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In this contribution, we provide a new mass lumping scheme for explicitdynamics in isogeometric analysis (IGA). To this end, an element formulationbased on the idea of dual functionals is developed. Non-Uniform RationalB-splines (NURBS) are applied as shape functions and their corresponding dualbasis functions are applied as test functions in the variational form, wheretwo kinds of dual basis functions are compared. The first type are approximatedual basis functions (AD) with varying degree of reproduction, resulting inbanded mass matrices. Dual basis functions derived from the inversion of theGram 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 transformationof the resulting system of equations based on NURBS as shape and testfunctions. Hence, it can be easily implemented into existing IGA routines.Treating the application of dual test functions as preconditioner reduces theadditional computational effort, but it cannot entirely erase it and thedensity of the stiffness matrix still remains higher than in standardBubnov-Galerkin formulations. In return applying additional row-sum lumping tothe mass matrices is either not necessary for IG or the caused loss of accuracyis lowered to a reasonable magnitude in the case of AD. Numerical examples showa significantly better approximation of the dynamic behavior for the duallumping scheme compared to standard NURBS approaches making use of row-sumlumping. Applying IG yields accurate numerical results without additionallumping. But as result of the global support of the IG dual basis functions,fully populated stiffness matrices occur, which are entirely unsuitable forexplicit dynamic simulations. Combining AD and row-sum lumping leads to anefficient computation regarding effort and accuracy.

An efficient mass lumping scheme for isogeometric analysis based on approximate dual basis functions