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

O'Sullivan, S; Bird, R.E.; Coombs, W.M.; Giani, S.

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


Authors

S O'Sullivan

Dr Robert Bird robert.e.bird@durham.ac.uk
PDRA in Computational Solid Mechanics



Abstract

MATLAB is adept at the development of concise Finite Element (FE) routines, however it is commonly perceived to be too inefficient for high fidelity analysis. This paper aims to challenge this preconception by presenting two optimised FE codes for both continuous Galerkin (CG) and discontinuous Galerkin (DG) methods. Although this has previously been achieved for linear-elastic problems, no such optimised MATLAB script currently exists, which includes the effects of material non-linearity. To incorporate these elasto-plastic effects, the externally applied load is split into a discrete number of loadsteps. Equilibrium is determined at each loadstep between the externally applied load and the arising internal forces using the Newton–Raphson method. The optimisation of the scripts is primarily achieved using vectorised blocking algorithms, which minimise RAM-to-cache overheads and maximise cache reuse. The optimised codes yielded maximum speed gains of 25.7 and 10.1 when compared to the corresponding unoptimised scripts, for CG and DG respectively. It was identified that with increasing refinement of the mesh, the solver time begins to dominate the overall simulation time. This bottleneck has a greater disadvantage on the DG code, predominantly due the asymmetric nature of the global stiffness matrix. The implementation of an efficient solver would see further improvement to the overall run times, particularly for large problems.

Citation

O'Sullivan, S., Bird, R., Coombs, W., & Giani, S. (2019). Rapid non-linear finite element analysis of continuous and discontinuous Galerkin methods in MATLAB. Computers and Mathematics with Applications, 78(9), 3007-3026. https://doi.org/10.1016/j.camwa.2019.03.012

Journal Article Type Article
Acceptance Date Mar 6, 2019
Online Publication Date Apr 12, 2019
Publication Date Jan 1, 2019
Deposit Date Mar 7, 2019
Publicly Available Date Oct 4, 2019
Journal Computers and Mathematics with Applications
Print ISSN 0898-1221
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 78
Issue 9
Pages 3007-3026
DOI https://doi.org/10.1016/j.camwa.2019.03.012
Keywords elasto-plasticity, finite element analysis, discontinuous Galerkin, MATLAB code vectorization

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