Actions

Download Analytics Citations

Export to: EndNote  |  Zotero  |  Mendeley

Collections

This file is not currently in any collections.

Fast native-MATLAB stiffness assembly for SIPG linear elasticity Open Access

When written in MATLAB the finite element method (FEM) can be implemented quickly and with significantly fewer lines, when compared to compiled code. MATLAB is also an attractive environment for generating bespoke routines for scientific computation as it contains a library of easily accessible inbuilt functions, effective debugging tools and a simple syntax for generating scripts. However, there is a general view that MATLAB is too inefficient for the analysis of large problems. Here this preconception is challenged by detailing a vectorised and blocked algorithm for the global stiffness matrix computation of the symmetric interior penalty discontinuous Galerkin (SIPG) FEM. The major difference between the computation of the global stiffness matrix for SIPG and conventional continuous Galerkin approximations is the requirement to evaluate inter-element face terms, this significantly increases the computational effort. This paper focuses on the face integrals as they dominate the computation time and have not been addressed in the existing literature. Unlike existing optimised finite element algorithms available in the literature the paper makes use of only native MATLAB functionality and is compatible with GNU Octave. The algorithm is primarily described for 2D analysis for meshes with homogeneous element type and polynomial order. The same structure is also applied to, and results presented for, a 3D analysis. For problem sizes of 10^6 degrees of freedom (DOF), 2D computations of the local stiffness matrices were at least ≈ 24 times faster, with 13.7 times improvement from vectorisation and a further 1.8 times improvement from blocking. The speed up from blocking and vectorisation is dependent on the computer architecture, with the range of potential improvements shown for two architectures in this paper.

Descriptions

Resource type

Dataset

Contributors

Creator: Bird, R. ¹
Creator: Coombs, W.M. ¹
Creator: Giani, S. ¹

¹ Durham University, UK

Funder

Engineering and Physical Sciences Research Council

Research methods

Other description

Keyword

linear elasticity
symmetric interior penalty
discontinuous Galerkin
stiffness matrix
MATLAB
efficient

Subject

Location

Language

Cited in

doi:10.1016/j.camwa.2017.08.022

Identifier

ark:/32150/r1xs55mc04f
doi:10.15128/r1xs55mc04f

Rights

Creative Commons Attribution 4.0 International (CC BY)

Publisher

Durham University

Date Created

File Details

Depositor

R.E. Bird

Date Uploaded

22 August 2017, 09:08:18

Date Modified

6 September 2017, 16:09:34

Audit Status

Audits have not yet been run on this file.

Characterization

File format: zip (ZIP Format)

Mime type: application/zip

File size: 6596

Last modified: 2017:09:06 16:20:00+01:00

Filename: Figure_data_FAST_SIPG.zip

Original checksum: e1228c32253e887abd788cc180b228a0