A fast and efficient MATLAB-based MPM solver: fMPMM-solver v1.1

Abstract

Abstract. 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, such as 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 proven useful for 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. We accelerate the MATLAB-based implementation of the MPM method by using the numerical techniques recently developed for FEM optimization in MATLAB. These techniques include vectorization, the use of native MATLAB functions and the maintenance of optimal RAM-to-cache communication, among others. We validate our in-house code with classical MPM benchmarks including (i) the elastic collapse of a column under its own weight; (ii) the elastic cantilever beam problem; and (iii) existing experimental and numerical results, i.e. granular collapses and slumping mechanics respectively. We report an improvement in performance by a factor of 28 for a vectorized code compared with a classical iterative version. The computational performance of the solver is at least 2.8 times greater than those of previously reported MPM implementations in Julia under a similar computational architecture.

An explicit GPU-based material point method solver for elastoplastic problems (ep2-3De v1.0)

“…The GPU-based algorithm relies heavily on the use of arrays p2e and e2n (Wyser et al, 2020a). Elements are numbered with an increasing index.…”

“…The wall-clock time for Model 1b is t GPU = 1470.5 s (25 min), and the number of iterations per second is 85.5 iterations s −1 for n mp = 819 200. As a preliminary example, the same numerical model was performed by Wyser et al (2020a), who reported 19.98 iterations s −1 for n mp = 12 800. Proportionally, this corresponds to a performance gain factor of 275 for the GPU-based implementa- tion (ep2-3De v1.0) over the MATLAB-based implementation (fMPMM-solver v1.1) (Wyser et al, 2020a).…”

“…We propose an explicit GIMPM implementation in a threedimensional configuration on a single GPU and multiple GPUs (ep2-3De v1.0), taking advantage of the efficient vectorized algorithmic structure of the MPM solver proposed by Wyser et al (2020a). Our GPU-based solver relies on built-in functions of atomic operations for the mapping between material points and their associated nodes (i.e.…”