|Title:||ON THE TRUE AND SPURIOUS EIGENVALUES BY USINGTHE REAL OR THE IMAGINARY-PART OF THE METHODOF FUNDAMENTAL SOLUTIONS||Authors:||Chen, I. L.
Kuo, P. S.
|Keywords:||Method of fundamental solutions;singular value decomposition;spurious eigenvalue;right unitary;left unitary||Issue Date:||8-Jan-2013||Publisher:||World Scientific||Journal Volume:||10||Journal Issue:||2||Start page/Pages:||1341003||Source:||International Journal of Computational Methods||Abstract:||
In this paper, the method of fundamental solutions (MFS) of real-part or imaginary-part kernels is employed to solve two-dimensional eigenproblems. The occurring mechanism of spurious eigenvalues for circular and elliptical membranes is examined. It is found that the spurious eigensolution using the MFS depends on the location of the fictitious boundary where the sources are distributed. By employing the singular value decomposition technique, the common left unitary vectors of the true eigenvalue for the single- and double-layer potential approaches are found while the common right unitary vectors of the spurious eigenvalue are obtained. Dirichlet and Neumann eigenproblems are both considered. True eigenvalues are dependent on the boundary condition while spurious eigenvalues are different in the different approach, single-layer or double-layer potential MFS. Two examples of circular and elliptical membranes are numerically demonstrated to see the validity of the present method and the results are compared well with the theoretical prediction.
|Appears in Collections:||河海工程學系|
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.