IGA2025

Keynote

The prospects of interpolatory spline functions for mass lumping

  • Voet, Yannis (École polytechnique fédérale de Lausanne)
  • Sande, Espen (École polytechnique fédérale de Lausanne)
  • Buffa, Annalisa (École polytechnique fédérale de Lausanne)

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Since the early days of finite element analysis, ad hoc (diagonal) approximations of the mass matrix have been paramount for speeding up the solution process of explicit time integration schemes in structural dynamics. The nodal quadrature method is one of the most successful mass lumping strategies for spectral finite element discretizations. This method, which uses the Gauss-Lobatto nodes both as element nodes and quadrature points, critically relies on the interpolatory nature of Lagrange basis functions. Unfortunately, this property is generally lost for spline-based discretization techniques and the nodal quadrature method does not have any straightforward equivalent in isogeometric analysis (IGA). Interpolatory spline bases, which had mostly been abandoned in favor of the B-spline basis, have recently resurfaced for extending the construction of the nodal quadrature method to IGA. In this talk, we discuss the pros and cons of interpolatory spline functions to determine whether they constitute a viable pathway for high order mass lumping techniques.