Rapid non-linear finite element analysis of continuous and discontinuous Galerkin methods in MATLAB

O’Sullivan, Stephen; Bird, Robert; Coombs, William M.; Giani, Stefano

doi:10.1016/j.camwa.2019.03.012

Cited by 5 publications

(1 citation statement)

References 35 publications

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“…Bird et al (2017) concluded that vectorization alone results in a performance increase of between 13.7 and 23 times, whereas blocking only improved vectorization by an additional 1.8 times. O'Sullivan et al (2019) recently extended the works of Bird et al (2017) and Dabrowski et al (2008) to optimized elasto-plastic codes for continuous Galerkin (CG) or discontinuous Galerkin (DG) methods. In particular, they proposed an efficient native MATLAB function, accumarray(), to efficiently assemble the internal force vector.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2020

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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.

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