To the top

Page Manager: Webmaster
Last update: 9/11/2012 3:13 PM

Tell a friend about this page
Print version

Topological optimization … - University of Gothenburg, Sweden Till startsida
To content Read more about how we use cookies on

Topological optimization of the evaluation of finite element matrices

Journal article
Authors R.C. Kirby
Anders Logg
L. Ridgway Scott
A.R. Terrel
Published in SIAM Journal on Scientific Computing
Volume 28
Issue 1
Pages 224-240
ISSN 1064-8275
Publication year 2006
Published at Department of Mathematical Sciences, Mathematics
Pages 224-240
Language en
Keywords Finite element , Minimum spanning tree , Optimized algorithm , Variational form
Subject categories Mathematics, Computational Mathematics


We present a topological framework for finding low-flop algorithms for evaluating element stiffness matrices associated with multilinear forms for finite element methods posed over straight-sided affine domains. This framework relies on phrasing the computation on each element as the contraction of each collection of reference element tensors with an element-specific geometric tensor. We then present a new concept of complexity-reducing relations that serve as distance relations between these reference element tensors. This notion sets up a graph-theoretic context in which we may find an optimized algorithm by computing a minimum spanning tree. We present experimental results for some common multilinear forms showing significant reductions in operation count and also discuss some efficient algorithms for building the graph we use for the optimization. © 2006 Society for Industrial and Applied Mathematics.

Page Manager: Webmaster|Last update: 9/11/2012

The University of Gothenburg uses cookies to provide you with the best possible user experience. By continuing on this website, you approve of our use of cookies.  What are cookies?