Rapid material point method analysis for massive problems using MATLAB

For problems in solid mechanics involving large deformations and non-linear behaviour, the Finite Element Method is often not ideal due to issues arising with mesh distortion. This has led to a number of alternative methods being developed, such as the Material Point Method which discretises the physical problem using material points which move through an unchanging background mesh as the material deforms. Increasing computational efficiency is a continuous goal of numerical simulations and previous investigations have found that the integration points in a standard Finite Element Method can be grouped into blocks and calculations can be performed on multiple points at once. This paper describes similar vectorisation and blocking modifications to an existing MATLAB-based Material Point Method code for large deformation problems to achieve significant improvements in code runtimes. It was shown that the speed-up factors achieved are dependent on the size of blocks used, reaching optimal performance at the point where the cache limit of the computer is reached, after which a reduction in performance is observed