复杂形状物体上标量亥姆霍兹方程三维诺伊曼问题的数值解

MMET '96. VIth International Conference on Mathematical Methods in Electromagnetic Theory. Proceedings Pub Date : 1996-09-10 DOI:10.1109/MMET.1996.565728

I. Lifanov, I. Lifanov, S. Novikov

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摘要

本文研究标量亥姆霍兹方程的三维外边界诺伊曼问题。利用双层势，将该问题简化为第一类超奇异积分方程。提出了求解任意形式物体上的超奇异积分方程的数值方法。该方法是一种离散涡型方法。对球面的精确解与数值解进行了比较。给出了立方体和平板的计算结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Numerical solution of 3-D Neuman problem for scalar Helmholtz equation at the bodies of complex shapes

Our paper is concerned with solving the 3D outside boundary Neuman problem for the scalar Helmholtz equation. By means of the double layer potential, this problem reduces to the hypersingular integral equation of the 1-st kind. The numerical method for solving the hypersingular integral equation at bodies of arbitrary form is proposed. This method is a method of discrete vortex type. Comparison of the exact solution for a sphere with the numerical one is carried out. Results of the computation for a cube and for a plate are presented.

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MMET '96. VIth International Conference on Mathematical Methods in Electromagnetic Theory. Proceedings

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