On the spurious eigensolutions for the real-part boundary element method

Abstract

In this paper, the eigensolutions are derived by using seven determinants of the direct searching approach. Seven determinants include the complex-valued, real and imaginary parts of determinant using the complex-valued kernel as well as the determinant by using the real-part, and imaginary-part kernels as well as the multiple reciprocity method (MRM). It is found that spurious eigensolutions of the real-part BEM match well with those of the MRM for the one-dimensional case. The idea of the Combined Helmholtz Exterior integral Equation Formulation method (CHEEF) in conjunction with the singular value decomposition (SVD) technique can be applied to suppress the occurrence of spurious eigenvalues. Possible failure CHEEF points are also examined. Updating terms and updating documents are employed to extract out the true and spurious eigenvalues. Two and three dimensional cases are straight-forward to be extended. Their spurious eigenvalues are also explored.