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Study on the true and spurious eigensolutions of two-dimensional cavities using the dual multiple reciprocity method

机译：用双重多重互易法研究二维空腔的真伪参本解

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摘要

In this paper, true and spurious eigensolutions for a circular cavity using the dual multiple reciprocity method (MRM) are analytically derived and numerically verified by the developed program. The roots of spurious eigenequation are found analytically by using symbolic manipulation software. A more efficient method is proposed by choosing a fewer number of equations from the dual MRM instead of all of the equations in the dual MRM. Numerical experiments are performed by using dual MRM program for comparison purposes. A circular cavity of radius 1 m with Neumann boundary conditions is considered, and the results match very well between the theoretical prediction and the numerical experiments for the first four true eigenvalues and the first two spurious eigenvalues. Also, a noncircular case of square cavity is numerically implemented. The true eigensolutions can be easily solved by the dual MRM program in conjunction with the singular value decomposition technique. At the same time, the boundary modes and the multiplicities of the true eigenvalues can also be determined.
机译：在本文中，使用双重多重互易方法（MRM）对圆腔的真和伪本征解进行了解析推导，并通过所开发的程序进行了数值验证。伪特征方程的根源可以通过使用符号操纵软件来分析地找到。通过从对偶MRM中选择较少数量的方程而不是对偶MRM中的所有方程，提出了一种更有效的方法。为了进行比较，使用双重MRM程序进行了数值实验。考虑具有Neumann边界条件的半径为1 m的圆腔，其结果与前四个真实特征值和前两个伪特征值的理论预测和数值实验非常吻合。而且，在数值上实现了方形腔的非圆形情况。真正的本征解可以通过双重MRM程序结合奇异值分解技术轻松解决。同时，还可以确定真实特征值的边界模式和多重性。

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