On the Numerical Dispersion of the Radial Point Interpolation Meshless (RPIM) Method in Lossy Media

Abstract

A general formula for numerical dispersion of the two-dimensional time-domain radial point interpolation meshless (2-D RPIM) method is analytically derived. Numerical loss and dispersion characteristics of the RPIM method with both Gaussian and multiquadric basis functions are investigated. It is found that numerical loss and dispersion errors of the RPIM vary with types of basis functions used and associated parameters, number of the nodes, and medium conductivities. In addition, condition numbers of the moment matrix of the meshless methods can also increase numerical dispersion errors. With a reasonable condition number of the moment matrix, the radial point interpolation meshless methods perform generally better than the FDTD method in terms of numerical dispersion errors.