On the Numerical Dispersion of the Radial Point Interpolation Meshless Method

The numerical dispersion of the time-domain radial point interpolation meshless (RPIM) method is investigated in this letter. It is found that numerical dispersion relationship of RPIM method shares the same form as that of a second-order central finite-difference time-domain method but with the additional factor introduced by the radial basis functions, when i) the two methods deploy the same nodal distribution for problem-domain discretization and ii) the local support domain of the RPIM method is defined to enclose only four adjacent nodes. Such an observation indicates that the RPIM method is a more general method and can be reduced to the conventional finite-difference time-domain method under certain conditions. In addition, comparisons between the meshless method and the finite-difference time-domain method are shown under different conditions.