ECCOMAS 2024

New insights into the variational isogeometric collocation method

  • Möller, Matthias (Delft University of Technology)
  • Vorechovsky, Miroslav (Brno University of Technology)

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Isogeometric Analysis (IGA) has become a widely accepted methodology for solving (initial-)boundary value problems in complex domains. Like its predecessor, the finite element method, IGA exists in multiple variants -- Galerkin IGA, collocation IGA, and least-squares collocation IGA. While the first variant yields the most accurate solutions, collocation-based IGA is computationally more efficient as it bypasses the costly assembly of system matrices via numerical integration. Gomez et al. made an attempt to unify both approaches by exploiting Cauchy's mean-value theorem of integral calculus and show that Galerkin and collocation IGA are equivalent for a specific choice of collocation points. In this talk, we will revisit the so-called variational isogeometric collocation method and show that for certain types of problems, collocation points at which Galerkin and collocation IGA methods coincide can be derived systematically by utilizing the concept of higher order moments.