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.
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TL;DR: In this article, it was shown that the complex coordinate stretching and diagonal anisotropy formulations of the perfectly matched layer are equivalent in a general orthogonal coordinate system setting.
Abstract: It is shown that the complex coordinate stretching and diagonal anisotropy formulations of the perfectly matched layer are equivalent in a general orthogonal coordinate system setting. The results are obtained by taking advantage of the tensorial invariance of the line element.
29 citations
TL;DR: By examining the displacement coordinate metric three modes of constrained optimization for large molecules and clusters are suggested and the final mode is particularly interesting because it can result in computational savings.
Abstract: By examining the displacement coordinate metric three modes of constrained optimization for large molecules and clusters are suggested. The first method corresponds to a conventional optimization using internal coordinates. The second mode has applications with respect to both internal and cartesian coordinates. The final mode is particularly interesting because it can result in computational savings. A mixture of both internal and cartesian coordinates is specified where these coordinates are usually a subset of the molecules or clusters total coordinate set. In the optimization only a subset of the energy derivatives need be evaluated reducing the computational effort associated with the gradient calculation.
28 citations
TL;DR: A unified theory of the Laplace transform analytic-element method (LT-AEM) for solving transient porous-media flow problems is presented in this paper, which uses superposition and boundary collocation with Laplace-space convolution to compute flexible semi-analytic solutions.
Abstract: A unified theory of the Laplace-transform analytic-element method (LT-AEM) for solving transient porous-media flow problems is presented. LT-AEM applies the analytic-element method (AEM) to the modified Helmholtz equation, the Laplace-transformed diffusion equation. LT-AEM uses superposition and boundary collocation with Laplace-space convolution to compute flexible semi-analytic solutions from a small collection of fundamental elements. The elements discussed are derived using eigenfunction expansions of element shapes in their natural coordinates. A new formulation for a constant-strength line source is presented in terms of elliptical coordinates and complex-parameter Mathieu functions. Examples are given illustrating how leaky and damped-wave hydrologic problems can be solved with little modification using existing LT-AEM techniques.
27 citations
TL;DR: In this paper, the Lax matrix for the Chaplygin system on the sphere with velocity dependent potential was obtained starting with the matrix for other integrable systems separable in elliptic coordinates on the surface.
27 citations
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