Dispersion Properties of the Partition of Unity Method and Explicit Dynamics
In this paper, we focus on the dispersion properties of the partition of unity method. To this end, we consider the semi-discretized wave equation and determine the resulting numerical phase and group velocities when using a consistent mass matrix and a lumped mass matrix. Our results clearly show that the vartiational mass lumping approach due to  yields comparable dispersion properties than the consistent mass matrix approach. Thus, the lumped mass matrix approach attains very similar accuracy at substantially lower computational cost than the consistent mass matrix in simulations of dynamic behavior.
Meshfree Methods for Partial Differential Equations VII