Comparison and unification of material-point and optimal transportation meshfree methods

Elizaveta Wobbes*, Roel Tielen, Matthias Möller, Cornelis Vuik

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

3 Citations (Scopus)
57 Downloads (Pure)


Both the material-point method (MPM) and optimal transportation meshfree (OTM) method have been developed to efficiently solve partial differential equations that are based on the conservation laws from continuum mechanics. However, the methods are derived in a different fashion and have been studied independently of one another. In this paper, we provide a direct step-by-step comparison of the MPM and OTM algorithms. Based on this comparison, we derive the conditions, under which the two approaches can be related to each other, thereby bridging the gap between the MPM and OTM communities. In addition, we introduce a novel unified approach that combines the design principles from B-spline MPM and the OTM method. The proposed approach does not contain user-defined parameters and can decrease the costs of the standard OTM method. Moreover, it allows for the use of a consistent mass matrix without stability issues that are typically encountered in MPM computations.

Original languageEnglish
Pages (from-to)113-133
Number of pages21
JournalComputational Particle Mechanics
Volume8 (2021)
Issue number1
Publication statusPublished - 2020

Bibliographical note



  • B-spline
  • Consistent mass matrix
  • Material point
  • Maximum entropy
  • Meshfree
  • Optimal transportation


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