Topic
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.
Papers published on a yearly basis
Papers
More filters
26 Aug 2007
TL;DR: It is argued that it is thus possible to construct well structured discretisations which imply equation systems with very high solution properties.
Abstract: In this paper several numerical concepts for the solution of elliptical boundary value problems will be compared with regard to their efficiency, computational load and accuracy. Especially regions which are images of rectangles and cuboids of coordinate transformations will be considered. I argue that it is thus possible to construct well structured discretisations which imply equation systems with very high solution properties. The approaches discussed will be tested with instructive examples in the light of their advantages and disadvantages.
TL;DR: In this article, exact closed-form expressions are presented for the solution to Laplace's equation everywhere in a specific cavity-backed aperture problem, where a symmetrically placed slot enables the static field in a half-space above a hard or soft ground plane to penetrate into the interior of an elliptically shaped cavity.
Abstract: Exact, closed-form expressions are presented for the solution to Laplace's equation everywhere in a specific cavity-backed aperture problem. A symmetrically placed slot enables the static field in a half-space above a hard or soft ground plane to penetrate into the interior of an elliptically shaped cavity. Separation-of-variables in elliptic coordinates yields a summable series, whereupon the aperture field or its normal derivative appears naturally as a series of edge-condition weighted Chebyshev polynomials in the Cartesian coordinates. Analytic coefficients explicitly display simple dependence upon the cavity and point-source geometry.
TL;DR: In this article, a special selection of the Euler angles is made, according to which one axis of the rotating coordinate system is related to the center of mass of electrons, and the hierarchy of the hyperspherical coordinates R, α, and θ allows sequential quantization with respect to these variables to be performed.
Abstract: A special selection of the Euler angles is made, according to which one axis of the rotating coordinate system is related to the center of mass of electrons. The hierarchy of the hyperspherical coordinates R, α, and θ allows sequential quantization with respect to these variables to be performed. The complex structure of the potential with respect to the R coordinate leads to the use of a quasi-classical approximation. The energy spectrum of doubly excited S-states of a He atom is determined. The results are compared to other published data.
01 Jan 2009
TL;DR: In this article, a semi-analytical formulation of the velocity potentials in elliptical coordinates is proposed for predicting the extreme elevation of the free surface, in the fluid domain between ship-shaped structures in close proximity.
Abstract: The hydrodynamic interaction of waves with arrays of vertical elliptical cylinders is considered. The present paper aims at developing of an efficient calculation method for predicting the extreme elevation of the free surface, in the fluid domain between ship-shaped structures in close proximity. Linear potential theory is employed and the solution method is based on the semi-analytical formulation of the various velocity potentials in elliptical coordinates, using series expansions of Mathieu functions and the so-called addition theorem for Mathieu functions.Copyright © 2009 by ASME