A new meshless method for eigenproblems using radial basis function

Abstract

In this lecture, a new meshless method for solving eigenproblems using the radial basis function (RBF) is proposed. By employing the imaginary-part fundamental solution as the RBF, the diagonal and off-diagonal coefficients of the influence matrices are easily determined. True eigensolutions in conjunction with spurious eigensolutions occur at the same time. To verify this finding, the circulant is adopted to analytically derive the true and spurious eigenequations in the discrete system for a circular domain. In order to obtain the true and spurious eigenvalues, the singular value decomposition (SVD) technique of updating technique is utilized. Several examples, including 2-D and 3-D interior acoustics and plate eigenproblems, are demonstrated analytically and numerically to see the validity of the present method.