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

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...

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

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...

Comparison between Material Point Method and meshfree schemes derived from optimal transportation theory

Both the Material Point Method (MPM) and meshfree schemes based on optimal transport theory have been developed for efficient and robust integration of the weak form equations originating from computational mechanics. Although the methods are derived in a different fashion, their algorithms share many similarities. In this paper, we outline the...

Recent Developments to Improve the Numerical Accuracy

A High Order Material Point Method

The classical material point method (MPM) developed in the 90s is known for drawbacks which affect the quality of results. The movement of material points from one element to another leads to non-physical oscillations known as ‘grid crossing errors’. Furthermore, the use of material points as integration points renders a numerical quadrature...