On the True and Spurious Eigensolutions Using Circulants for Real-Part Dual BEM

Abstract

It has been found recently that the multiple reciprocity method (MRM), the real-part BEM and the imaginary-part BEM result in spurious eigenvalues for eigenproblems. In this paper, a circular domain is considered as a demonstrative example. Based on the dual framework of real-part BEM, the true and spurious eigenvalues can be separated by using the singular value decomposition technique (SVD). To understand why the spurious eigenvalues occur, analytical derivation by discretizing the circular boundary into a discrete system is employed and results in a circulants. By using the SVD updating terms, the true eigensolutions can be extracted by merging the two influence matrices in dual BEM. The spurious eigensolutions can be filtered out by using the SVD updating documents where the other two influence matrices are combined.