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Elliptic coordinate system

About: Elliptic coordinate system is a research topic. Over the lifetime, 670 publications have been published within this topic receiving 11135 citations. The topic is also known as: elliptical coordinate system & elliptic coordinates.


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01 Mar 1983
TL;DR: In this article, a code for the generation of boundary-fitted coordinate systems for general two-dimensional regions with boundaries of arbitrary shape and with internal obstacles and boundary intrusions, arbitrary in shape and number, is described and instructions for input and use are given.
Abstract: : A code (WESC0R) for the generation of boundary-fitted coordinate systems for general two-dimensional regions with boundaries of arbitrary shape and with internal obstacles and boundary intrusions, arbitrary in shape and number, is described and instructions for input and use are given. The coordinate system is generated from the numerical solution of a system of elliptic partial differential equations with provision for controlling the spacing of the coordinate lines in the field. The transformed (computational) region is rectangular with the obstacles and intrusions transformed to slits and/or slabs. A small code to distribute points on various fundamental curves with exponential concentration is also described. This front-end code can be used to construct boundary point distributions for input to the coordinate code. A plot code for the coordinate system is also included. The boundary-fitted coordinate systems generated by this code may be used as a basis for the numerical solution of partial differential equations for any physical problem of interest. This procedure will be particularly useful where numerical models are used to analyze flow problems with complex boundary conditions. Typical examples are riverine analysis or the design and evaluation of selective withdrawal outlet works. (Author)

4 citations

Journal ArticleDOI
TL;DR: In this paper, the wave functions of isoelectronic ions in terms of confocal elliptic coordinates have been studied and a simple, model wave function for several states has been developed.
Abstract: We have discussed some general properties of the wave functions of ${\mathrm{H}}_{2}^{+}$ and its isoelectronic ions, in terms of confocal elliptic coordinates. Based on the asymptotic properties when the electron is far away from the nuclei, and the coalescence properties when it is close to one of the nuclei, we have developed simple, model wave functions for several states. These wave functions are simple enough to provide a clear insight into the structure of the wave functions, and yet accurate enough to provide energies close to the exact values.

4 citations

Journal ArticleDOI
TL;DR: In this article, an analytical method for the solution of direct and inverse problems of heat conduction, thermoelastic stresses and heat transfer by singly and doubly taking integral transformations with respect to unilateral parabolic variables and by implementing the method of finite elements of the orthogonal residual projection in a certain functional space over the entire range of variation of bilateral elliptical coordinates is suggested.

4 citations

Journal ArticleDOI
TL;DR: The elements of the kinetic energy matrix G of CX 2 (CN) 2 using several sets of internal symmetry coordinates have been calculated and discussed in this article, where the elements of G of CN 2 have been shown to have a similar behavior.

4 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20237
202211
202111
202010
201913
201810