Geometric optimization of the evaluation of finite element matrices

作     者：Kirby, Robert C. Scott, L. Ridgway 

作者机构：Univ Chicago Dept Comp Sci Chicago IL 60637 USA Univ Chicago Computat Inst Chicago IL 60637 USA Univ Chicago Dept Comp Sci Chicago IL 60637 USA Univ Chicago Dept Math Chicago IL 60637 USA 

出 版 物：《SIAM JOURNAL ON SCIENTIFIC COMPUTING》 (工业与应用数学会科学计算杂志)

年 卷 期：2007年第29卷第2期

页      面：827-841页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：finite element variational form optimized algorithm graph theory 

摘      要：This paper continues earlier work on mathematical techniques for generating optimized algorithms for computing finite element stiffness matrices. These techniques start from representing the sti. ness matrix for an a. ne element as a collection of contractions between reference tensors and an element-dependent geometry tensor. We go beyond the complexity-reducing binary relations explored in [R. C. Kirby, A. Logg, L. R. Scott, and A. R. Terrel, SIAM J. Sci. Comput., 28 ( 2006), pp. 224 - 240] to consider geometric relationships between three or more objects. Algorithms based on these relationships often have even fewer operations than those based on complexity-reducing relations.