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

TL;DR

This paper presents a novel higher-order accurate mass lumping technique for explicit isogeometric methods, utilizing approximate dual basis functions to improve accuracy and boundary condition handling while maintaining computational efficiency.

Contribution

It introduces a new mass lumping approach based on approximate dual basis functions that correctly incorporates Dirichlet boundary conditions and preserves higher-order accuracy.

Findings

Achieves accuracy comparable to traditional Galerkin methods

Maintains explicit formulation benefits with improved accuracy

Demonstrated robustness through spectral analysis and benchmarks

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.