8, Higher order accurate mass lumping for explicit isogeometric methods based on approximate dual basis functions
This paper introduces a mathematical framework for explicit structural dynamics, employing approximate dual functionals and row-sum mass lumping. We demonstrate that the Petrov–Galerkin method developed in our previous work—utilizing row-sum mass lumping—can be interpreted as a Galerkin method with a customized higher-order accurate mass matrix. Unlike prior work, our method correctly incorporates Dirichlet boundary conditions, while preserving optimal spatial accuracy. The mathematical analysis is substantiated by spectral analysis, two-dimensional linear benchmarks illustrating robustness under mesh distortion and a three-dimensional geometrically non-linear forced vibration analysis. The obtained results reveal that our approach achieves accuracy and robustness comparable to a traditional Galerkin method employing the consistent mass formulation, while retaining the explicit nature of the lumped mass formulation.