Comparison between Material Point Method and meshfree schemes derived from optimal transportation theory
Lisa Wobbes (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Roel Tielen (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Matthias Möller (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Kees Vuik (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Vahid Galavi (Deltares)
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Abstract
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 close resemblance of MPM and Optimal Transportation Meshfree (OTM) schemes. Aside from a theoretical analysis, the methods are compared numerically using a one-dimensionalbenchmark.