Imperial College London
Alternate

ProfessorPaulKelly

Faculty of Engineering, Department of Computing

Professor of Software Technology
 
 
 
//

Contact

 

+44 (0)20 7594 8332p.kelly Website

 
 
//

Location

 

Level 3 (upstairs), William Penney Building, room 304William Penney LaboratorySouth Kensington Campus

//

Summary

 

Publications

Citation

BibTex format

@article{Sun:2020:10.1177/1094342020945005,
author = {Sun, T and Mitchell, L and Kulkarni, K and Klockner, A and Ham, DA and Kelly, PHJ},
doi = {10.1177/1094342020945005},
journal = {International Journal of High Performance Computing Applications},
pages = {629--644},
title = {A study of vectorization for matrix-free finite element methods},
url = {http://dx.doi.org/10.1177/1094342020945005},
volume = {34},
year = {2020}
}
Download

RIS format (EndNote, RefMan)

TY  - JOUR
AB  - Vectorization is increasingly important to achieve high performance on modern hardware with SIMD instructions. Assembly of matrices and vectors in the finite element method, which is characterized by iterating a local assembly kernel over unstructured meshes, poses difficulties to effective vectorization. Maintaining a user-friendly high-level interface with a suitable degree of abstraction while generating efficient, vectorized code for the finite element method is a challenge for numerical software systems and libraries. In this work, we study cross-element vectorization in the finite element framework Firedrake via code transformation and demonstrate the efficacy of such an approach by evaluating a wide range of matrix-free operators spanning different polynomial degrees and discretizations on two recent CPUs using three mainstream compilers. Our experiments show that our approaches for cross-element vectorization achieve 30% of theoretical peak performance for many examples of practical significance, and exceed 50% for cases with high arithmetic intensities, with consistent speed-up over (intra-element) vectorization restricted to the local assembly kernels.
AU  - Sun,T
AU  - Mitchell,L
AU  - Kulkarni,K
AU  - Klockner,A
AU  - Ham,DA
AU  - Kelly,PHJ
DO  - 10.1177/1094342020945005
EP  - 644
PY  - 2020///
SN  - 1094-3420
SP  - 629
TI  - A study of vectorization for matrix-free finite element methods
T2  - International Journal of High Performance Computing Applications
UR  - http://dx.doi.org/10.1177/1094342020945005
UR  - http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000554544900001&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
UR  - https://journals.sagepub.com/doi/10.1177/1094342020945005
UR  - http://hdl.handle.net/10044/1/90136
VL  - 34
ER  -
Download