Extension of B-spline Material Point Method for unstructured triangular grids using Powell–Sabin splines

Pascal de Koster*, Roel Tielen, Elizaveta Wobbes, Matthias Möller

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

10 Citations (Scopus)
60 Downloads (Pure)


The Material Point Method (MPM) is a numerical technique that combines a fixed Eulerian background grid and Lagrangian point masses to simulate materials which undergo large deformations. Within the original MPM, discontinuous gradients of the piecewise-linear basis functions lead to the so-called grid-crossing errors when particles cross element boundaries. Previous research has shown that B-spline MPM (BSMPM) is a viable alternative not only to MPM, but also to more advanced versions of the method that are designed to reduce the grid-crossing errors. In contrast to many other MPM-related methods, BSMPM has been used exclusively on structured rectangular domains, considerably limiting its range of applicability. In this paper, we present an extension of BSMPM to unstructured triangulations. The proposed approach combines MPM with C1-continuous high-order Powell–Sabin spline basis functions. Numerical results demonstrate the potential of these basis functions within MPM in terms of grid-crossing-error elimination and higher-order convergence.

Original languageEnglish
Pages (from-to)273-288
JournalComputational Particle Mechanics
Volume8 (2021)
Issue number2
Publication statusPublished - 2020


  • B-splines
  • Grid-crossing error
  • Material Point Method
  • Powell–Sabin splines
  • Unstructured grids


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