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Research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, numerical analysis, and computer science during the period April 1, 1985 through October 2, 1985 is summarized.
The Caltech Concurrent Computation Program wwhich studies basic issues in computational science is described. The research builds on initial work where novel concurrent hardware, the necessary systems software to use it and twenty significant scientific implementations running on the initial 32, 64, and 128 node hypercube machines have been constructed. A major goal of the program will be to extend this work into new disciplines and more complex algorithms including general packages that decompose arbitrary problems in major application areas. New high-performance concurrent processors with up to 1024-nodes, over a gigabyte of memory and multigigaflop performance are being constructed. The implementations cover a wide range of problems in areas such as high energy and astrophysics, condensed matter, chemical reactions, plasma physics, applied mathematics, geophysics, simulation, CAD for VLSI, graphics and image processing. The products of the research program include the concurrent algorithms, hardware, systems software, and complete program implementations.
This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, numerical analysis, and computer science during the period April 1, 1987 through October 1, 1987.
This report summarizes research conducted at the Institute for Computer Applications Science and Engineering in applied mathematics, numerical analysis, and computer science during the period October 2, 1987 through March 31, 1988.
The Institute conducts unclassified basic research in applied mathematics, numerical analysis, and computer science in order to extend and improve problem-solving capabilities in science and engineering, particularly in aeronautics and space. The major categories of the current Institute for Computer Applications in Science and Engineering (ICASE) research program are: (1) numerical methods, with particular emphasis on the development and analysis of basic numerical algorithms; (2) control and parameter identification problems, with emphasis on effective numerical methods; (3) computational problems in engineering and the physical sciences, particularly fluid dynamics, acoustics, and structural analysis; and (4) computer systems and software, especially vector and parallel computers. ICASE reports are considered to be primarily preprints of manuscripts that have been submitted to appropriate research journals or that are to appear in conference proceedings.
Research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, numerical analysis, and computer science is summarized.
An attempt is made to show that the Cartan theory of partial differential equations can be a useful technique for applied mathematics. Techniques for finding consistent subfamilies of solutions that are generically rich and well-posed and for introducing potentials or other usefully consistent auxiliary fields are introduced. An extended sample calculation involving the Korteweg-de Vries equation is given.
Key results are documented from attending the 4th workshop on verification, validation, and testing. The most interesting part of the workshop was when representatives from the U.S., Japan, and Europe presented surveys of VV&T within their respective regions. Another interesting part focused on current efforts to define industry standards for artificial intelligence and how that might affect approaches to VV&T of expert systems. The next part of the workshop focused on VV&T methods of applying mathematical techniques to verification of rule bases and techniques for capturing information relating to the process of developing software. The final part focused on software tools. A summary is also presented of the EPRI conference on 'Methodologies, Tools, and Standards for Cost Effective Reliable Software Verification and Validation. The conference was divided into discussion sessions on the following issues: development process, automated tools, software reliability, methods, standards, and cost/benefit considerations.
Wavelets are an exciting new topic in applied mathematics and signal processing. This paper will provide a brief review of wavelets which are also known as families of functions with an emphasis on interpretation rather than rigor. We will derive an indirect use of wavelets for the solution of integral equations based techniques adapted from image processing. Examples for resistive strips will be given illustrating the effect of these techniques as well as their promise in reducing dramatically the requirement in order to solve an integral equation for large bodies. We also will present a direct implementation of wavelets to solve an integral equation. Both methods suggest future research topics and may hold promise for a variety of uses in computational electromagnetics.
A summary of research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, numerical analysis, and computer science during the period 1 Oct. 1991 through 31 Mar. 1992 is presented.
Developed for the NASA Johnson Space Center and Life Sciences Directorate by GE Government Services, the Microcomputer Integrated Real-time Acquisition Ground Equipment (MIRAGE) system is a portable ground support system for Spacelab life sciences experiments. The MIRAGE system can acquire digital or analog data. Digital data may be NRZ-formatted telemetry packets of packets from a network interface. Analog signal are digitized and stored in experimental packet format. Data packets from any acquisition source are archived to a disk as they are received. Meta-parameters are generated from the data packet parameters by applying mathematical and logical operators. Parameters are displayed in text and graphical form or output to analog devices. Experiment data packets may be retransmitted through the network interface. Data stream definition, experiment parameter format, parameter displays, and other variables are configured using spreadsheet database. A database can be developed to support virtually any data packet format. The user interface provides menu- and icon-driven program control. The MIRAGE system can be integrated with other workstations to perform a variety of functions. The generic capabilities, adaptability and ease of use make the MIRAGE a cost-effective solution to many experimental data processing requirements.
This paper describes the approach and results of an effort to characterize plant growth under various environmental conditions at the Johnson Space Center variable pressure growth chamber. Using a field of applied mathematics and statistics known as design of experiments (DOE), we developed a test plan for varying environmental parameters during a lettuce growth experiment. The test plan was developed using a Box-Behnken approach to DOE. As a result of the experimental runs, we have developed empirical models of both the transpiration process and carbon dioxide assimilation for Waldman's Green lettuce over specified ranges of environmental parameters including carbon dioxide concentration, light intensity, dew-point temperature, and air velocity. This model also predicts transpiration and carbon dioxide assimilation for different ages of the plant canopy.
The study applies mathematical methods of control theory to the problem of control of fluid flow with the long-range objective of developing effective methods for the control of turbulent flows. Model problems are employed through the formalism and language of control theory to present the procedure of how to cast the problem of controlling turbulence into a problem in optimal control theory. Methods of calculus of variations through the adjoint state and gradient algorithms are used to present a suboptimal control and feedback procedure for stationary and time-dependent problems. Two types of controls are investigated: distributed and boundary controls. Several cases of both controls are numerically simulated to investigate the performances of the control algorithm. Most cases considered show significant reductions of the costs to be minimized. The dependence of the control algorithm on the time-descretization method is discussed.
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.