  We present a mass lumping approach based on an isogeometric Petrov-Galerkin
method that preserves higher-order spatial accuracy in explicit dynamics
calculations irrespective of the polynomial degree of the spline approximation.
To discretize the test function space, our method uses an approximate dual
basis, whose functions are smooth, have local support and satisfy approximate
bi-orthogonality with respect to a trial space of B-splines. The resulting mass
matrix is ``close'' to the identity matrix. Specifically, a lumped version of
this mass matrix preserves all relevant polynomials when utilized in a Galerkin
projection. Consequently, the mass matrix can be lumped (via row-sum lumping)
without compromising spatial accuracy in explicit dynamics calculations. We
address the imposition of Dirichlet boundary conditions and the preservation of
approximate bi-orthogonality under geometric mappings. In addition, we
establish a link between the exact dual and approximate dual basis functions
via an iterative algorithm that improves the approximate dual basis towards
exact bi-orthogonality. We demonstrate the performance of our higher-order
accurate mass lumping approach via convergence studies and spectral analyses of
discretized beam, plate and shell models.
