  In this contribution, we provide a new mass lumping scheme for explicit
dynamics in isogeometric analysis (IGA). To this end, an element formulation
based on the idea of dual functionals is developed. Non-Uniform Rational
B-splines (NURBS) are applied as shape functions and their corresponding dual
basis functions are applied as test functions in the variational form, where
two kinds of dual basis functions are compared. The first type are approximate
dual basis functions (AD) with varying degree of reproduction, resulting in
banded mass matrices. Dual basis functions derived from the inversion of the
Gram matrix (IG) are the second type and already yield diagonal mass matrices.
We will show that it is possible to apply the dual scheme as a transformation
of the resulting system of equations based on NURBS as shape and test
functions. Hence, it can be easily implemented into existing IGA routines.
Treating the application of dual test functions as preconditioner reduces the
additional computational effort, but it cannot entirely erase it and the
density of the stiffness matrix still remains higher than in standard
Bubnov-Galerkin formulations. In return applying additional row-sum lumping to
the mass matrices is either not necessary for IG or the caused loss of accuracy
is lowered to a reasonable magnitude in the case of AD. Numerical examples show
a significantly better approximation of the dynamic behavior for the dual
lumping scheme compared to standard NURBS approaches making use of row-sum
lumping. Applying IG yields accurate numerical results without additional
lumping. But as result of the global support of the IG dual basis functions,
fully populated stiffness matrices occur, which are entirely unsuitable for
explicit dynamic simulations. Combining AD and row-sum lumping leads to an
efficient computation regarding effort and accuracy.
