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

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

Wobbes, Elizaveta (TU Delft Numerical Analysis)
Tielen, R.P.W.M. (TU Delft Numerical Analysis)
Möller, M. (TU Delft Numerical Analysis)
Vuik, Cornelis (TU Delft Numerical Analysis)

2020

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.

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

http://resolver.tudelft.nl/uuid:f49ba802-f6da-4c1f-ae4c-e5c61d6f6a6d

https://doi.org/10.1007/s40571-020-00316-7

2196-4378

Computational Particle Mechanics, 8 (2021) (1), 113-133

Green

Institutional Repository

journal article

© 2020 Elizaveta Wobbes, R.P.W.M. Tielen, M. Möller, Cornelis Vuik