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

Research output: Contribution to journalArticleScientificpeer-review

36 Downloads (Pure)

Abstract

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
Number of pages21
JournalComputational Particle Mechanics
Early online date2020
DOIs
Publication statusPublished - 1 Feb 2020

Keywords

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

Fingerprint Dive into the research topics of 'Comparison and unification of material-point and optimal transportation meshfree methods'. Together they form a unique fingerprint.

  • Cite this