tested on several examples. Also a comparison has been made with
the existing codes VODPK and IMEXRKC, and the efficiency (CPU time versus accuracy) is shown to be at least competitive
with the efficiency of these solvers.
NTIS
Partial Differential Equations; Time Dependence
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INSTRUMENTATION AND PHOTOGRAPHY
Includes remote sensors; measuring instruments and gages; detectors; cameras and photographic supplies; and holography. For aerial
photography see 43 Earth Resources and Remote Sensing. For related information see also 06 Avionics and Aircraft Instrumentation;
and 19 Spacecraft Instrumentation and Astrionics.
20100017023 Naval Air Systems Command (PMA-234), Patuxent River, MD USA
LOCO with a Shipboard Lidar
Concannon, Brian M; Prentice, Jennifer E; Jan 2008; 16 pp.; In English
Contract(s)/Grant(s): MIPR-N0001408WX20747
Report No.(s): AD-A517452; No Copyright; Avail.: Defense Technical Information Center (DTIC)
The long term goal of this research is to demonstrate an independent ability to use light detection and ranging (lidar)
technology to survey and characterize the optical structure of the marine water column. The Sea Time Resolved Optical Layer
Lidar (SeaTROLL) is a 532 nm lidar system designed for shipboard deployment to investigate the phenomenon of plankton
formation into discrete thin layers. The phenomenonology of biological thin layers that can be investigated using lidar are the
identification of layer regional distribution, frequency of occurrence, horizontal extent, vertical structure, temporal cycles,
optical density, and potentially, unique optical characteristics that identify layer composition. Biological thin layers are defined
as concentrations of phytoplanktonic and/or zooplanktonic organisms occurring in a vertical thickness of several centimeters
to several meters with contiguous horizontal extents on the order of kilometers. A solid body of work has established the
existence of thin layers of biological organisms in both fjord and coastal ocean environments. Observations of these structures
indicate that they are episodic and that their formation is induced by a combination of stratification and vertical shear (Cowles
et al., 1998, Cowles, 2003). The initial studies of the physical, biological, and chemical processes associated with thin layers
have shown that they are dynamic structures in the spatial domain, that they can persist for days to weeks, and that their
biological and chemical rate processes are substantially more intense than those in the surrounding water column (Hanson and
Donaghay, 1998; Dekshenieks et al., 2001). We do not know the extent of their presence throughout the marine environment,
how important thin layers are to the overall productivity of the regional coastal ecology, or how they may interact with the
oceanic ecosystem.
DTIC
Optical Radar; Optical Density; Productivity
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