The plane waves method for axisymmetric Helmholtz problems

Andreas Karageorghis

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The plane waves method for axisymmetric Helmholtz problems

机译：轴对称亥姆霍兹问题的平面波方法

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摘要

The plane waves method is employed for the solution of Dirichlet and Neumann boundary value problems for the homogeneous Helmholtz equation in two- and three-dimensional domains possessing radial symmetry. The appropriate selection of collocation points and unitary direction vectors in the method leads to circulant and block circulant coefficient matrices in two and three dimensions, respectively. We propose efficient matrix decomposition algorithms which make use of fast Fourier transforms for the solution of the systems resulting from such a discretization. In conjunction with the method of particular solutions, the method is extended to the solution of inhomogeneous axisymmetric Helmholtz problems. Several numerical examples are presented.

机译：对于具有径向对称性的二维和三维域中的齐次亥姆霍兹方程，采用平面波方法求解Dirichlet和Neumann边值问题。在该方法中适当选择搭配点和单一方向矢量会分别导致二维和三维的循环和块循环系数矩阵。我们提出了一种有效的矩阵分解算法，该算法利用快速傅里叶变换来解决这种离散化所产生的系统问题。结合特定解的方法，该方法扩展到非均匀轴对称亥姆霍兹问题的解。给出了几个数值示例。

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来源
《Engineering analysis with boundary elements》 |2016年第8期|46-56|共11页
作者
Andreas Karageorghis;
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作者单位

Department of Mathematics and Statistics, University of Cyprus/ΠANEΠIΣTHMIO KYΠPOY. P.O. Box 20537, Nicosia/△EYKΩΣIA, Cyprus;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
Plane waves method; Collocation; Matrix decomposition algorithm; Fast Fourier transforms; Helmholtz equation;

机译：平面波法;搭配;矩阵分解算法;快速傅立叶变换;亥姆霍兹方程;

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2. Generalized plane wave discontinuous Galerkin methods for nonhomogeneous Helmholtz equations with variable wave numbers [J] . Long Yuan, Qiya Hu International journal of computer mathematics . 2020,第1a4期

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3. Comparisons of three kinds of plane wave methods for the Helmholtz equation and time-harmonic Maxwell equations with complex wave numbers [J] . Yuan Long, Hu Qiya Journal of Computational and Applied Mathematics . 2018,第期

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5. Fictitious domain decomposition methods for a class of partially axisymmetric problems: Application to the scattering of acoustic waves. [D] . Hetmaniuk, Ulrich Ladislas. 2002

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6. On the scattering of torsional waves from axisymmetric defects in buried pipelines [O] . Wenbo Duan, Ray Kirby, Peter Mudge -1

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7. Learning Dominant Wave Directions For Plane Wave Methods For High-Frequency Helmholtz Equations [O] . Fang, Jun, Qian, Jianliang, Zepeda-Núñez, Leonardo, 2016

机译：学习平面波方法的主导波方向高频亥姆霍兹方程
8. Coupled Fe (Finite Element) and Hie (Helmholtz Integral Equation) Method for Exterior Acoustics of Axisymmetric Shells [R] . James, J. H. 1987

机译：轴对称壳体外部声学耦合Fe（有限元）和Hie（亥姆霍兹积分方程）方法

The plane waves method for axisymmetric Helmholtz problems

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