Geometric Optimization of the Evaluation of Finite Element Matrices

This paper continues earlier work on mathematical techniques for generating optimized algorithms for computing finite element stiffness matrices. These techniques start from representing the stiffness matrix for an affine element as a collection of contractions between reference tensors and an eleme...

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Bibliographic Details
Published inSIAM journal on scientific computing Vol. 29; no. 2; pp. 827 - 841
Main Authors Kirby, Robert C., Ridgway Scott, L.
Format Journal Article
LanguageEnglish
Published Philadelphia Society for Industrial and Applied Mathematics 01.01.2007
Subjects
Algorithms
Applied mathematics
Computer science
Fourier transforms
Geometry
Linear algebra
Optimization
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Summary:This paper continues earlier work on mathematical techniques for generating optimized algorithms for computing finite element stiffness matrices. These techniques start from representing the stiffness matrix for an affine 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.
ISSN:1064-8275
1095-7197
DOI:10.1137/060660722