Simulation of Electro-Optical System
Development of the Application Program Library for Mathematical Simulation of Three-Dimensional Complex Structure Electron-Optical Systems.
Tech Area / Field
- PHY-RAW/Radiofrequency Waves/Physics
3 Approved without Funding
NIIIT (Pulse Techniques), Russia, Moscow
Project summaryPractice demands that mathematical simulation of physical processes be one of the most urgent aims. In particular many processes are described by means of linear boundary problems for Laplac, Poisson, Gelmholz, Maxwell, heat conductivity equations where a multitude of boundary points forms a surface limited in three-dimensional euclidean space (area) S. There are different methods for numerical solution of those problems, but the most used ones are those which are based on the boundary integral equation apparatus. The latter is caused by the fact that the defined in all the three-dimensional euclidean space boundary problem can be reformulated as a boundary integral equation on the surface S; this lowers essencially the order of the latter while transferring to a grid problem. Hereby the numerical study of many specific process mathematical models was carried out. Also, if the surface S has a complex configuration, large relative dimensions, and is multiply connected, the quantification of the boundary integral equations leads to the large order linear algebraic equation systems (several thousands and more) with the filled matrixes. Solution of such systems if possible at all is in most cases connected with numerical instability and requires great machine resources. That is why the class of the problems to be solved numerically is limited to some great extent and includes basically one-dimensional surfaces (closed and open loops), single connected surfaces of canonical form and small dimensions. Altogether, development of computing technology, transputer creation, emerge of vector and parallel computers leads to the necessity of developing basically new approaches for making numerical methods and their software, which take into account special features of the new generation computing technology. All the above said things have determined the new direction in numerical solution of the mathematical physics linear boundary problems based on the boundary integral equation method, theoretical and group methods and iteration algorithms (as the known ones as the newly developed ones). The said direction is being developed by the RIPT scientists together with the MSU (Moscow State University) scientists. A part of the obtained results had been published and presented at symposiums (12 articles). The obtained numerical methods are tens and hundreds times more economical than the existing ones and more stable when realized numerically. The said methods had been successfully used to solve different application problems but most of the problems had been put for solving by the Military-Industrious Complex of the CIS.
Development and progran realization of mathematical model of an image tube is one of the most practically important field of application of the approach destribed. An image tube may include the focusing electrodes formed by axially-symmetric surfaces of various shape, cutting diaphragms of a given configuration, and the deflection system consisting both of rectangular and trapeziform elements. A close agreement between computational and experimental data for image tubes of various types can be achieved if the order of an approximating mesh problem is about 3000-5000. As the numerical experiments show, further increase of the discretization order does not lead to anywhere near noticeable results changing. This fact demonstrates high computational stability of numerical techniques being proposed. Computation of the electrostatic charge density on the boundary electrodes, potantial field values at the nodes of a spatial mesh, as well as subsequent computation of electron beams each being consisting of 1000 trajectories, takes about lO min, 1min, and 30s correspondingly when Pentium-90 is used.Aims of the work: usage of the developed methods for numerical solving of the different application problems intended for peaceful purposes.
Purposes of the work.
- Creation of the Application Programm Library (APL) in order to simulate different devices and processes, in the first place, three-dimensional complex structure electron-optical systems such as image intensifies, photoelectronic multipliers, oscillographic tubes, electronic microscopes and so on.
- Further development of numerical methods which permit to essencially broaden the class of application problems, allowing approximate solution.
- The said methods should be acceptable to be used for multiprocessor as well as for monoprocessor computers.
The fundamental and applied results of this work will be published so that the world scientific community could access them and will be reported at the appropriate symposiums and congresses.
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