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Showing papers on "Elliptic coordinate system published in 2002"


Journal ArticleDOI
TL;DR: In this paper, a second-order-accurate finite difference method for the cylindrical coordinate system is developed, and it is rigorously proved that energy conservation in discretized space is satisfied when appropriate interpolation schemes are used.

160 citations


Journal ArticleDOI
TL;DR: In the course of checking their work on the symbolic calculation of molecular integrals over Slater orbitals, this paper obtained some results in substantial disagreement with two recent articles that describe numerical schemes.
Abstract: In the course of checking our work on the symbolic calculation of molecular integrals over Slater orbitals, we obtained some results in substantial disagreement with two recent articles that describe numerical schemes. We believe that these schemes suffer from digital erosion, possibly because recurrence formulas were used outside their regions of stability. Our results were obtained using the ζ-function method, which expands the orbital on one atom onto the other, and integrates in polar coordinates. They were checked using elliptic coordinates. Both sets of calculations were performed symbolically. We summarize these calculations and discuss the impact of symbolic calculation on the accuracy of molecular computations.

35 citations


Journal ArticleDOI
TL;DR: In this article, an unconditionally stable finite-difference time-domain (FDTD) method in a cylindrical coordinate system is presented, where the time step is no longer restricted by the stability condition, but by the modeling accuracy.
Abstract: An unconditionally stable finite-difference time-domain (FDTD) method in a cylindrical coordinate system is presented in this paper. The alternating-direction-implicit (ADI) method is applied, leading to a cylindrical ADI-FDTD scheme where the time step is no longer restricted by the stability condition, but by the modeling accuracy. In contrast to the conventional ADI method, in which the alternation is applied in each coordinate direction, the ADI scheme here performs alternations in mixed coordinates so that only two alternations in solution matching are required at each time step in the three-dimensional formulation. Different from its counterpart in the Cartesian coordinate system, the cylindrical ADI-FDTD includes an additional special treatment along the vertical axis of the cylindrical coordinates to overcome singularity. A theoretical proof of the unconditional stability is shown and numerical results are presented to demonstrate the effectiveness of the cylindrical algorithm in solving electromagnetic-field problems.

26 citations


Journal ArticleDOI
TL;DR: In this paper, a wavelet family augmented by special edge functions is used to solve the quantum eigenvalue equations for the hydrogen molecular ion H2+ in the Born-Oppenheimer approximation.
Abstract: Multiscale wavelets are used to solve the quantum eigenvalue equations for the hydrogen molecular ion H2+ in the Born–Oppenheimer approximation Normally restricted to Cartesian systems, “wavelets on the interval” (a normal wavelet family augmented by special edge functions) have recently been applied to such boundary value problems as the hydrogen atom in spherical polar coordinates [J Mackey, J L Kinsey, and B R Johnson, J Comp Phys 168, 356 (2001)] These methods are extended here to ground and excited electronic states of the simplest molecule, for which the electronic Hamiltonian is separable in confocal elliptic coordinates The set of curvilinear coordinate quantum systems for which wavelet bases have been applied is thus enlarged

17 citations


Journal ArticleDOI
TL;DR: In this article, it was shown that a subset of the multidimensional Euler equations can be diagonalized, but not the entire set, and the authors extended the formulation of the conservation equations into the local stream-wise coordinate system to the time-dependent, 2D and 3D conservation equations.
Abstract: In dealing with multidimensional simulations, many authors have shown that a major cause of numerical dispersion errors is due to the flow being skewed to the coordinate axes. Crane and Blunt [1] have shown that the stream-wise transformations can reduce the numerical errors associated with the multidimensional transport equations. However, it has been proven that no transformation can completely diagonalize the multidimension conservation equations. It shall be demonstrated that a subset of the multidimensional Euler equations can be diagonalized, but not the entire set. The formulation of the conservation equations into the local stream-wise coordinate system is extended to the time-dependent, two- and three-dimensional (2D and 3D) conservation equations. At any point in space, there exists a set of local rotations that aligns the fluid velocity vector coincident with the stream-wise coordinate; hence, the fluid velocity components orthogonal to the stream-wise coordinate are identically zero. Such transformations result in a subset of PDEs that are diagonalized, namely, the mass, total energy, and principal momentum density PDEs. However, the orthogonal momentum component conservation PDEs are not diagonalized and are multidimensional; these PDEs are responsible for streamline bending.

13 citations


Posted Content
TL;DR: In this article, a fast algorithm to find apparent horizons is presented, which uses an explicit representation of the horizon surface, allowing for arbitrary horizon resolutions and, in principle, shapes.
Abstract: I present a fast algorithm to find apparent horizons. This algorithm uses an explicit representation of the horizon surface, allowing for arbitrary horizon resolutions and, in principle, shapes. Novel in this approach is that the tensor quantities describing the horizon live directly on the horizon surface, yet are represented using Cartesian coordinate components. This eliminates coordinate singularities, and leads to an efficient implementation. The apparent horizon equation is then solved as a nonlinear elliptic equation with standard methods. I explain in detail the coordinate systems used to store and represent the tensor components of the intermediate quantities, and describe the grid boundary conditions and the treatment of the polar coordinate singularities. Last I give as examples apparent horizons for single and multiple black hole configurations.

10 citations


Journal ArticleDOI
Zi-Niu Wu1
TL;DR: This note considers a one-dimensional problem and shows that there is a parameter range within 0 and it is shown that the traditional Eulerian approach and Lagrangian approach to describing fluid flows can be combined.

9 citations



01 Jan 2002
TL;DR: This paper takes 3-,4-,7-, parameter transfer model to accomplish calculation from Xi'an 80 coordinate system to WGS-84 coordinate system.
Abstract: Based on coinciding 174 triangular points from coordinate system 1980 with GPS-A.B networks, this paper takes 3-,4-,7-, parameter transfer model to accomplish calculation from Xi'an 80 coordinate system to WGS-84 coordinate system. After all, accuracy analysis is discussed in this Paper.

4 citations



Journal ArticleDOI
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.

Proceedings ArticleDOI
16 Dec 2002
TL;DR: In this article, a new approach to the theoretical study of the electron beam-wave interaction in arbitrary RF structures is presented, where the permittivity tensor and the permeability tensor can be found in the moving coordinate system for the beam while that for the plasma can be located in the lab coordinate system.
Abstract: A new approach to the theoretical study of the electron beam-wave interaction in arbitrary RF structures is presented in this paper. In any such interaction system, there are two coordinate systems: the lab system; the rest coordinate system for the plasma, if it exists; and the moving coordinate system for the electron beam. Both the electron beam and the plasma are considered special media with different characteristics. The permittivity tensor and the permeability tensor can be found in the moving coordinate system for the beam while that for the plasma can be found in the lab coordinate system. Then, making use of the transformation of electromagnetic fields in Minkovski space and the Lorentz transformation of the 4D wave vectors, all the physics quantities in the moving coordinate system can be transferred into the lab coordinate system. Then the Maxwell's equations with the transferred constitutive tensors should be used to derive the desired dispersion equation. This new approach is a very efficient and accurate method for the study of electron beam-wave interactions.