Higher order accurate mass lumping for explicit isogeometric methods based on approximate dual basis functions

Abstract

This paper introduces a mathematical framework for explicit structural dynamics, employing approximate dual functionals and rowsum mass lumping. We demonstrate that the approach may be interpreted as a Petrov-Galerkin method that utilizes rowsum mass lumping or as a Galerkin method with a customized higher-order accurate mass matrix. Unlike prior work, our method correctly incorporates Dirichlet boundary conditions while preserving higher order accuracy. The mathematical analysis is substantiated by spectral analysis and a two-dimensional linear benchmark that involves a non-linear geometric mapping. Our 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.

References in corpus (3)

• A mathematical theory for mass lumping and its generalization with applications to isogeometric analysis
• Isogeometric Bézier dual mortaring: Refineable higher-order spline dual bases and weakly continuous geometry
• Towards higher-order accurate mass lumping in explicit isogeometric analysis for structural dynamics

Cited by in corpus (3)

• On the efficiency of explicit and semi-explicit immersed boundary finite element methods for wave propagation problems
• A theoretical study on the effect of mass lumping on the discrete frequencies in immersogeometric analysis
• A dual lumping procedure for static condensation in mixed NURBS-based isogeometric elements with optimal convergence rates for arbitrary open knot vectors