Fast native-MATLAB stiffness assembly for SIPG linear elasticity

Bird, Robert; Coombs, William M.

doi:10.1016/j.camwa.2017.08.022

Cited by 6 publications

(8 citation statements)

References 14 publications

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“…More recently, Bird et al (2017) extended the vectorized and blocked algorithm presented by Dabrowski et al (2008) to the calculation of the global stiffness matrix for discontinuous Galerkin FEM considering linear elastic problems using only native MATLAB functions. Indeed, the optimization strategy chosen by Dabrowski et al (2008) also relied on non-native MATLAB functions, e.g.…”

Section: Introductionmentioning

confidence: 99%

“…sparse2 of the SuiteSparse package (Davis, 2013). In particular, Bird et al (2017) showed the importance of storing vectors in a columnmajor form during calculation. Mathematical operations are performed in MATLAB by calling LAPACK, written in Fortran, in which arrays are stored in column-major order form.…”

Section: Introductionmentioning

confidence: 99%

“…Hence, element-wise multiplication of arrays in columnmajor form is significantly faster; thus, vectors in columnmajor form are recommended whenever possible. 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.…”

Section: Introductionmentioning

confidence: 99%

“…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%

“…We did not consider the blocking technique initially proposed by Dabrowski et al (2008), as an explicit formulation in MPM excludes the global stiffness matrix assembly procedure. The performance gain mainly comes from the vectorization of the algorithm, whereas blocking has a less significant impact over the performance gain, as stated by Bird et al (2017). The vectorization of MATLAB functions is also crucial for a straight transpose of the solver to a more efficient language, such as the C-CUDA language, which allows the parallel execution of computational kernels of graphics processing units (GPUs).…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%