Fast and efficient MATLAB-based MPM solver (fMPMM-solver v1.0)

Abstract

Abstract. In this contribution, we present an efficient MATLAB-based implementation of the material point method (MPM) and its most recent variants. MPM has gained popularity over the last decade, especially for problems in solid mechanics in which large deformations are involved, i.e., cantilever beam problems, granular collapses and even large-scale snow avalanches. Although its numerical accuracy is lower than that of the widely accepted finite element method (FEM), MPM has been proven useful in overcoming some of the limitations of FEM, such as excessive mesh distortions. We demonstrate that MATLAB is an efficient high-level language for MPM implementations that solve elasto-dynamic and elasto-plastic problems, such as the cantilever beam and granular collapses, respectively. We report a computational efficiency factor of 20 for a vectorized code compared to a classical iterative version. In addition, the numerical efficiency of the solver surpassed those of previously reported MPM implementations in Julia, ad minima 2.5 times faster under a similar computational architecture.