Open AccessA GPU-based caching strategy for multi-material linear elastic FEM on regular grids
Author(s) -
Christian Schlinkmann,
Michael Roland,
Christian Wolff,
Patrick Trampert,
Philipp Slusallek,
Stefan Diebels,
Tim Dahmen
Publication year - 2020
Publication title -
plos one
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.99
H-Index - 332
ISSN - 1932-6203
DOI - 10.1371/journal.pone.0240813
Subject(s) - finite element method , computer science , computational science , multigrid method , parallel computing , node (physics) , convergence (economics) , pyramid (geometry) , block (permutation group theory) , matrix (chemical analysis) , computation , algorithm , materials science , mathematics , geometry , physics , mathematical analysis , partial differential equation , economics , composite material , economic growth , quantum mechanics , thermodynamics
In this study, we present a novel strategy to the method of finite elements (FEM) of linear elastic problems of very high resolution on graphic processing units (GPU). The approach exploits regularities in the system matrix that occur in regular hexahedral grids to achieve cache-friendly matrix-free FEM. The node-by-node method lies in the class of block-iterative Gauss-Seidel multigrid solvers. Our method significantly improves convergence times in cases where an ordered distribution of distinct materials is present in the dataset. The method was evaluated on three real world datasets: An aluminum-silicon ( AlSi ) alloy and a dual phase steel material sample, both captured by scanning electron tomography, and a clinical computed tomography (CT) scan of a tibia. The caching scheme leads to a speed-up factor of ×2-×4 compared to the same code without the caching scheme. Additionally, it facilitates the computation of high-resolution problems that cannot be computed otherwise due to memory consumption.