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This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, fluid mechanics, and computer science during the period October 1, 1992 through March 31, 1993.
In the fall of 1994, Russia will launch a spacecraft to Mars. France is involved in many scientific experiments which are onboard the spacecraft, as PI or CI. Some days before the Mars orbit insertion maneuver, two small stations and two penetrators will be injected into an entry trajectory. They will carry out for at least six months in situ analysis on the Martian surface. Two years later, a second spacecraft will be launched. It will carry the French balloon and a small rover. The scientific data of these landers will be relayed to earth via the spacecraft. However, during the first 20 days of their mission, Mars Observer will be used. To this end, a Mars balloon relay will be used, which will receive the data from the landers and store them into the memory of the Mars Observer camera. The spacecraft will also be used to localize the landers with the help of relative one-way Doppler measurements. An international cooperative is set up for this process, including JPS, Russian ballistic centers (Babakine, Institute of Applied Mathematics, Moscow Flight Control Center), and CNES Toulouse. Another task dedicated to the space mathematics division of CNES is to support the French scientists to prepare their telecommands and to analyze their telemetry. This second part is integrated into the French ground segment created for the Mars 94/96 mission. This paper describes the method used in CNES for the localization process, the support provided to the scientists, and the links for the data exchange.
Several reports are attached to this document which contain the results of our research at the end of this contract period. Three of the reports deal with our work on generating surface grids. One is a preprint of a paper which will appear in the journal Applied Mathematics and Computation. Another is the abstract from a dissertation which has been prepared by Ahmed Khamayseh, a graduate student who has been supported by this grant for the last two years. The last report on surface grids is the extended abstract of a paper to be presented at the 14th IMACS World Congress in July. This report contains results on conformal mappings of surfaces, which are closely related to elliptic methods for surface grid generation. A preliminary report is included on new methods for dealing with block interfaces in multiblock grid systems. The development work is complete and the methods will eventually be incorporated into the National Grid Project (NGP) grid generation code. Thus, the attached report contains only a simple grid system which was used to test the algorithms to prove that the concepts are sound. These developments will greatly aid grid control when using elliptic systems and prevent unwanted grid movement. The last report is a brief summary of some timings that were obtained when the multiblock grid generation code was run on the Intel IPSC/860 hypercube. Since most of the data in a grid code is local to a particular block, only a small fraction of the total data must be passed between processors. The data is also distributed among the processors so that the total size of the grid can be increase along with the number of processors. This work is only in a preliminary stage. However, one of the ERC graduate students has taken an interest in the project and is presently extending these results as a part of his master's thesis.
The mechanics of wave propagation in the presence of obstacles is of great interest in many branches of engineering and applied mathematics like electromagnetics, fluid dynamics, geophysics, seismology, etc. Such problems can be broadly classified into two categories: the bounded domain or the closed problem and the unbounded domain or the open problem. Analytical techniques have been derived for the simpler problems; however, the need to model complicated geometrical features, complex material coatings and fillings, and to adapt the model to changing design parameters have inevitably tilted the balance in favor of numerical techniques. The modeling of closed problems presents difficulties primarily in proper meshing of the interior region. However, problems in unbounded domains pose a unique challenge to computation, since the exterior region is inappropriate for direct implementation of numerical techniques. A large number of solutions have been proposed but only a few have stood the test of time and experiment. The goal of this thesis is to develop an efficient and reliable partial differential equation technique to model large three dimensional scattering problems in electromagnetics.
This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, fluid mechanics, and computer science during the period 1 Oct. 1994 - 31 Mar. 1995.
Eigenvalues and eigenfunctions of linear operators are important to many areas of applied mathematics. The ability to approximate these quantities numerically is becoming increasingly important in a wide variety of applications. This increasing demand has fueled interest in the development of new methods and software for the numerical solution of large-scale algebraic eigenvalue problems. In turn, the existence of these new methods and software, along with the dramatically increased computational capabilities now available, has enabled the solution of problems that would not even have been posed five or ten years ago. Until very recently, software for large-scale nonsymmetric problems was virtually non-existent. Fortunately, the situation is improving rapidly. The purpose of this article is to provide an overview of the numerical solution of large-scale algebraic eigenvalue problems. The focus will be on a class of methods called Krylov subspace projection methods. The well-known Lanczos method is the premier member of this class. The Arnoldi method generalizes the Lanczos method to the nonsymmetric case. A recently developed variant of the Arnoldi/Lanczos scheme called the Implicitly Restarted Arnoldi Method is presented here in some depth. This method is highlighted because of its suitability as a basis for software development.
This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, fluid mechanics, and computer science during the period 1 Oct. 1996 - 31 Mar. 1997.
This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, fluid mechanics, and computer science.
This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics. fluid mechanics, and computer science during the period April 1, 1999 through September 30. 1999.
This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, computer science, fluid mechanics, and structures and materials during the period October 1, 1999 through March 31, 2000.
This report summarizes research conducted at ICASE in applied mathematics, fluid mechanics, computer science, and structures and material sciences during the period April 1, 2000 through September 30, 2000.
This report summarizes research conducted at ICASE in applied mathematics, computer science, fluid mechanics, and structures and material sciences during the period October 1, 2000 through March 31, 2001.
This report summarizes research conducted at ICASE in applied mathematics, computer science, fluid mechanics, and structures and material sciences during the period April 1, 2001 through September 30, 2001.
This report summarizes research conducted at ICASE in applied mathematics, fluid mechanics, computer science, and structures and material sciences during the period October 1, 2001 through March 31, 2002.
This report contains the 2004 annual progress reports of the Research Fellows and students of the Center for Turbulence Research in its eighteenth year of operation. Since its inception in 1987, the objective of the CTR has been to advance the physical understanding of turbulent flows and development of physics based predictive tools for engineering analysis and turbulence control. Turbulence is ubiquitous in nature and in engineering devices. The studies at CTR have been motivated by applications where turbulence effects are significant; these include a broad range of technical areas such as planetary boundary layers, formation of planets, solar convection, magnetohydrodynamics, environmental and eco systems, aerodynamic noise, propulsion systems and high speed transportation. Numerical simulation has been the predominant research tool at CTR which has required a critical mass of researchers in numerical analysis and computer science in addition to core disciplines such as applied mathematics, chemical kinetics and fluid mechanics. Maintaining and promoting this interdisciplinary culture has been a hallmark of CTR and has been responsible for the realization of the results of its basic research in applications. The first group of reports in this volume are directed towards development, analysis and application of novel numerical methods for ow simulations. Development of methods for large eddy simulation of complex flows has been a central theme in this group. The second group is concerned with turbulent combustion, scalar transport and multi-phase ows. The nal group is devoted to geophysical turbulence where the problem of solar convection has been a new focus of considerable attention recently at CTR.
This volume presents technical issues involved in applying mathematical techniques known as Formal Methods to specify and analytically verify aerospace and avionics software systems.
Optical survey data taken using the NASA Michigan Orbital Debris Survey Telescope (MODEST) gives us an opportunity to statistically sample faint object population in the Geosynchronous (GEO) and near-GEO environment. This paper will summarize the MODEST survey work that has been conducted by NASA since 2002, and will outline the techniques employed to arrive at the current population estimates in the GEO environment for dim objects difficult to detect and track using current systems in the Space Surveillance Network (SSN). Some types of orbits have a higher detection rate based on what parts of the GEO belt is being observed, a straightforward statistical technique is used to debias these observations to arrive at an estimate of the total population potentially visible to the telescope. The size and magnitude distributions of these fainter debris objects are markedly different from the catalogued population. GEO debris consists of at least two different populations, one which follows the standard breakup power law and one which has anomalously high Area-to-Mass Ratios (1 to approx. 30 square meters per kilogram; a sheet of paper = approx. 13 square meters per kilogram). The Inter-Agency Space Debris Coordination Committee (IADC) is investigating objects in GEO orbits with anomalously high Area-to-Mass Ratios (AMRs). The ESA Space Debris Telescope discovered this population and has and its properties of inclinations (0 to 30 degrees), changing eccentricities (0 and 0.6), and mean motions (approx. 1 rev), will be presented. The accepted interpretation of this orbital behavior is that solar radiation pressure drives the perturbations causing time varying inclinations and eccentricities. The orbital parameters are unstable for this population and thus difficult to predict. Their dim visual magnitudes and photometric variability make observations a challenge. The IADC has enlisted a series of observatories (participating institutions: University of Michigan/CTIO, Astronomical Institute University of Bern, Boeing LTS / AMOS, Keldysh Institute of Applied Mathematics) at different longitudes. Complete observational coverage over periods of days to months will provide a better understanding of the properties, such as solar radiation pressure effects on orbital elements, size, shape, attitude, color variations, and spectral characteristics. Results from recent observational programs will be summarized, and includes a description of the orbit elements prediction processes, a summary of the metric tracking performance, and some photometric characteristics of this class of debris.
The Kirchhoff formula for a moving surface is very useful in many wave propagation problems, particularly in the prediction of noise from rotating machinery. Several publications in the last two decades have presented derivations of the Kirchhoff formula for moving surfaces in both time and frequency domains. Here we present a method originally developed by Farassat and Myers in time domain that is both simple and direct. It is based on generalized function theory and the useful concept of imbedding the problem in the unbounded three-dimensional space. We derive an inhomogeneous wave equation with the source terms that involve Dirac delta functions with their supports on the moving data surface. This wave equation is then solved using the simple free space Green's function of the wave equation resulting in the Kirchhoff formula. The algebraic manipulations are minimal and simple. We do not need the Green's theorem in four dimensions and there is no ambiguity in the interpretation of any terms in the final formulas. Furthermore, this method also gives the simplest derivation of the classical Kirchhoff formula which has a fairly lengthy derivation in physics and applied mathematics books. The Farassat-Myers method can be used easily in frequency domain.